Prior Experience

It is expected that students will present a range of prior experience of working with numbers, geometric shapes, measurement, and data. Students are expected to be able to count a small set of objects by ones, at least.

Session One

In this first session students explore an activity called ‘Handfuls' which was first developed by Ann Gervasoni from Monash University, Melbourne. Handfuls could become a regular part of lessons during the year.

1. Ignite the students' prior knowledge by asking them what they already know about mathematics. Discuss the purpose of the unit, which is to find out some information about the class and use it to help them with their maths learning.
    
2. Begin the 'Handfuls' activity by modeling taking a handful of objects from a container. Place the collection on the mat in a disorganised arrangement.
    
3. Estimate how many things you got in your handful (You may need to explain that an estimate is an educated guess).
    
4. Ask your students to write the number on a small piece of paper and show it to you. This is a way to see who can write numbers, avoids calling out, and buys time for students to think.
   How can we check how many things there are?
    
5. An obvious first approach is to count by ones. Organising the objects in a line then touching each one as it is counted is a supportive approach.
   
    
6. Look for students to suggest other ways, such as counting in twos or fives.  Students can find skip counting difficult in several ways; not realising that counting in composites gives the same result as counting in ones, not knowing the skip counting sequence, and dealing with the ‘leftovers’. What to do with leftovers is an interesting discussion topic.
   
    
7. Tell the students that you want them next to take their own handfuls.  Ask the students to record on paper how they counted their collection, particularly what groupings they used. Tell them to count their handfuls in at least two different ways. Try to take photographs of the handfuls for use in the group discussion.
    
8. Observe as you wander around to see if students can:
   • Reliably organise their collections and count in ones
   • Use composites like twos, fives and tens to skip count collections
   • Use tens and ones groupings to count the collections, using place value.
      
9. After all the students have taken handfuls and recorded their counting methods, use one of these two methods to extend the task:
   • Let students travel to the handful collections of other students, estimate or count how many things are in the collection, then compare their methods with that of the original student. The recording of the original student can be turned over then revealed after the visitor has estimated and counted.
   • Share the recording strategies students created as a class. Use photographs to drive discussion about the best counting strategies for given collections.
      
10. Apply the counting strategies to two questions:
    • Can you get more in a handful with your preferred hand than your other hand?
    • Can you get more in a handful when the things are bigger or smaller?
       
11. Discuss what their ‘preferred hand’ is, that is, are they right or left handed? You might act out taking a handful with your other hand and comparing the number of objects you got with your preferred hand. You might also demonstrate getting a handful or small things, then a handful of larger things. Ask students to predict what will happen, then go off to explore the two questions. Suggest recording on the same pieces of paper so they can compare other handfuls to the original attempt.
     
12. After a suitable time, ask the students to re-gather as a class with their recording sheets. Discuss possible answers to the questions. Interesting questions might be:
    • What side are our preferred hands?
    • Do we always get the same number in a handful if we use the same hand?
    • How big are objects that are too hard to gather in a handful?
       
13. You might make a display of the recording sheets for other students to look at. Other variations of the handfuls task might be:
    • Students try different ways to increase the number of objects they can gather in one handful.
    • Exploring one more or less than a given handful.
    • Using tens frames or dice patterns to support counting the objects in a handful.
    • Gather multiple handfuls and counting.
    • Sharing a handful into equal groups 

Session Two

In this session, called “Our Favourites” students explore category data and how it might be displayed. The data comes from their responses, so the displays provide useful information about the class. You may wish to replace the images provided in Copymaster 1 with images of sports that you know are popular with your students.

1. Begin by asking the students to choose which of the sports shown on Copymaster 1 they like to play the most. Provide the students with copies of the strips to cut out the square of their choice. It is important that each student makes a single choice, cuts out the square and not the picture, and places it in the container in the centre.
    
2. Once all of the data is in, tip the contents of the container on the mat.
   If we want to find out the favourite sport, what could we do?
    
3. Students usually suggest sorting the squares into category piles. A set display like that is a legitimate way to present the data.
   Could we arrange the squares, so it is easier to see which sport has the most and the least squares?
    
4. Students might suggest putting the squares in line with a common baseline (starting point). They might suggest a ‘ruler’ alongside, so it is not necessary to count the squares in each category. They might suggest arranging the categories in ascending or descending order of frequency and adding a title and axis labels.
   
    
5. Create the picture graph on a large piece of paper by gluing the squares in place. Display the graph in a prominent place.
   
   The students will now choose other ‘favourites’ to use as data. Copymaster 2 provides some strips of favourites including favourite fruit, fast food, pet, vegetable, way to travel to school, and after school pastime. You may wish to create your own strips using ‘favourites’ that are relevant to your group of students.
    
6. If using prepare copies of Copymaster 2, cut the copies into strips and put each set of strips with a container and several pairs of scissors. Spread the containers out throughout the room. The students visit each ‘station’ and make a choice by cutting out a square and putting the square into the container. You may need to discuss what each strip is about before students do this.
    
7. Once the data gathering is complete put the students into small groups with a set of data to work on. Remind them to create a display that tells someone else about which category is the most and least favourite. Watch to see if your students can:
   • sort the data into categories
   • display the data using a common baseline and possibly a scale
   • label each category and provide a title for the graph
      
8. After a suitable period, bring the class together to discuss what the data displays show. Can your students make statements about…?
   • highest and lowest frequencies
   • equal frequencies
   • patterns in the distribution, such as the way it is shaped
   • inferences about why the patterns might be, e.g. It is summer so people might like vegetables like tomatoes.

Session Three

In this session your students use the language of two-dimensional shapes to provide instructions to other students. The use of te reo Māori vocabulary for shapes could also be introduced and used within this session.

You need multiple sets of shapes. Ideally there is a set of shapes for each pair or trio of students. Attribute blocks are used below to illustrate the activity but other shape-based materials such as those below are equally effective.

“Make Me” is an activity that can be used throughout the year with different materials to develop your students’ fluency in using geometric language for shape and movement.

Pattern Blocks	Logic (Attribute) Blocks	Geometric Solids

1. Begin by discussing the shapes in a set. Ask questions like:
   • What shape is this? How do you know?
   • What is the te reo Māori name for this shape?
   • What features does the shape have to have to be called a …?
      
2. Draw students’ attention to features like sides and corners. You might also venture into symmetry if you have a mirror available.
   Where could I put the mirror, but it still looks like the whole shape?
    

3. Use two shapes positioned together to draw out the language of position. For example:

   The porowhita/circle is below the tapawhā rite/square.	The porowhita is in front of the tapawhā rite.	The circle is on the right side of the square.

4. Show students how to play the “Make Me” game. Create an arrangement of four shapes. Here is an example:
   
    
5. Ask students to give you instructions so you can make this arrangement using your set of shapes. Respond to what students tell you very literally. For example, if they say “The circle is on top of the square” you might put the circle in front of the square. An important point is that the person giving instructions cannot point or touch the blocks. Encourage the students to use the te reo Māori words for the shapes.
    
6. Next, ask a student to arrange three or four blocks in a place that nobody else can see. Send a different student to look at the arrangement and come back to tell you how to make it. The instruction giver may need to make return trips to the arrangement to remember exactly how it looks. At the end, check to see that what you make matches the original arrangement.
    
7. Students then work in pairs or threes, each with a set of shapes. You go to a place they cannot see and arrange a set of shapes. Be mindful of drawing out the need for students to use language about features of shapes (side, corner) and position (right, left, above, below, etc.). One student from each team is the instruction giver, the other students are the makers. The instruction giver views the arrangement and returns to the group as many times as they need. The makers act on the instructions. When they feel the arrangement is correct the whole team can check with the original. Make sure each student has an opportunity to be the instruction giver.
   Look to see whether your students:
   • give precise instructions using correct names for shapes, features and position
   • act appropriately to instructions for action with shapes.
      
8. Students can independently make their own arrangements of shapes. Take photographs of the arrangements. Use one or two images to help students to reflect on the intentions of the session. Create a list of important words for display including the te reo Māori words (not all may be relevant to your set of shapes):
   
9. Students could write a set of instructions to build an arrangement from a photograph. This might also be done as a class if the literacy demands are too high.

Session Four

In this session students compare items by mass (weight).

1. Begin by asking students what the words light and heavy mean. Ask a couple of students to find a light object in the classroom and identify a heavy object. Young students frequently identify heavy as immovable so expect them to point out bookshelves and other objects they cannot personally move. 
    
2. Get two objects from around the room that are similar but not equal in mass.
   How could we find out which thing is heavier?
   Students usually suggest that the objects can be compared by hefting, that is holding one object in each hand.
    
3. You might have several students heft the objects to see if there is a consistent judgment.
   What can we say about the weight of these two objects?
   Look for statements like, “The book is heavier than the stapler,” or “The stapler is lighter than the book.”
    
4. Create two cards with the words “lighter” and “heavier” and set them a distance apart on the mat.
    
5. Next, get a collection of five objects of different weights and appearances.
   Let’s put these objects in order of weight. Who thinks they could do that?
    
6. Let students come up and heft the objects and place them somewhere on the lighter to heavier continuum. Be aware of these issues:
   • Students may have trouble controlling the order relations. Ordering five objects by twos involves complex logic.
   • Objects of equal weight (or indiscernible difference in weight) occupy the same spot on the continuum.
   • Size, as in volume, is not a good indicator of weight. Small objects, such as rocks, can be heavier than big objects, such as empty plastic containers.
      
7. After the five objects are placed on a continuum, give the students a personal task.
   I want you to find five things from around the classroom and put them in order of weight. You can use hefting if you want but we have other balances you can use. You will need to record for us, so we know the order of the objects.
    
8. Let the students order their five chosen items and record their findings. 
   Look to see if your students can:
   • Recognise which of two items is heavier by hefting or using a balance.
   • Co-ordinate the pairs of objects to get all five objects in order.
      
9. After a suitable time, gather the class to compare their findings and discuss issues that arose. Frequently, students are surprised that similar looking items do not have the same weight. Crayons, glue sticks and books are good items to illustrate the point that the same kind of objects does not mean equal weight.

Session Five

In this session students look for repeating patterns and connect elements in the pattern with ordinal numbers.

1. Demonstrate creating four different repeating patterns using geometric shapes, images of native birds, natural materials, etc. At the end of each pattern progression ask questions like:
   • What do you notice about the pattern? (You are looking for students to see the element of repeat)
   • What comes next?
   • What object will be at … number 10? … number 15?... etc. (You are looking for students to apply generalisation about the element of repeat, e.g. All even numbers have a red square.)
      
2. Ensure that patterns 3 and 4 have two variables and the sequence is different for those variables. For example, in pattern 3 geometric shapes could be used to show shape and colour variable (e.g. a yellow, red, yellow, red… colour sequence while shape could have a circle, hexagon, rectangle, circle, hexagon, rectangle, … sequence) and in pattern 4 images of native birds could be used to show animal and orientation variables (e.g. Kiwi, Tuī, Kererū, Takahe, … sequence while orientation could be a right, left, right, left, … sequence). 
    
3. Provide students with a range of materials to form sequential patterns with. The items might include milk lids, blocks, toy plastic animals, locally sourced natural resources, images of native birds, geometric shapes, etc. Give them a copy of the strip that can be made from Copymaster 3 after it is enlarged onto A3 size (x 1.41).
    
4. Let students create their own patterns. Look for students to:
   • create and extend an element of repeat
   • use one or more variables in their pattern
   • predict ahead what objects will be for given ordinal numbers, e.g. The 16^th object.
      
5. Take photographs of the patterns to create a book, and ask students to pose problems about their patterns.  Students can record the answers to their problem on the back of the page.
    
6. Discuss as a class how to predict further members of a pattern. Strategies might include:
   • Create a word sequence for each variable, e.g. blue, yellow, red, blue, yellow, red... 
   • Use skip counting sequences to predict further members, e.g. If the colour sequence is blue, yellow, blue, yellow,… then every block in the ordinal sequence 2, 4, 6, … etc. is yellow.

Getting Started

1. Introduce the problem by sharing a picture of a native frog:

   5 frogs live in a pond. 
   If 2 of the frogs are sitting on the rock, how many are hiding in the pond?
   How many different ways are there for the frogs to be, in and out of the water? (There are 6 ways for the frogs to be in and out of the water: none on rock and 5 in pond, 1 on rock and 4 in pond, 2 on rock and three in pond… etc.) Numbers spoken in Te reo Māori can be used also.
    

2. Brainstorm ways to solve the first part of the problem.  Strategies of drawing a picture, using equipment or acting it out could be raised.   
    

3. Encourage the students to tell you how they know the number of frogs hiding in the pond.  Allow the students to describe their ideas and encourage explanations.

   How did you know how many frogs were hiding?
   Tell us about your thinking.
   Could there be any other number of frogs hiding if 2 are on the rock? 
   How do you know?
    

4. Have the students plan ways to record their solution.  Possibilities include drawing a picture, a diagram, some writing, a flip-fold page or taking a photo and recording their explanation of their thinking.
    

5. Read the second part of the problem and let the students try to solve this, in pairs or on their own.  (The frogs need to be treated as identical or there are multiple solutions for each number pairing.)  Let the students experiment with the pairings of the digits.  The following questions may help support their problem solving:

   How do you know how many frogs are on the rock?
   Does there always have to be a frog on the rock? Or hiding in the pond?
   How are you keeping track of the ways that you find?
    

6. To conclude the session, have several students share their findings, including the method of recording, with the class.  Ensure several different methods of recording are presented and discuss the different ways students used to think about the hiding frogs.  

Exploring

Over the next two to three days, revisit the problem with the frogs in the pond, varying the number of frogs living in the pond and sitting on the rock.  Explain that because the pond is such a nice place to live, more frogs keep moving in.  When reading numbers, use both English and te reo Māori. 

Three appropriate number combinations to use would be:

6 frogs live in the pond, begin with 3 on the rock. 
8 frogs live in the pond, begin with 2 on the rock
9 frogs live in the pond, begin with 4 on the rock. 

These problems are provided on the problem copymaster. 

Each day follow a similar lesson structure to the introductory session, with students becoming more independent in their search for solutions as the week progresses. Conclude each session by having students share their solutions and compare their different ways of working. 

Sharing

As a conclusion to the weeks work, have the class work together to make a wall chart illustrating the different combinations of frogs in and out of the water, when 7 frogs are living in the pond (8 possible combinations):

1. Introduce the problem – have a large copy for all to use, appropriate for display at the end of the session.
   Seven frogs live in a pond. 
   They like to sit on the rock in the middle of the pond or hide in the water.
   How many different ways are there for the frogs to be, in and out of the water?
    
2. Have students work in pairs or individually to come up with a solution.  
    
3. Pose the following questions as the students work on the solution:
   How many frogs are there altogether?
   How many are on the rock? How many are hiding?
   How do you know?
   How could you find out?
   How are you keeping track of the ways that you find?
   Tell me about your thinking.
    
4. As a class, discuss the different combinations possible and list these together. 
    
5. Split the students into groups, with each group responsible for illustrating one of the number combinations.  Illustrations could use a range of media (paint, crayon and dye etc) or the frog copymaster could be provided for students to use.  
    
6. Have the students share their work. 
    
7. Display the students' illustrations alongside the problem and revisit the work as appropriate.   Alternatively, the illustrations could be made into a big book, using the problem as a cover.

Session 1

In this session we measure the capacity of containers by counting the number of dinosaurs they hold.

1. Gather the class on the mat and show them a small empty container and a bag of plastic dinosaurs. Ask:
   How many dinosaurs do you think would fit in this container?
   How can we check?
2. Place the dinosaurs in the container one at a time counting as each one is added.
   One, two, three, four...
3. When the container is full ask the students to state how many dinosaurs the container holds. Record this on a label and attach to the container.
4. Show the class another container and ask them once more to guess how many dinosaurs it would hold.
5. Count in ones as the dinosaurs are added to the container.
   How many dinosaurs does this container hold?
6. Ask for a volunteer to record the number on a label to attach to the container.
7. With both containers on display ask:
   Which container holds the most dinosaurs?  
   How do you know?  (This will reinforce the order and sequence of numbers.)
8. Give small groups of students a container and enough dinosaurs to fill them.  Write that number on the label and attach it to the container.
   
9. Gather the students back together as a class to share.  Put those with the same number of dinosaurs together.
   Do these containers hold the same number or dinosaurs? (check). 
   Are they the same?

Session 2

In the following sessions the students create cylinders to contain a given number of dinosaurs.  The challenge is to create a cylinder that contains exactly the given number of dinosaurs.  The activities give students the opportunity to practice counting objects in ones, and to order and compare numbers using objects. This is a good opportunity for your students to practice counting in te reo Māori.

1. Gather the students as a class and show them a cylinder made from a rectangle of lightweight card.  The base of the cylinder is a piece of paper held in place with tape. 
   How many dinosaurs do you think it would hold exactly? (Discuss that exactly means that no more dinosaurs could fit into the cylinder.)
2. Count the dinosaurs one by one into the cylinder.
3. Tell the students that they are toy dinosaur manufacturers and that they sell their dinosaurs in packages of ten. Their task is to make a cylinder that holds exactly 10 dinosaurs.
4. Provide a selection of different sizes of lightweight card rectangles to make a range of cylinders (short and wide, tall and narrow).  
5. Ask the students to work with a partner to first take 10 dinosaurs and then make a cylinder.  When they have completed one cylinder they can be challenged to make a different cylinder that also holds exactly 10 dinosaurs.
6. As the students construct their cylinders circulate asking questions:
   Please count your dinosaurs to me. 
   Does your cylinder fit exactly 10 dinosaurs? 
   Can you fit any more dinosaurs in your cylinder? 
   Are cylinders a good container for dinosaurs? Why or why not? 
   Could you make a cylinder for 20 dinosaurs? What would it be like?
7. Gather the students back together to share the cylinders constructed.
   What do you notice about the cylinder?
   Can you see any cylinders which are exactly the same?
   What do you think that a cylinder for 20 dinosaurs would look like?
8. Challenge the students to think about how cylinders can look different but still hold the same amount.

Sessions 3-4

In these sessions the students continue their exploration of the capacity of cylinders by constructing cylinders for a given number of dinosaurs.  As the containers are created they are displayed in order of capacity. Many opportunities are provided for one-to-one counting and sequenceing of numbers in English and te reo Māori.

1. Gather the students together as a class and ask them to identify the numerals 1-20 as displayed on numeral cards.  As the numbers are identified, place them into a “hat".
2. Ask the students in partners to select a numeral card from the “hat".  Instruct them to create a cylinder to fit that number of dinosaurs.
3. When the cylinder has been created, direct the students to write the numeral on the outside of the cylinder.
4. Ask the students to place their cylinders, in order, at the front of the classroom. 
   Where does your cylinder belong?
   How do you know it comes after __?
   Which cylinder will come after your one?
5. At the end of the session gather the students together to look at and compare the capacity of the cylinders.
   How many dinosaurs does this one hold?
   Which one holds one (2, 3..) more? How do you know?
   Which one holds one (2, 3..) less? How do you know?
6. Discuss the different shapes and sizes of the cylinders.
   Which cylinders look the biggest?
   Do they hold the most dinosaurs?

Session 5

In today’s session each student makes a cylinder.  We then use the cylinder to see how many objects (cubes, dinos, etc) can fit exactly into our cylinder.

1. Give each pair of students a piece of card and paper to construct a cylinder. 
2. As they construct the cylinders ask them to guess how many dinosaurs they think would fit in their cylinder.
3. Gather the students together on the mat and show them a selection of small objects that they are to use to fill their cylinders.  These may include: cubes, pebbles, toothpicks, toy animals, counters, marbles etc.
4. Place the objects on tables around the room.
5. Ask the students to take turns at each of the tables filling their cylinder with the objects.  Suggest that each student has a turn counting the objects by ones into the cylinder while their partner listens and checks their count.  Tell them to record the number of objects onto the recording sheet.
6. As the students work, check their one-to-one counting and the numbers that they are writing onto the recording sheet.

Begin this series of lessons by reading or recounting the story of the gingerbread man. It is a well known story which students enjoy. Continue to retell the story, or parts of the story, throughout the week to help maintain the focus for the activity sessions. Consider using different stories, that may better reflect the cultural diversity of your class (e.g. The legend of Matariki and the six sisters, the story of the stone that blocked the road round the Cape at Matauea, Safotu). The gingerbread templates could be adapted to reflect any characters.

As students work promote the use of language that makes comparisons between lengths, for example the same length, shorter than, longer than. Emphasise the importance of making sure both objects are lined up at one end when comparisons are being made. Model this by showing the difference in measurements when items are, and are not, lined up correctly.

Session One: Gingerbread Families

In this Session students order a family of gingerbread men from shortest to tallest, using a variety of measuring words.

Provide each student with a copy of the gingerbread family sheet (Copymaster 1).

• Discuss the family. Encourage students to visually estimate lengths before cutting out the gingerbread men.
  Who is the tallest?
  Who is the shortest?
  If we were to put the gingerbread men in a line from tallest to shortest, who would be first?
  Who would be second? Third?
• Have the students cut out the gingerbread family and order them from tallest to shortest. Emphasise the importance of making sure their feet are all in line when comparing heights.
• Colour in the gingerbread family as desired and glue onto a black backing sheet.

Session Two: Something Taller, Something Shorter

In this Session students find classroom objects that are taller than a gingerbread man, shorter than a gingerbread man or the same size as a gingerbread man. Items from nature, or from other contexts for learning could also be used here (e.g. branches, trees, rulers, kete).

Session Three: Building Bridges

In this Session students build a model bridge to go over a local river drawn on a large sheet of paper.

1. Provide each student with a gingerbread man template (Copymaster 2) and ask them to cut him out.
2. Discuss the height of the man.
   Who can think of something in our classroom that is longer than the gingerbread man?
   Who can think of something that is shorter than the gingerbread man?
3. Provide each student with a recording sheet (Copymaster 3) and ask them to find and draw onto the sheet five things that are longer than the gingerbread man, five things that are shorter than the gingerbread man and five things that are the same length as the gingerbread man.
4. Compare the objects that are found.
   Did anybody find the same objects?
   Did anyone find something unique?
5. Students can check the charts of others by re-measuring objects around the room to see whether they are longer, shorter or the same size as the gingerbread man.
6. Show students a drawing/painting of a river and ask them about the story. How did the gingerbread man cross the river in the story?
   What could we build to help him cross this river?
7. Provide the students with blocks, card and sellotape to make bridges. Leave the “river” at the table where they are working so they can directly compare the width of the river with the lengths of the bridges they are making.
8. Once the bridges are complete, have the students place them over the river to see if they are long enough.
   Could the gingerbread man go over this bridge? Is it long enough?
9. They can also compare the lengths of their bridges with the bridges of others. Who has the longest bridge?
   Who has the shortest?
   Whose bridge is longer / shorter than Paul’s?

Session Four: Gingerbread Men Chains

In this Session students make and decorate chains of gingerbread men (or other chosen characters, e.g. Matariki) then compare the lengths of their chains. This could be related to how many people in each student's whānau. 

1. Show the students how to make a chain of gingerbread men by folding a strip of paper, tracing around a template and cutting out the shape. Emphasise the importance of not cutting the “hands” off on the folds so the gingerbread chain remains joined.
2. Students select a strip of paper, then make and decorate a chain of gingerbread men.
3. Have students compare the lengths of the chains they have made
   Who has the longest / shortest chain?
   Which chains are longer / shorter than Andrew’s?
4. Ask students to join all the chains they have made together and estimate how far the chain will stretch.
5. As a class, decide which chains are the longest and shortest. Write sentences to describe these (e.g. Tama’s chain is the longest. Mia’s chain is the shortest). Support students write sentences to display beside their character chains, that describe the length of their chain in comparison to the length of another student’s chain (e.g. my chain is longer than Mia’s, and shorter than Tim’s). Display these sentences beside the chains.

Session Five: Get Dressed Man!

In this Session students cut out clothes to fit a template of a gingerbread man.

1. Provide students with a template of a gingerbread man (Copymaster 2) and a variety of coloured paper to use to make clothes.
2. Discuss with students what the gingerbread man would like to wear.
   How big will his clothes need to be?
   How can we make sure the clothes we make will fit him?
   If you have reframed the context of this lesson (e.g. around How Māui slowed the sun) you could make further links by investigating what early Māori and Pasifika people wore)
3. Ask the students to make some clothes for the gingerbread man, and demonstrate how they could trace around the man to make sure the clothes are big enough.
4. Once the clothes are completed students can compare the sizes of the clothes they have made before they paste them onto the men.
   Who has made the longest pair of trousers?
   Whose trousers are shorter than Emily’s?
5. If desired students can complete their gingerbread man by drawing a face on him and glueing on wool for hair.

Session 1: Chasing Cats

In this session students use the story "Hairy Maclary, Scatter Cat" by Lynley Dodd, to provide a context in which to use the language of movement and position and to provide opportunities to move themselves as they act out parts of the story.

1. Read the story to the students. Encourage discussion about the cats and Hairy Maclary. Relate to their own experiences of cats and pets. 
   Can you describe where Butterball Brown is sitting?
   Where is Hairy Maclary hiding?
   Where does Slinky Malinky go when Hairy Maclary chases him?
   Can you describe where Mushroom Magee went?
2. Get students in pairs to role-play with one as Hairy Maclary and the others as one of the other cats. Get the students to describe the position of the two characters to start with and where they end up. Encourage the students to describe the paths they take.
   Where is Scarface Claw hiding?
   Where is Hairy Maclary?
   Where will Scarface Claw chase him to?
   How will Hairy Maclary get there?
3. Each student or pair draws a scene from the story and provides a caption about the position of the characters or a description of the movement. These will be used as a wall display or made into a big book to share as part of each maths session. This could also be recorded on a digital device to me made into a powerpoint. 

Session 2: Where is Hairy Maclary?

In this session we describe the position of ourselves and of objects. We follow and give instructions about where to place items in the classroom.

1. Reread "Hairy Maclary, Scatter Cat!" or revisit the previous session’s work by reading the wall display or book made of the students' work.
   Talk about where we are sitting, trying to get students to be specific in the description they give.
   I am sitting on a chair, next to the teaching station, at the front of the mat.
   Where are you sitting?
   Can you tell me who is behind and in front of you?
   Are you near the front or the back of the mat?
   Is anyone sitting beside you?
2. With a partner, students move to other parts of the room and describe their position to their partner.
   I am on a chair, at the art table, near the back of the room.
   I am under a table, beside a chair, in the middle of the room.
3. Introduce cards with pictures of Hairy Maclary drawn on them (these need to be colour-coded or made slightly different from one another so that you know who each card belongs to, to avoid arguments as students begin the activity).
4. Explain the ‘Where is Hairy Maclary?’ game. Students work in pairs. One student hides Hairy Maclary and gives the other student a description of where to find him. That student searches. Model the giving and following of directions. As the class completes this activity, rove and encourage the students to be specific in their descriptions.
   You said Hairy Maclary is on a chair.
   Is there anything next to the chair?
   Is the chair at a table?
5. Gather the class back together and encourage students to share their reflections of the activity. They might tell you what made descriptions easy, or difficult, to follow. You could write down these notes and record them on a display (e.g. a powerpoint or poster).

Session 3: Look at Me Go!

In this session the students explore movement sequences by both explaining a path taken and by giving and following instructions for paths in the classroom and in the playground. They further explore the ideas using cut outs of the Hairy Maclary characters.

1. Recap the situation, describing where we are sitting and being specific about our positions.
   Are you sitting in the same place on the mat as you were yesterday?
   Who is sitting next to you?
   Who could describe where one of their friends is sitting today?
2. Place "Hairy Maclary, Scatter Cat!" somewhere in the classroom.
   I need someone to get me the Scatter Cat! book.
   Choose a student to get it.
   You will need to listen very carefully to the instructions I am going to give you to find it.
   Give a sequence of instructions to get the book. For example,
   Turn to face the back of the classroom.
   Walk forwards until you get to a table.
   Go underneath the table, the book is on the chair in front of you.
3. Students work with a partner to give and follow sequences of instructions. Students could give instructions on how to get from their chair to their bag, how to get from the classroom door to the sink, how to get from the board to their browsing box, etc.
4. If it is fine, take the class outside to explore sequences of instructions further. Set up an obstacle course or describe a path for students to take over the playground equipment. Again they can explore giving and following instructions with a partner in a specified area of the playground.
5. Move-it Hairy Maclary! Back in the classroom introduce cards showing Hairy Maclary and indicating him moving around the classroom e.g. a picture showing him going under a table or over a chair. Give a set of cards to each pair of students along with a Hairy Maclary cut out from the previous session. One partner holds the instruction cards and describes where Hairy Maclary needs to go. The other student moves Hairy Maclary according to the instructions. Encourage the students to shuffle the cards around and create lots of different paths for Hairy Maclary to follow.
6. If your students are familiar with using poi, E Rere Taku Poi could be used to conclude this session. In this action song, students practice following the directions roto (in), raro (on), iho (under), runga (above), waho (out). There are many videos online that show the actions to this song.

Session 4: Turning, Turning, Turning

In this session we explore half and quarter turns using points of reference in the classroom to indicate the direction for turning. Some students may already be familiar with left and right and they will be given the opportunity to explore this.

1. Gather the students on the mat and get them to stand in their own space (This activity cold also be taken outside). If there isn’t room in the mat area, get the students to spread around the room. Get the students to describe where they are and what they are facing.
   Where are you standing?
   What can you see straight in front of you?
2. Get the students to turn around once.
   Slowly turn around until you can see the same as you can see now.
   How far have you turned?
3. Talk about turning half way and get the students to think about what they might see when they have turned half way.
   Where will you be facing if you turn half way?
   Will you still be looking at me?
   What part of you will I be able to see?
   Get the students to turn half way.
4. Get the students to turn to face the front again. Talk about making a quarter turn or turning sideways.
   When we turned a full turn or a half turn everyone ended up facing the same way.
   Do you think that will happen if we turn sideways (make a quarter turn)?
   Turn to one side. (Make a quarter turn.)
   Some students will have turned one way and some the other. If this doesn’t happen and everyone is facing the same way then, as the teacher, model having turned the other way.
   We need to be more specific about where we are turning.
   What could we add to the instructions to make them easier to follow and to make sure we end up facing the same way around?
   Gather students' suggestions, which may include:
   • you have to say which way to turn;
   • you need to say what to face when you are finished;
   • you have to say turn to the door or turn to the library corner;
   • you need to say left or right.

Get the students to make quarter turns. This time include specific instructions about the direction in which they should turn. Include left and right in these instructions and take note of those who are able to move accordingly.

5. Students work in pairs to give instructions for turning. The teacher roves to encourage students to talk about whole, half and quarter or sideways turns and to encourage specific appropriate directions.
   How far round did you turn?
   Did your partner end up facing where you thought he would?
   What other instructions do you need to give to make sure he does?
6. Gather the students back and talk about giving instructions for how to get to different parts of the classroom or school (recap. from Session 3). Talk about including instructions about turning. Give as an example:
   Start at the board facing the back of the classroom.
   Walk forward until you get to the edge of the mat.
   Turn to face the sink (or make a right turn).
   Walk forward until you get to the sink.
   Pick up a paintbrush.
   Make a half turn.
   Walk forward until you get to the mat.
   Turn to face the easel board (or make a left turn).
   Walk forward to give me the paintbrush.
7. In pairs the students give and follow sequences of instructions including turning. They could also use the Hairy Maclary cut outs for this.
8. The game Mau Rākau could be used to conclude this session and consolidate learning around directional terms. 

Session 5: Keep on Moving

We wrap up the unit with independent exploration of the ideas presented. The students will work in pairs to role-play from the story and to give and follow instructions for paths around the classroom. The teacher will rove and question and encourage specific language and careful instructions.

1. Hairy Maclary Puppet show
   In pairs or small groups, the students use the "Hairy Maclary, Scatter Cat!" book and cardboard cut out puppets to retell the story.
2. Block Buildings
   Provide students with plans of buildings to make with the classroom blocks. These can be drawn onto cards and could use about 5 blocks per building.
   In pairs, one student holds a plan card and explains how to make the building, while the other student follows the instructions. (The second student should not be able to see the card.)
   Cut outs of Hairy Maclary can then be placed in different positions on the buildings.
3. Where is Hairy Maclary?
   Students in pairs, play the game presented in Session 2.
4. Move-it Hairy Maclary!
   In pairs, students play the game presented in Session 3.
5. Big Book Reading
   Students read the big book, wall display or view the powerpoint made in Session 1.
6. How Can I Get There?
   In pairs, students give and follow instructions to move around the classroom as in Session 3. Encourage students to use turns and right and left if they are able to.
7. You Be Hairy Maclary and I’ll be Scarface Claw
   Students role-play from the story as in Session 1.

Getting Started

Begin the week by sharing the book Greedy Cat. If you do not have the book, a copy or a video is available online.

(For very young students the teacher may need to record a statement about the cat under the picture, for example, "a fluffy cat").

1. Discuss the pictures in the book. Talk about the things the students notice about Greedy Cat. Emphasise the attributes of Greedy Cat. 
2. Students talk about their own cat (ngeru) or the pet or cat that they would like to have.
3. Students draw a cat on their rectangle of paper (1/8 of the A4).

Exploring

Collect the cat pictures and photocopies these onto A4 sheets. One copy of all the cats will be needed for each pair of students. (Note: If colour is the attribute used you will need to colour copy the cats).

1. Explain that we are going to investigate "What are the types of cats the students in our class have or would like to have? (this is the investigative question).
   In our last session we drew pictures of cats. We will use these pictures to collect information (data). What information do you think we could collect from looking at these cards? Record students' ideas somewhere visible. 
2. The teacher spreads the original drawings out for the class to see.
   Can you see any cats that are the same or similar? How?  
   What cats are different? How?
3. These cats are placed in a pile and given to the child who named the category.
   How many cats are there in the pile? One, two, three... tahi, rua, toru .....
   As a class, count the number of cats in the pile.
   The question is repeated until all the cats are sorted.
   Use this counting activity as an opportunity to strengthen the number sequences and one-to-one correspondence of the word name with the item with, students who are emergent (stage 0) on the Number Framework. Ask for volunteers to count the objects, asking them to justify their count. Students at stages 1 and 2 might count by pointing to or touching the objects while students at higher stages may use images of the numbers and be able to 'see' that a group is, for example, four, without needing to count the objects. Discuss the different counting strategies demonstrated by students.
4. Repeat the process encouraging the students to be more "creative" in their nomination of categories. Get the students who already have a pile of cats to restate the category that they used so that they don’t forget this category. This reinforces the sorting of data.
   Who do you think has the most cats?
   How do you know? Show me.
   If the students do not use one-to-one matching you may need to model this.
   Students at stage 4 or above may be able to find the difference between the sets by counting-on or back.
5. How can we tell who has the most cats?
   Once the categories have been matched 1-1 (in a line) attach the pictures onto a chart.
   Record statements beside the chart of cats about the number in each category, and some comparisons between categories.

Over the next two days work with the students to develop investigative questions about cats and to use the photocopied pictures (data) to find the answers.

6. Brainstorm possible areas we could explore and develop investigative questions.
   What size cats do we have?
   What types of coats do our cats have?
   What sorts of tails do our cats have?
7. The pairs select and record the investigative question they want to work on. They then sort and display the cat pictures (1-1 to form a pictograph) to answer their investigative question.
   Repeat this with another investigative question (if time allows).
8. Conclude the exploration by pinning up the cat displays on the wall to share with everyone (this may include parents and whānau). Each pair selects one of their displays to tell the class about. Question, prompt and support as needed to elicit appropriate oral language including statistical language.

Reflecting

Today we look at a set of "big cats" (for instance, lions and tigers) and pose possible investigative questions. Other animals could be used here depending on the interests and experiences of the children.

1. Display photos of cats. Discuss the photos.
   Does anyone know the names of these animals?
   Where might they live?
   Have you ever seen any of these? Where?
2. After a general discussion focus on the possible questions areas of interest that could be answered explored using the photos.
   What kind of things could we find out about "big cats" from these pictures?
   (For example: patterns on their coat, types of tails Are there more spotty cats than stripey cats? Do all cats have bushy tails?)
3. Develop investigative questions together and list the questions on a chart. E.g. What are the patterns on the coats of the big cats?
4. Leave the investigative questions and the pictures for the students to explore.

The sessions in this unit are organised as collections of activities. Students will benefit from repeating these activities many times. Variations to many of the activities are included to support students in exploring ideas in a controlled way, and in making connections and generalisations. Choose from these activities and variations, and repeat them as necessary. Furthermore, although these activities are given as stand-alone tasks, they could be used as follow-up stations in response to whole class teaching. 

You should adapt the contexts reflected in these problems to be relevant, meaningful, and engaging for your students.

Session One: Groupings with five and beyond.

Learning quantities by instant recognition (subitising) is supported by literature as an ideal starting point. Research shows that three-year-old children can immediately recognise the greater of two sets in the range 1-4 if it matters to them. Some psychologists believe babies note changes to quantities in the number range 1-3. All number-based lessons for young students should include grouping activities to build up knowledge of number facts, and later place value structures. A little practice everyday, in an environment of risk taking, can greatly enhance students’ fact knowledge and make the transition away from one-by-one counting easier when the time is right.

This session utilises a range of materials when looking at five based grouping; a slavonic abacus, five-based tens frames, unifix (or similar) cubes, and students’ hands. Connecting two of these representations at a time is a powerful way to develop grouping knowledge. The examples below illustrate grouping tasks in the number range 5-10 but the tasks are transferable to smaller and larger quantities.

1. Finger pattern pairs

• An important connection is between the parts that make ten. If a student knows that in 7 + ? = 10 the missing number is three, then they may transfer that fact to the answer the problem 3 + ? = 10. 
• For example:
  Show me seven fingers.
  How many more fingers make ten? How many fingers are you holding down?
  Write 7 + 3 =10 and say, “Seven plus three equals ten.”
  Show me three fingers.
  How many more fingers make ten? How many fingers are you holding down?

Variations

• Students work in pairs. One student makes a number up to ten with their fingers. The other says the number and writes the numeral for it big in the air.
• Find different ways to make a number to ten, for example, seven can be 5 + 2, 3 + 4, 1 + 6 and 0 + 7.
• Finding ways to make numbers between 10 and 20 is possible in pairs or threes.
   

2. Slavonic Abacus and Finger Patterns

• The Slavonic abacus is five based. The purpose of the colouring is to enable instant recognition of a quantity without counting. Try not to use counting to confirm a quantity, as that is counter-productive to the intention of either knowing the quantity or working it out from known facts.
• For example:
  Make a number in the range 5 to 10 on the top row. Can you move all of the counters at once instead of of one counter at a time? 
  Show me that many fingers. Note that this gives all students time to work out an answer and it also provides a way for you to see what each student is thinking.
  How many beads are there?
  How did you know there were eight?

2. Encourage grouping-based strategies, such as “I can see five and three” and “There are two missing from ten, so I held two fingers down.”

Variations

• Ask the students to convince a partner about how many beads have moved.
• Ask the students to write the number for the beads on a mini whiteboard then show you.
• Move to “ten and” groupings such as ten and four to develop teen number knowledge. Students work in pairs to show that many fingers or write the number on a mini whiteboard.
   

3. Five based tens frames

• Hold up a single tens frame, such as nine, for no longer than one or two seconds. The aim is for students to image the five-based patterns rather than count the dots one by one.
  How many dots did you see?
  Show me that number on your fingers.
  Write that number big in the air for me.
• Discuss the structure that students saw. E.g.“I saw five and four.” “I saw one missing from ten.” I saw three threes.”

Variations

• Play tens frame flash in pairs or threes. Players take turns to be the ‘flash’ and show the tens frames, with the other students stating the number of dots on each tens frame as quickly as possible.
• Instead of writing the number, talk to a partner about what you saw.
• Write what is found with symbols like, 8 + 2 = 10, 10 – 2 = 8.
• Progress to two tens frames being shown. Start with numbers less than five, e.g. four and three. Move to ten and another tens frame for teen numbers, e.g. ten and six. Try ‘close to ten’ frames, like nine and eight, with another tens frame, e.g. nine and five.
   

3. Cube stack

• Begin with a stack of ten cubes made from five of two colours. Like the slavonic abacus the colours are used to support non-counting methods to establish quantity. Like the tens frame and abacus activities students can match a quantity you hold up, using their fingers or writing the number. However, finding a missing part encourages part-part-whole knowledge. 
• Show the students a stack of cubes with some missing (put into your pocket). Show the stack for a second or two then hide it.
• Ask, “How many cubes did you see?” “How do you know?” “How many did I put in my pocket?”
• Praise risk-taking even if the answers are incorrect and try to offer knowledge that might be helpful. For example:
  “I think there are eight because I saw five and two.”
  “Good work. This would be eight (showing five and three). Can you fix it?”
  After the students have found the missing part reveal it from your pocket to check.

Variations

• Students play in pairs with one being the hider and the other the estimator.
• Start with a number other than ten, e.g. eight stacks made of five and three.
• Students match stacks to finger patterns to help them find the number of missing cubes.
• Students write equations for the stacks problems, e.g. 7 + ? = 10.
• Progress to taking some cubes from each end. Progress to using two stacks of ten to start, depending on the number knowledge of the students.

Session Two: Counting as one-to-one matching.

Students need to simultaneously develop proficiency with number sequences going forwards and backwards by one, and their capacity to apply those sequences to counting tasks. Ideally students’ ability to say word sequences develops either ahead of, or alongside, their need to apply it. Therefore, students who can count collections up to ten should be learning number sequences beyond ten.

1. Hundreds board

• After practising forwards and backwards counting by ones on a hundreds board ask questions like:
  Can you find the number 8 without counting up or down?
  What number comes after eight?
  What number comes before eight?
• Note that this activity practises numeral to word connection. Build collections alongside to get a three-way connection which includes materials.
   

2. Slavonic abacus

• A Slavonic abacus can help develop quantity to word connections and quantity to numeral connections if used alongside a hundreds board. 
• Say the numbers out loud with students as you move the beads.
  Note that when practising the backward number sequence it is the amount that remains, not the bead removed, that is counted. Zero is an important number to say at the end, as the expression of the absence of quantity (no beads).
   

2. Frogs in a bucket

• Link the numbers before and after a given number to adding one and subtracting one from a given collection. Use toy animals or other objects and a plastic container so there is a loud ‘plunk’ as objects go into the container. The frog animation gives an example of this with frogs in a bucket.
  We had 15 frogs and one jumped out.
  How many frogs are in the bucket now?
• Increase the number of objects in the container beyond ten so that students attend to the one more/one less principle rather than image actions inside the container. Avoid putting in the objects one at a time after ten. Throw them in as imaginary groups. For example, a nice sequence is…
  8 frogs and one more… 17 frogs and one more… 29 frogs and one more… 99 frogs and one more
  7 frogs and one less… 15 frogs and one less… 27 frogs and one less…
• Extend the problems to two more/less, three more/less and beyond as students’ understanding and control of sequences grows. Where needed, link explicitly to the number sequence by referring to a hundreds board.

Jenny Young-Loveridge established long ago that students find counting a collection given to them easier than forming a collection of their own for the same number. “Counting before forming” does not mean a strict order for instruction, it is just an indicator of relative difficulty. Through experience we want young students to consider, "What can be changed without altering the count?" 

3. Changing the size, shape, colour (attributes) of the objects

• Begin with a set of objects in a readily subitised arrangement. Sets of plastic animals, cars, fruit, etc. are cheap and easily purchased. For example, begin with a set of six cars. 
• Tell the students to take a "photograph" (i.e. mentally) of the collection and stash it in their mind. Ask the students to close their eyes and say, “I am going to change something. Try to hold the picture in your mind.” 
• Change the objects for a different kind – vary shape, colour and size to add more challenge. For example, change the cars for teddies.
  
  
   
• Ask the students to open their eyes and say, “How many things can you see now?” Look for students to recognise that the number of items is unchanged though the items vary from the original ones. 
• Aim for acceptance that the number is unchanged by means other than one-by-one counting, though use counting as a ‘fall back’ strategy if needed.

Variations

• Students may begin to say the number is invariant (never changing) because it has been the last few times, without necessarily accepting that number is conserved. 
• Introduce the one more/one less principle by varying the number of new objects by one while still retaining the original layout. See if the students detect the change and trust invariance enough to build on it.
  
   
• Make the variations more significant such as adding or subtracting more than one and changing some parts of the arrangement.
• Play ‘Odd one out' (see Copymaster One). Students must identify a reason for a card being different from the other two. One of the differences can be number of items in the collection. Students build up their use of logic, particularly classification. Answers to the Copymaster: In the left hand set on the first page possible answers are: top card – teddies are sitting down; middle card – different amounts of teddies in each row; or bottom card – nine teddies (others have eight).
   

3. Changing the spatial layout of the objects
   Piaget’s original experiments with spatial layout involved two collections of objects. First, he laid out two collections one above the other, like this:
   
   
   Children were asked the equivalent of, “Are there more blue teddies, green teddies or are there the same number?” Most young children tended to equate the length of a collection with number.
   Next, one collection was spread out like this and the question was repeated:
   
   
   Young children often believed that the number had changed as the objects were rearranged and opted for blue as the ‘biggest’ collection. Piaget called trust in the count under change to spatial arrangement “conservation of number.”

Variations: Similar activities to those given above for change to colour, size, shape etc. can be carried out with spatial arrangement. 

• Begin with a set of objects with some similar characteristics so that students can easily recall the objects that are present. Ask your students to take a photograph in their mind of the collection. Ask them to close their eyes and tell you what they can see. This promotes attendance to structure, the organisation of a pattern. Encourage structural responses such as “There were two of each animal”, “The animals were on a hexagon”, and “Three on top, three on the bottom.”
  
  
   
• Vary the spatial layout of the objects by expanding or contracting the length or area of the collection. Ask the students to open their eyes, then tell you if there are still the same number of objects, and how they know.
  
  
   
• Make minor variations to the total number as well as the spatial layout so that students are required to trust the invariance of the count and build with it or take from it.
  
  
   
• Domino count. Students will need 13 plastic containers, a whiteboard pen and at least one set of dominoes.
  The task is to create ‘bins’ for all dominoes that have the same number of dots, in total. Students use the whiteboard pen to label the bin with the numeral and word that matches the total. For example, the 8 (eight) bin will hold these dominoes:
  
  Once the bins are created students can arrange the dominoes in a pattern like this (for the six bin). They can also write the number fact for each domino.
  
  Ask questions like, “What comes next in the pattern? [4|2]” “Have you already got that domino?” Look at which bins have the most dominoes in them and which have the least. Ask why that happens. Discuss what zero means in this context, “Nothing of something – no dots!”
   

4. Developing the abstraction principle

• The abstraction principle involves the idea that non-tangible items such as sounds, touches, and ideas can be counted. Developing students’ capacity to count items they cannot see and feel is important because we want them to realise that numbers are ideas. Students ready for extension can carry out thought experiments with imaginary objects and anticipate what happens with real objects. One way to encourage abstraction is to connect visible and tangible objects with sounds and touches. 
• Play the game, “Messages”, with the students in pairs. The students sit back to back with one student facing the teacher. The teacher shows then withdraws a pattern card (Copymaster Two) to the first student in the pair. That student turns around and gently “pokes”  or taps the number of dots they saw on their partner’s back. The partner shows how many dots they felt by holding up that many fingers. Both players turn around to check to see if the number of fingers matches the dot pattern.
• Play the game "Pattern Match". Put the students in groups of three or four. Each group needs a set of pattern cards and a set of digit cards. Spread the pattern cards out so they are separated individually and lying face down on the mat. Shuffle the digit cards and put them in a pack, face down, in the centre. Players take turns to turn over the top digit card then use their memory to turn over one of the pattern cards. If the cards match the player keeps both cards and has another turn. Once all of the cards are matched the player with the most pairs wins. Discuss with the class how they recognise some patterns instantly. Look for students to use combinations of smaller groupings, e.g. “I know it’s seven because four and three are seven.”

Session Three

The initial technical aspects of counting involve a one-to-one match between objects in a collection and the set of whole number names and symbols. Once the whole number counting scheme is learned students need to develop a more sophisticated idea of what counting does. The cardinality principle involves understanding that the last number counted tells about the whole collection, and the last word is not simply naming that last counter. Counting strips (Copymaster 3) used with transparent counters are very useful is helping students to appreciate cardinality as well as the significance of the one-to-one and stable order principles.

1. Ask the students to count a set of seven counters, making sure that they use at least three different colours. Place your own set of five counters on the strip, one colour at a time, beginning at one. Ask the students to copy you using their collection, starting with a given colour.
    
2. After placing the third counter ask the students, “What number will the last counter go on?” Students who understand cardinality know that the last counter will go on the digit seven.
    
3. Get your students to remove the seven counters off their strips. 
    
4. Ask: “We started with the blue counters first. What will happen if we start with a different colour, like yellow? What number will the last counter go on?” 
    
5. Invite students to share their ideas. Get them to check their predictions by replacing the counters starting with the other coloured counters. This activity is about the order irrelevance principle.
    
6. Repeat the activity with larger collections of counters, and different mixes of colours. Thirteen and 24 are good numbers, especially the later because students need to image the extension of the strip. After three different collections students are likely to say that the order of counting the colours make no difference, i.e. “The last count is always the same.” Be aware that they may be saying this because it has occurred three times in sequence, not because they recognise the cardinal (measuring) nature of counting.

Variations

Integrating several principles of counting will show whether students trust the count (cardinality) and can build on that trust.

1. Demonstrate the activity above, using other examples of collections on the number strip. Include examples where the counters are not correctly placed (put more than one on the same number or leave gaps). Students should recognise that the objects must be in one-to-one correspondence in invariant sequence. Look for students to recognise that some last counts do not always tell the correct whole amount.

• Progress to adding onto a collection. Begin by asking the students to put a given number of counters onto their number strip. Using one colour is useful. For example, place 8 red counters on the numbers 1 through 8.
   
• Tell the students that you are going to add three green counters to the collection.
  Ask: How many counters there will be then? How do you know? 
  Students may tell you that the next numbers covered will be 9, 10, and 11. Note that it is important that students realise that the result of adding one or removing one from a collection is given by the next number after or before in the number sequence.
   

2. Progress to students imaging the addition of counters. Imaging can be developed by asking problems that are beyond the numbers of the strip, e.g. 19 counters, add four. Imaging can also be developed by turning the strip over, so the digits are not visible, and still placing counters onto the strip. 
    

• Removing counters from a collection is more complex than adding on for two reasons. First, the backwards whole number counting sequence tends to be harder to master, especially in the teens and back from low thirties. Second the answer to subtraction is the number of counters that remain rather than the number name of the last counter that is removed. Both reasons can be responsible for errors in early subtraction.
   
• Ask the students to make a collection, say nine, and place the counters onto their number strip.
   
• Tell them you are going to take away two counters from the strip. How many counters will be left then?
  Expect the students to anticipate the correct action (removing the counters from 9 and 8).
  Look for students to apply cardinality by telling you that seven counters will be left?
   

3. Progress to examples that develop imaging through turning over the strip but still putting on counters, and going beyond the scope of the numbers strip, e.g. 21 – 3 = ? and 100 – 5 = ­­­? 
    

• Put the students in pairs to pose similar problems, one student making a collection of counters with mixed colours and the other student getting them to predict the result of adding or removing up to 5 counters of one colour. The students’ predictions can be checked, if necessary, by placing counters on a number strip.

Session Four

Comparison of two collections is a common task in real life. Along with joining collections, and partitioning collections, comparison forms the suite of problem types to which addition and subtraction are applied. Comparison offers students a chance to trust their counting and apply their understanding of the one more and one less principle.

1. Pose the following problem to the students using the pictures from Copymaster 4 to make a storyboard. The pictures can be snipped and copied to an Interactive Whiteboard or made into cardboard icons and fastened onto a storyboard using Velcro dots. Alternatively use equipment available in your class. Here is an example:
   Here are 5 puppies and 6 bones. Is there a bone for each puppy?   
   
2. Discuss how the problem might be solved. Students may suggest matching the puppies and bones in one-to-one correspondence to find out if any bones are left over or if any dogs end up with no bone. Counting both collections and using the whole number sequence to anticipate the difference is a more sophisticated strategy because it applies easily to collections of any size. Using one to one matching to anticipate the result of 99 bones with 101 dogs would be a lengthy process.
3. You might illustrate difference by using two number strips with different coloured counters. Build five and six like this:
   
   
   Visually students can see that one more added to five results in six. So, in the puppy situation there will be one extra bone.
    
4. Vary the puppies and bones problems by increasing the numbers and differences up to three. This will encourage anticipation using trusting the count and make one-to-one matching more cumbersome. Keep the differences no more than three and use spatial grouping to encourage grouping strategies to count the number of puppies and bones.
   
   For example, How many dogs are there? How many bones are there? Is there a bone for each dog?
   
   On the number strip the problem solution looks more obvious:
   
   
   Note the difference of two can be found by counting up from 14 to 16, or by counting down from 16 to 14.
    
5. Progress to imaging by turning the number strips over and building each collection. Without the numerals present students will need to image the counting on or back process. 

Variations

• Increase the number size of both collections so students generalise the process of finding differences by addition or subtraction.

Independent activity about differences might take two forms.

1. Provide the students with copies of the pictures from Copymaster 4. Using these pictures students can make up their own comparison problems for another student to solve.  For example: “How many more cars are needed to fill all the garages?”
   
   After students have completed their problems put them into groups of four to share. Bring the class together to discuss strategies for solving the problems. The problems can be made into a book of difference problems for independent work or class discussions.
    
2. Alternatively use or make up two dice with appropriate numbers. For example, one wooden cube might be labelled 4, 5, 6, 7, 8, 9 and the other 8, 9, 10, 11, 12, 13. The two cubes are rolled, and sets made of the numbers that come up, e.g. 12 cars and 9 garages. Students work out the difference between the numbers, e.g. “Three more garages are needed.”

Session Five

The most significant understanding that develops from counting is that collections can be partitioned and recombined without conservation of number being disturbed. Part-whole understanding, as it is referred to commonly, is an extension of Piaget’s principle of conservation of number. Two components of part-whole understanding are significant:

• Trusting the count as collections are partitioned and recombined
• Appreciation of the strategic use of partitioning to make calculations easier and for transfer to similar calculations

Animals on the farm 
This activity is aimed initially at the first component though it can be extended to include the second component.

1. Draw a farm with paddocks joined by fences on a sheet of paper or the whiteboard. Copymaster 5 has a template if you want to create laminated sheets for student use. Plastic farm animals are commonly available at toy retailers and dollar shops. Use counters to represent animals if needs be. Ask a student to put ten animals on their farm or use a single farm as an instructional focus.
    
2. Tell your students to watch as you move one or two animals across the “bridges” to a different paddock. Ask, “How many animals are on the farm now?” Some students are likely to recount while some may accept that the total number is invariant. Repeat, moving animals until the students accept that the total number of animals has not changed. Note that your students may indicate acceptance of the previous number based solely on repetition rather than conservation. So the repetition needs to be disrupted so students apply trust in the count.
    
3. Move two or three animals to different paddocks, then put another animal on the farm in an obvious way.  Ask, “How many animals are on the farm now?” Students who trust their previous counting are likely to realise that, in effect, one more animal has been added so the next number, eleven, gives the new number of animals. Similarly move some animals around then remove two animals. 
    
4. Have students can work in pairs with a Farmyard card (Copymaster 5) and some counters or plastic farm animals. They begin by putting ten animals on the farm. Then they take turns to rearrange the existing animals, then add or remove up to three animals, all while their partner is watching. The partner must then work out how many animals are now on the farm. Encourage your students to avoid counting the animals unless it is to confirm the number.
    
5. An extension of the activity is to introduce a “barn” in the form of a plastic cup. Begin with a given number of animals on the farm, say ten. Tell the students to close their eyes. Move some animals around and then place a plastic cup (barn) over the animals in one paddock. Tell the students the same animals are on the farm but some are in the barn. Ask them how many animals they think are in the barn. Discuss their strategies for working the missing number out. Encourage risk taking with a focus on grouping strategies, close approximations lead to known and trusted facts.
    
6. Students can play the barn game in pairs. They can record their answers as equations, e.g. 4 + 2 + 4 = 10. The number of animals they work with can be varied to create more challenge.
    
7. The farm scenario can be used to develop powerful strategies for working out 9 + and 8 + facts. Be aware that students will need to know the ‘teen’ code as prior knowledge, e.g. 10 + 4 = 14 (Fourteen means four and ten). Start with nine animals on one side of the farm and five on the other. 
   Ask, “How many animals are on this (left) side? (nine) How do you know?” “How many animals are on this side? (five) How do you know?“ “How many animals are on the farm altogether?”
    
8. Encourage students to use grouping strategies to count the number of animals. One by one counting is helpful to illustrate the power of ‘up over ten’ strategies.
    
9. Once the answer is accepted (14) move one animal from right to left to form ten and four. “How many animals are on the farm now?” provides same example of developing 9 + facts.
    
10. Record equations to help the students to see patterns that can lead to know facts, e.g. “For 9 + something just take one off the something and make it a teen number.” Similarly for 8 + facts two animals need to be moved.
     
8. Extend the problem up through ten to more complex examples, e.g. “There are 29/79/99 animals on this side and five animals on this side. How many animals are there altogether?“

Session Six

Skip counting is the process of counting in multiples of two or more. Some researchers, such as Anghilerri, believe that learning skip counting sequences assists students in developing multiplicative thinking. In the early years of primary school, counting in twos, fives and tens is sensible as these sets of multiples have patterns that make them easy to remember. The patterns can also lead to divisibility rules, such as “a whole number can be divided into equal sets of five if the number ends in 0 or 5”, e.g. 35 divides equally by five. Sometimes the sequences can be extended to include threes and fours, although these sequences are harder to remember.

As with other counting it is vital to connect number patterns with quantities and words, and to use different senses. Prediction of further numbers in a counting sequence helps to develop generalisations about which numbers belong and do not belong.

1. Begin with body percussion and saying a one by one sequence. Have students touch their chest on odd numbers and their knees on even numbers (or similar). Move to ‘being goldfish’ on the odd counts by mouthing but not saying those words. So only the even numbers are spoken as knees are touched. 
    
2. Use a hundreds board to highlight the spoken numbers. Interactive hundreds boards are readily available online.
    
3. Ask predictive questions such as “Will we touch our knees when we say twenty-six? How do you know? What about 39?” “How can we know if a number is even?”
    
4. As students become proficient at reciting the skip counting sequence by twos, tens or fives, apply these sequences to quantity. For example, you might get 14 students to stand up and ask questions like:
   “If they line up in pairs, will each student have a partner? Will there be a person without a partner?” If appropriate, use this activity to develop a definition of numbers as odd or even.
    
5. Put bundles of ten ice block sticks on the mat in sequence or have students hold up hands of five to develop skip counting of tens and fives.
    
6. Use the slavonic abacus and the hundreds board alongside one another. Move some counters on the abacus explicitly in sets of two.  Ask the students how many beads you have moved. For example:
   
   Note how trusting the count is needed to accept that the skip count of “2, 4, 6, 8” gives the total number of beads. Extend the difficulty of the problems by:
   • Moving more sets of two counters, e.g. over ten, over twenty, etc.
   • Masking what is moved so all students can hear is the click of movement, this requires a double tracking of skip counting sequence and number of counts
   • Reversing the process by asking how many sets of two you have moved, e.g. “I moved 14 beads. How many twos?”
   • Introduce an odd bead but still privilege counting by twos, for example:
     
      
4. At some point look at the skip counting sequences purely in symbolic form. Use a hundreds board display with highlighting to show the multiples.
   
   
   Ask pattern based questions:
   • “Will 68 be in the counting by two sequence? How do you know? Will 100? Will 91?”
   • “What is the same about all the numbers in the counting by five sequence? The counting by ten sequence.”
   • “What numbers are not in the counting by two sequence? How are these numbers the same? How are they different?’
      
5. Link the charts to problem with quantity. For example:
   “Here are eight pairs of shoes. Where is the total number of shoes on our charts? How do you know?”
   
   Note that students need to identify that the twos sequence applies and that the answer is the eighth count. You might record this fact as 8 x 2 = 16 and address what the symbols mean. Multiplication is expected later, starting at Level Two but the ideas can be started much earlier.
    
6. Link skip counting to divisibility with problems like:
   "Here are nine children. Can they all find a partner? How do you know?"
   
   "Here are 18 children. Can they all find a partner? How do you know?" (Look for students to make links to the answer for 9 children)
   

Session 1: Loopy Shapes

In this activity we sort shapes according to attributes. Working with blocks in this exploration gives ākonga a chance to construct their own understandings about shapes and how they are related.

1. Gather ākonga around a supply of shape blocks, mosaic tiles and attribute blocks.
   Do you see any ways that these blocks are alike? How are they alike?
   Can you see any blocks that are different? How are they different?
2. Use one of the categories suggested by the ākonga to sort the blocks.
   Let’s sort the shapes by size and see how many we have.
3. Put three loops of string or make chalk circles or set rings/hula-hoops out for ākonga to sort the blocks in.
4. Begin by putting a small shape in one of the loops.
5. Distribute the shapes and have ākonga sort them into the three loops.
6. Look at and discuss the shapes in the loops.
   Which loop has the most? Check by counting.
   Do the shapes in this loop have other things in common?
7. Sort the blocks using another attribute. Some possibilities are:
   • colour
   • shapes with 3, 4, 5 or 6 sides
   • shapes that are round and shapes that aren’t

Let ākonga work in small groups to sort sets of shapes in a number of different ways. Circulate among the groups encouraging ākonga to describe the classification used. Tuakana/teina groupings could work well here. 

Session 2: I spy a shape

In this session we play a version of ‘I spy’ ( or 'Kei te kite ahau') that helps ākonga focus on the shapes around them and the number of sides the shapes have.

1. I spy a shape with four sides. You walk through it when you come into the classroom. What is the object?
2. Have the ākonga who guesses correctly go to the door and count the number of sides. Record this on a chart.
3. I spy another object with four sides. This one we look out of. What is the object?
4. Once more get the guesser to count and check the number of sides.
5. Let ākonga take turns giving clues about a shape in the class for others to guess. Each time get the guesser to check the number of sides.
6. Encourage ākonga to give information about the relative length of the sides of the shape. For example, all sides are the same length; this side is longer.

After the game has been played several times get ākonga to draw pictures of 3- or 4-sided shapes in the room. Alternatively you could go for a walk outside to look for shapes and then get ākonga to draw these. Some ākonga may draw irregular 3- or 4- sided shapes such as a trapezium or isosceles triangle, this could be used as a teachable moment to extend some ākonga. Glue the drawings onto charts according to the way that ākonga classify them.

Discuss the charts.
What are some of the things you notice about the shapes you found?
Which did you find more of? Why do you think this is?
Do you know what we call these shapes?

Session 3: In the bag

Which shape is in the bag? Today we reach into feely bags to see if we can work out the shape by touch alone.

1. Gather ākonga together in a circle on the mat (mahi tahi model). Show them 5 shapes on the floor including 2D and 3D shapes. These could be small blocks, mosaic tiles or attribute blocks.
2. Show ākonga the feely bag.
   One of these shapes is in the bag. I wonder if you can tell me which one just by feeling it?
3. Pass the bag around the circle so that each ākonga can feel the shape. Encourage them to think about the shape. Remind them that they shouldn’t point or call out which shape they think it is so that everyone gets a chance.
4. As each ākonga feels the shape in the bag, get them to say one thing they notice about it.
   Tell me something you notice about the shape in the bag.
5. Once each ākonga has had a turn to feel in the bag, ask them to say which shape they thought it was. Then reveal the hidden shape.
   Is this the shape you were expecting?
6. Secretly change the shape in the bag and play again as a whole class.
7. In small groups or pairs, ākonga play the game again as the teacher circulates and questions. Change the types of shapes according to the needs of your ākonga. 
   Can you describe what you can feel?
   Which shape do you think it is? Why?

Session 4: Dominoes

In this session we use the mosaic shapes as dominoes for ākonga to explore shapes and match side lengths as they form a trail of shapes.

1. Gather ākonga in a circle on the mat. Tip the mosaic tiles onto the mat in the middle of the circle.
2. Tell them they are going to play a game of shape dominoes. They are going to match shape sides that are the same length to make a trail around the mat.
3. Let ākonga informally explore sides of the same length by fitting two or more shapes together.
4. Place a tile on the floor and get ākonga next to you to choose a shape that could go next.
   Are there other ways that you could place that shape tile?
   Are there any ways that shape tiles wouldn’t work?
5. Continue around the circle until each ākonga has had a turn.
6. Ākonga can continue playing the game in small groups (a tuakana/teina model could work well), with the teacher circulating and questioning.
   What can you tell me about the shape tile you have chosen to go next?
   Why did you choose that shape tile?

Session 5: Shape makers

In this session we use loops of string or wool to form shapes using ourselves as the corners. We extend the idea using geoboards and rubber bands.

1. Gather ākonga on the mat.
2. Have a long piece of thick string or wool and talk about the shape of the string.
   Who can tell me about this piece of string? (Long, curly, wiggly, etc.)
3. Hold the string in a long straight line and then let it fall onto the floor in a muddle and get ākonga to describe how the shape has changed.
   What was the string like when we held it tight?
   What was it like on the floor?
   How else could we hold the string or put it on the floor to change its shape?
4. Encourage ākonga to make suggestions about the form of the string and to use their own language to describe it.
5. Get each ākonga to hold part of the string and get them to move backwards to form a circle using the whole class and again encourage them to describe the shape in their own language.
6. Using a shorter length of string.  Get small groups of ākonga to hold the string and to explore the shapes that can be made.
   What sort of shapes can you make with three people? (or 4 or 5 people etc.)
   How many sides will the shape have?
   Do all the sides have to be the same length?
7. Get ākonga to continue exploring string shapes in small groups as the teacher circulates and questions.
8. Using rubber bands and geoboards, ākonga can to explore the same ideas.
9. The geoboard shapes can be sorted into several sets (as with Loopy Shapes, Session 1) and ākonga can talk about the similarities and differences between the shapes they have made including, number of sides and lengths of sides.
10. This can be used to make a chart for display. Photos could be taken of the geoboard shape creations.

Session 1

This session explores simple 2-element patterns around the theme of a daisy.

1. Read and/or listen to the nursery rhyme "Mary, Mary Quite Contrary". Consider using this poem in your literacy teaching to enhance its relevance.
2. Talk about what might be in Mary’s garden. Name some flowers and talk about them. If possible show the students a daisy – note the petals.
3. Using the cut petals and a centre circle, the teacher partially constructs a "daisy" with a regular 2-element pattern using coloured petals. The pattern could be yellow, white, yellow, white, …
4. Can you read my pattern?
   What will the next petal be?
   How do you know?
5. Students explore and create their own "daisies".
6. Students share and describe their daisy pattern with the class.

Session 2

Using the same nursery rhyme theme again, explore patterns with flowers.

1. Reread the nursery rhyme.
2. Mary likes to keep her garden neat and tidy. She plants flowers in patterns.
   Model this idea using magnetic backed coloured flowers on a magnetic board.
3. Can anyone continue my pattern?
4. Select a student to complete the pattern of coloured flowers.
5. Invite two or three students to create a flower pattern in front of the class using the magnetic flowers.
6. What is the pattern here?
   Can we read this pattern?
   What will come next?
   How do you know?
7. Students construct their own garden flower patterns using the flower cut outs. Move around the students and discuss what they are doing.
   Tell me your pattern.
   What will come next?
   How do you know?"

Session 3

Simple patterns are again explored but this time using a card game.

Use the copymaster to make a set of cards. Now create baseboards with ten squares. Attach two flower cards to the first two squares to form the beginning of a pattern:

1. Students work in pairs. They each select a baseboard that has the outline of a pattern.
2. The students take it in turns to take a card from the pile. If it is part of their pattern they place it in the correct place on the baseboard. If not needed the card is put at the bottom of the pile of cards.
3. Repeat with the same baseboard and with different baseboards.
4. Move around the students and discuss what they are doing.
   Tell me your pattern.
   What will come next?
   How do you know?

Session 4

Instead of using flowers we now use vegetables to make 2-element and even 3-element patterns.

1. Tell the following story:
   Mary likes to grow vegetables. In her garden she grows carrots, tomatoes, pumpkins and kūmara. She grows her vegetables in patterns.
2. Model a 2-element vegetable pattern for the class, for example, carrot, carrot, tomato, carrot, carrot, tomato...
3. The class reads and predicts the pattern.
4. Explain how gardeners sometimes use cloches (mini glasshouses) to protect plants as they are growing. 
   Mary often uses these in her vegetable garden.
5. The teacher covers part of her pattern with a "cloche".
6. Can you tell me what is hidden inside the cloche?
   How do you know?"
7. Students construct vegetable gardens and cover part of their "garden" with a cloche. Working with a partner they try to predict which vegetables are hidden.
8. More able students can move to constructing a vegetable garden using 3 different vegetables.

Session 5

The students guess the missing members of a vegetable pattern where more than 1 vegetable has been "eaten".

1. Make a vegetable pattern like the ones in the last session. But this time some vegetables are missing from the row. Tell the students that rabbits have got into Mary’s garden and eaten some of the vegetables. Start with just one eaten vegetable and gradually increase the number eaten to 3.
2. The students have to decide which vegetables have been eaten and place these in the correct places.
3. Are the vegetables in the right place? How do you know?
4. In pairs the students play the same game with their partner. They take turns forming the pattern and removing some of the vegetables.

Lesson One

1. Introduce Matariki, The Māori New Year, to your class. There are many picture books and online videos that could be used to introduce this context. Matariki begins with the rising of the Matariki star cluster, (Pleiades in Greek), in late May or June. For the previous three months the Matariki cluster is below the horizon so it cannot be seen. The rising signals the turn of the seasons and sets the calendar for the rest of the year.
2. Show your students the first few slides on PowerPoint 1. Discuss what stars are and how our sun is an example.
   What shape is a star?
   Today we are going to make some stars to display using shapes.
3. For each slide discuss how the left-hand star is made then built onto to form the right star. Encourage your students to use correct names for the composing shapes, such as triangle, square, hexagon, trapezium. If necessary, provide a chart of the shapes and their names for students to refer to. Using a set of virtual or hard-copy pattern blocks, support students to make the stars on slides three and four by copying the pattern. Model this for students (especially if using virtual pattern-blocks). It may also be beneficial for students to work collaboratively (mahi-tahi) during this task.
4. Encourage students to use the blocks to create their own stars. Slide 6 is a blank canvas of pattern blocks. With the slide in edit rather than display mode, you can use the blocks to form other patterns.
5. Copymaster 1 provides two different puzzles for your students. They cut out the pieces to form a star. Glue sticks or blue-tack can be used to fasten the parts in place.
6. Other Activities with Stars
   • Most star designs have mirror symmetry. That means that a mirror can be placed within the star, so the star appears complete. The reflection provides the missing half of the star. Demonstrate to your students how that works. Copymaster 2 provides four different star patterns. Give students small mirrors and ask them to find the places where a mirror can go so the whole star is seen. You could also demonstrate this on a PowerPoint, or using an online tool. An internet search for “online symmetry drawing tool” reveals a number of websites that could be used. Note that Star Four has no mirror symmetry so it is a non-example. Star Four does have rotational symmetry so it can map onto itself by rotation.
   • Copymaster 2 also has half stars on page two. Ask your students to complete the whole star. Be aware that attending to symmetry is harder when the mirror line is not vertical or horizontal. Can your students attend to perpendicular (at right angle) distance from the mirror line in recreating the other half?
7. Creating stars by envelopes
   • The diagonals of some polygons create beautiful star patterns. The most famous pattern is the Mystic Pentagram that is created within a regular pentagon. Video 1 shows how to get started and leaves students to complete the pattern. The exercise is good for their motor skills as well as their attendance to pattern and structure. Copymaster 3 has other shapes to draw the diagonals inside. Note that a diagonal need not be to the corner directly opposite, it can also go to any corner that it does not share a side with.
   • Nice questions to ask are:
     How do you know that you have got all the diagonals? (Students might notice that the same number of diagonals come from each corner)
     Does the star have mirror lines? How do you know?

Lesson Two

In this lesson your students explore family trees, working out the number of people in their direct whakapapa. This may be a sensitive topic for some students. Thinking about our relatives who are no longer with us, or have just arrived, is a traditional part of Matariki, the Māori New Year. According to legend, Matariki is the time when Taramainuku, captain of Te Waka O Rangi, and gatherer of souls, releases the souls of the departed from the great net. The souls ascend into the sky to become stars.

1. Begin by playing a video or reading a book about Ranginui (Sky Father) and Papatuanuku (Earth Mother), the mother and father of Māori Gods. 
2. Ask: How many parents (matua) do you have?
   That question needs to be treated sensitively but the focus is on biological parents, usually a father and mother. You might personalise the answer by telling your students the names of your mother and father. Draw a diagram like this, or use an online tool to create the diagram:
   
3. Ask:
   My mother and father had parents too. What are your parents' parents called?
   How many grandparents (koroua) do you have?
   Students may have different ways to establish the number of grandparents, such as just knowing, visualising the tree and counting in ones, or doubling (double two),
4. Extend the whakapapa tree further.
   
5. Ask: What do we call your grandparent’s parents? (Great grandparents, koroua rangatira)
   Nowadays, many students will still have living great grandparents. You might personalise the idea using your whakapapa.
   What do we call the parents of your great grandparents?
   Now I want you to solve this problem. How many great great grandparents do you have?
6. Encourage students to work in small groups. Provide materials like counters or cubes to support students. Ask students to draw the whakapapa diagram to four layers and record their strategy as much as they can. After an appropriate time, share strategies.
7. Discuss the efficiency of counting based strategies, counting by ones and skip counting in twos. Highlight more efficient methods such as doubling, e.g. 2 + 2 = 4, 4 + 4 = 8, 8 + 8 = 16.
8. Ask: Now let’s just think about our parents. If three children in this class invited their parents along, how many parents would that be?
   Use the context as a vehicle for introducing even numbers (multiples of two), Act out three children getting their parents (other students) and bringing them to school. Change the number of students and work out the total number of parents. Find a way to highlight the numbers that come up, such as shading the numbers on a virtual Hundreds Board.
9. Ask: Can anyone see a pattern in the numbers of parents?
   Students might notice that even numbers occur in the 0, 2, 4, 6, 8 columns of the hundreds board.
10. Introduce a challenge: If everyone in this class brought their parents along, how many parents would that be?
11. Ask the students to work in small teams with materials. Providing transparent counters and individual Hundred Boards will be useful but provide a range of options. Watch for your students to:
    • structure their model as "two parents for every one student"
    • deploy materials in an organised way to represent the whole class
    • use efficient counting strategies, to systematically find the number of parents
    • use recording to organise their thinking, particularly the use of number symbols.
12. Share the strategies students used with a focus on the points above. Depending on the current achievement of your students you might extend the problems. For example:
    • Ten parents came along. How many students brought them?
    • How big would our class be if 100 parents came along?
    • If every student in another class brought two parents along, could there be 54 parents? What about 53 parents? Etc.
    • If students in our class brought all their grandparents along, how many grandparents would that be?
    • If we had to provide a Matariki celebration for our grandparents, what food and drink would we need?
    • How much of each food and drink would we need?

Lesson Three

Matariki is a time for cultural activities, such as story-telling, music, and games. Titi Rakau is a traditional game that involves hitting and throwing sticks, usually to a rhythmic chant. It was used to enhance the hand-eye coordination of children and warriors. Rakau can be used as a vehicle for fractions and musical notation, as well as physical coordination. You can make the tasks below as simple or as difficult as you like.

1. Look at slide 1 of PowerPoint 2. 
   What fractions has the bar been broken into? (Quarters)
   Each of these notes (crotchet) is one quarter of a bar in this music.
2. Find a piece of music online with a clear 4/4 time signature. That means there are four crochet (quarter) beats to the bar. This timing is very common in popular music. “Tahi” released by Moana and the Moa Hunters in 1994 is a good example that is easily found online. Ask your students to clap in steady 1, 2, 3, 4, … time with a consistent time between claps as the music plays.
3. Introduce rākau, made from rolled up magazines taped together with duct tape. Students might practise hitting the ground with the ends of the sticks on every beat of the 4/4 time. This can be changed to beat one on the ground, and beat two ‘clapping’ the sticks together in the air, beat three on the ground, and beat four in the air, etc.
4. Introduce the rest symbol using slide 2 of PowerPoint Two. In 4/4 time the rest is for one beat. So the rhythm is ‘clap, clap, clap, rest, clap, clap, clap, rest…” as is used in “We will rock you,” by Queen. Slide 3 has a bar with two rests. See if the students can maintain that rhythm.
5. Slides 4 and 5 introduce the quaver which is a one-eighth note in 4/4 time. See if students can manage the two different rhythms, including the beamed (joined) quavers. Copymaster 4 can be made into cards, or cut out as is, to create different rhythmic bars in 4/4  time. Note that the semibreve (circular note) denotes the whole of four beats, and the minim (stemmed hollow note) denotes one half of a bar. A minim is equivalent to two crotchets.
6. Let your students make up a single bar using the cards. Encourage them to experiment with possible rhythms by trailing them with Rakau. Rests are usually part of Rakau to allow movement of the sticks from one position, e.g. floor, to another, e.g. chest. The rhythm a student creates can be played by another using Rakau.
7. Look for your students to:
   • Apply their knowledge of fractions, such as one half and two quarters make one whole (bar)
   • Recognise equivalence, such as two quarters make one whole or two eighths make one quarter.
8. Share the bar patterns that students create and play them with Rakau. Rhythms can also be checked by finding an online music composer for children and entering the notes. The software usually has playback.
9. Natural extensions of the task are:
   • Explore different time signatures. Many Māori action songs are in Waltz time (3/4) meaning that there are three crotchet beats to a bar. A crotchet is one third of a bar in that time signature and a quaver is one sixth of a bar.
     The popular chant associated with Ti Rākau (E Papa Waiari - available on YouTube) is in 6/8 time meaning there are six quaver beats to a bar. If you watch a video of a performance with Rākau the sticks are often hit on the ground on the first and fourth beats, or clicked together on the second, third, fifth and sixth beats.
   • Try to work out and record the rhythm of pieces of music, using the cards. Choose a difficulty that suits your students. For example, E rere taku poi, is in 4/4 time and is the tune to “My Girl.”  Kiri Te Kanawa’s recording of Te Tarahiki in 1999 features a six quaver rhythm in 3/4  time. 

Lesson Four

The rising of Matariki, in late May or June, signals to Māori that it is the start of a new year. It is appropriate for students to reflect on the passage of time. For young students there are important landmarks in the development of time, including:

• Recalling and sequencing events that occurred in their past.
• Anticipating events that might occur in the future.
• Recognising that time is independent of events, it progresses no matter what is occurring.

Cooking in a hāngī

In the first part of the lesson students work with the first two ideas, recalling the past and anticipating the future.

1. Show students a video about preparing and cooking a hāngī. There are many examples online. Before viewing the video prompt your students:
   Watch carefully. At the end of the video I will ask you about how to make a hāngī.
2. At times pause the video to discuss what might be occurring. Use the pause as an opportunity to introduce important language, like hāngī stones, kai (food), prepare, cover, serve, etc.
3. Give each pair or trio of students a copy of the first six pictures of Copymaster 5. 
   I want you to put the pictures in the order that they happened. Put them in a line. Be ready to explain why you put the pictures in that order.
4. You might allow groups to send out a ‘spy’ to check the order that other groups are using. After a suitable time let the groups ‘tour’ the lines that other groups have created and change their own line if they want to. Bring the class together to discuss the order of events.
   Why does this happen before this?
   Why does this happen after this?
5. Do your students recognise the consequential effect of order? e.g. The fire cannot be lit until the hole is dug and there is somewhere to put it.
6. Can the students recognise what events occurred between two events? e.g. Covering the food with soil and waiting four hours occurred between putting the food and stones in the hole and taking the cooked food out.
7. Discuss:
   What might have happened before the hole was dug?
   What might have happened after the food was served?
8. Ask students to draw and caption an event that occurred before the sequence of pictures, and another event that happened after. You could also provide a graphic organiser for students to use. For example, the food must be prepared before or while the hole is dug. It must be bought or gathered before it can be prepared. After the food is served it will be eaten. Copymaster 5, pictures 7 and 8 are before and after pictures.
9. Add students’ before and after pictures to the collection from Copymaster 5. You might create a wall display. Some before and after pictures might need to be sequenced. Picture 9 is an event (uncovering the hole) that occurs between two of the six events. Where does it go? Why?

Chances of a good year

In former times, tohunga, wise people of the village, looked at the sky before dawn to watch the rising of Matariki. They used the clarity of the stars to predict what the new year would bring. A clear sky with the stars of Matariki shining brightly signalled a good season for weather and the growing and harvesting of crops. A cloudy sky signalled bad luck.

1. At the rising of Matariki, some stars shine brightly while others do not. Each star has a special job. Use PowerPoint 3 to introduce the stars and their jobs. Play a game with Copymaster 6. The first page is a game board. Use the second page to make a set of 12 cards (bright stars, fuzzy stars, and clouds). The second page can be used to make three sets of the cards.
2. Put the gameboard down and spread the cards face down on the floor. Mix the cards up while students close their eyes. Students select cards one at a time to cover each of the seven stars. For example, Matariki might be covered by the card for a fuzzy star. Slide 2 of PowerPoint 3 shows a completed gameboard (click through it to place the cards).
   If you saw this, what would you predict?
3. Students should make comments like:
   There will be plenty of rain but not too much, and the crops will grow well.
   It is going to be a bit windy.
   There will be lots of food in the rivers, lakes and sea.
4. Let students play their own game of predicting the upcoming year. Look to see whether students consider what is on the set of cards in predicting what card might come next.
5. After playing the game discuss:
   • Is it possible to have a year where every star shines brightly? (No. There are six bright star cards and seven stars of Matariki)
   • What is the worst year you can have? (All two clouds and four fuzzy stars come up)
   • How likely is it that you will have a good year? (Quite likely since half the cards are bright stars and one third of the cards are fuzzy stars)

Lesson Five

This lesson involves making rēwena paraoa (potato bread). The process of making it takes three stages; preparing the ‘bug’, mixing and baking, then serving. Therefore, it is not a continuous lesson. Preparation and serving food are important activities for Matariki celebrations. It would be beneficial to invite older students, or community members, in to help with this session.

1. Explain: In the next three days we are going to make rēwena bread from potatoes. Why is the bread you buy at the supermarket so light and fluffy?
2. Some students may have made bread with their parents or grandparents and can talk about yeast as the ‘leavening’ agent. Play an online video of breadmaking and discuss what each ingredient contributes.
3. In rēwena bread the natural yeast from potatoes is used to raise the dough. The best potatoes are older taewa (Māori potatoes) which are small and knobbly, but any medium sized aged potato will do. One medium sized potato is needed per recipe (for three students).
4. Weighing the potatoes on kitchen scales is a good opportunity to introduce the students to the gram as a unit of mass. Can your students predict the weight of each potato? You might have a potato peeling competition, using proper peelers (not knives). Focus on peeling slowly, with control, as opposed to quickly and without control. The student who gets the longest peel wins. Naturally, you will need to measure the lengths of the peels and come up with a class winner.
5. To make one batch of ‘the bug’ cut up the potatoes into smaller bits and boil them in clean water (no salt) until they are soft. You might time how long that takes. Let the potatoes cool and don’t drain the water. Mash the potatoes, water included. Add in (for each recipe):
   2 cups of flour
   1 teaspoon of sugar
   Up to one cup of luke-warm water (as needed to maintain a paste-like consistency)
6. After you have made a bulk lot of ‘the bug’ put it into clean glass jars to ferment. Fill each jar to one third as the mixture will expand. Cover the jar with greaseproof paper and fix it with a rubber band. Over three of four days the mixture will ferment. Feed it daily with a mix of one teaspoon of sugar dissolved in half a cup of potato water. Your students will be intrigued by the foaming concoction that develops.
7. After ‘the bug’ has developed, let your students create their own batch of rēwena bread by following the recipe (PowerPoint 4). This is a good exercise in interpreting procedural language. Read the instructions to the class if necessary or use your most competent readers.
8. Once the bread is made it needs to be cut into slices.
   How many slices should we make?
   How thick will the slices be?
   How many cuts will we make?
9. You might explore sharing slices equally among different numbers of students. Naming the equal parts will introduce fractions. You might explore the different ways to cut a slice in half or quarters.

Getting Started

In this session we explore shapes and pictures and classify these as having line symmetry and not having line symmetry. Students are encouraged to use their own language to describe objects and pictures that have symmetry.

1. Gather students in a group and pass out a selection of paper shapes (Copymaster 1). Ask students to talk about the shapes and what they know about them. Ask students Can you find a way to fold your shape in half so both halves are exactly the same? Talk about which shapes are easy to do this with and which ones are more difficult (for example, compare the circle and the hexagon). Model how to fold some of the shapes in half, and encourage students to share their thinking with the class.
    
2. Ask students to draw a line on the fold that they discovered. Demonstrate with a mirror how holding a mirror on the fold line creates an image of the whole shape. Then demonstrate how holding a mirror on other fold lines wouldn't (for example, across the heart shape can create a diamond or a bumpy cloud shape, or across a triangle can create a quadrilateral or a diamond). Explain that the fold line that creates exactly the same halves side by side is the special line, called the line of symmetry, we will be looking for this week. 
    
3. Have a collection of objects and pictures available and place them in the centre of the mat along with mirrors, straws, scissors, magazines and two pieces of chart paper. Explain to the students that we are going to use these objects to find out if any have two sides that match exactly. 
    
4. Ask students to explore the objects and pictures on the mat and to choose one that has a line of symmetry and one that doesn’t. The language of symmetry could be introduced to describe the matching shapes.
   Why have you chosen that object?
   Try using the mirror to see if the sides will be the same.
   Can you put a straw down the line of symmetry? (folding line)
    
5. Ask students to sort their shapes onto two pieces of chart paper, one for shapes that have symmetry and one for those that don't, and to state why they have placed them where they have. Ask the rest of the students to check that each shape, object or picture is being placed on the appropriate piece of paper.
   How can we tell for sure?
    
6. Encourage students to identify the line of symmetry and for some pictures to indicate if there is more than one line. Ask the students to then offer two sentences to describe the two charts and how the objects have been classified.
    
7. Let the students independently continue to explore this idea by using magazines to locate a picture of something with a line of symmetry and something with no line of symmetry. Students can paste these pictures onto a piece of paper or into a maths book. They draw a line or paste a straw onto the symmetrical picture to show the line of symmetry and write a sentence to describe the two pictures.

Exploring

Over the next few days students explore things that have line symmetry (or reflection symmetry) as they complete a variety of activities using shapes, familiar objects, pictures, patterns. The students could be organised into small groups and rotated through the activities or they could work independently choosing from a range of activities or marking off completed activities on a contract. As you are monitoring the activities, encourage the use of the vocabulary related to symmetry: reflection (whakaata), line (rārangi), half (haurua), match (tūhono), etc

1. Pattern Match
   Templates showing a pattern made with mosaic tiles are provided for the students. Each pattern stops at a line.
   Students use mosaic tiles to complete the pattern so that it matches on each side of the line. The line is a line of symmetry.
   Teaching Notes:
   Templates could be made by drawing around mosaic tiles or setting up a pattern using the tiles and photocopying it.
2. Symmetrical Patterns
   One student uses concrete materials to create a simple pattern showing a reflective symmetrical pattern.
   Other students can locate the line of symmetry using a mirror or placing a straw (string, skewer, pencil, ice-block stick) along the line.
3. Splodge Butterfly Pictures
   Provide the students with an outline of a butterfly on pre-folded A4 paper or with a line down the middle as well as images of native butterflies such as the Red Admiral (Kahukura) or Rauparaha's Copper to see the reflective symmetry on their wings.
   Students paint splodges and patterns on one side of their butterfly.
   The paper is then folded to create the matching pattern on the other side of the paper.
   Students write a sentence about their picture either to describe how both sides are the same or to say something about the process for making the picture.
4. Place Mats
   Students fold an A4 piece of paper in half one way and then the other.
   They cut out shapes on the folds then unfold the shapes and mount them on paper with a contrasting colour.
   Students identify the lines of symmetry by drawing them in with a coloured pen.
   Some students may want to use more folds to create a more complicated pattern.
5. Leaf Lines
   Students collect leaves and explore the symmetry or lack thereof in different species. They can create a tray displaying different leaves and use straws or string to show the lines of symmetry found.
6. Pegboard Patterns
   Students create their own symmetrical patterns and get a friend to locate the line of symmetry.
7. Symmetrical Faces
   Students look in a mirror to see if both sides of their face look the same.
   Students take an outline drawing of a person and fold it in half to show a line of symmetry.
   They add details to the person to make it a picture of themselves, for example, clothing, facial features, hair.
   
   Outline drawings of tekoteko (carved, human-like figures) could also be used and symmetrical Māori designs such as koru could be added.
   Students can write a sentence about their picture being the same on both sides.

Reflecting

In this session, review the activities that have been completed over the last few days and revisit the class charts and individual charts made in the initial activity. The students are provided with opportunities to demonstrate their understanding of symmetry, to find examples of line symmetry within the classroom, and to create a symmetrical pattern to contribute to a class book.

1. Gather the students on the mat and get them to describe the sorts of activities they have been involved in over the week. Encourage them to talk about patterns that match and about lines of symmetry.
   What was special about the patterns we made with the butterfly outline?
   Why did we put a line down the pictures of ourselves (or the tekoteko)?
2. Revisit the charts made in the initial session and talk about the way the objects have been grouped.
   Why was this picture of a house put on this chart?
   Can you find the line of symmetry in this picture?
3. Get students to look at large objects in the classroom and to think about line symmetry, for example, the door, tables, chairs, the board. With a partner, get the students to find three things in the classroom that have line symmetry and to identify the line.
4. Gather the students back on the mat and show them a range of craft materials; coloured ice block sticks, pom poms, stickers, ink stamps, coloured toothpicks, pipe cleaners.
5. Give each student a piece of paper and get them to fold it down the middle.
6. Get the students to create a pattern by sticking on the craft materials on one side of the paper and then to mirror it on the other.
7. Get each student to write a sentence about their pattern and to draw in the line of symmetry.

A reminder; these activities emphasise quick recognition of amounts, rather than counting, and develop and model a number of ways of recording combinations (+) and separations (-). Each session includes several activities in which an idea is developed.

Session 1

SLO: To quickly recognise patterns within and for five.

Activity 1

If these activities are difficult for your learners, you might start with smaller numbers (e.g. 1). The activities could also be done in pairs of students with mixed abilities (tuakana/teina). Whilst students work in pairs, you could work with students requiring increased support. Students ready for extension could repeat the task, in pairs, with higher numbers (e.g. numbers to 10).

1. Have the students show five fingers. Ask “How many fingers?” and have the students ‘write’ the numeral 5 with their finger in the air and on the mat.
    

2. Show a large dice with dots. Ask the students to hold up five fingers when they can see five dots on the dice. Show faces of the dice to the students in a random order.

    
3. Show the numeral 5 on a card and ask what number it is? Show the word ‘five’ and explain that the symbol 5 is a quick way to write ‘five’. Point out they mean the same thing. Connect “five”, what we say, and 5, what we write. This could include the word "rima" as well. Explain that you have a pile of cards with 5 on them.
    
4. Pass the large dice around the group for individuals to roll. The rest of the class hold up five fingers when they spot five dots rolled. The teacher takes a 5 numeral card each time 5 is rolled. How many fives did the class/group roll? Count the cards together when everyone has had a turn.
    
5. Set a time (eg. play a short favourite waiata) and have the students work in pairs with one dice and a set of numeral cards showing 5. Students add a numeral card to a pile each time 5 is rolled and see which pair rolls the most fives in the given time. Check and compare ‘results’.
    
6. Provide 3 sets of numeral cards 1-5 and 3 sets of picture cards (Copymaster 1), and a dice to each pair of students. A tuakana/teina model could work well here.
   
   Set a short time limit and have the students take turns to roll the dice, find the numeral card and picture card to match. The first student to complete a complete set of numeral and picture cards 1 – 5 OR all three ‘five’ numeral cards and pictures is the winner.

Activity 2

1. Introduce fives frames cards. Discuss with the students that a full card shows five dots. Establish their understanding that the whole line is full. There is no need to count them.
        
    
2. Set a short time limit. Have the students collect recording materials and work in pairs with one pile of five frames that show dots to five. They turn their pile upside down then take turns to turn over the five frames. Each student records the numeral for the number of dots shown. Encourage the students to support their partner in the task. The next card is turned when both have recorded their numeral. Conclude with each student circling the fives they recorded and by reporting the total to the class.

Activity 3

1. Models putting your hand in the bag and drawing out between one and five counters. Lays them on the mat and ask, Is it five?
    
2. Pass around (at least) one bag of counters of one colour. Ask the question, who can get five? Each student puts their hand in the bag, quickly takes a small handful without counting them and places them in one action on the mat, ensuring none overlays another. Ask, Is it five? Encourage the student to recognise the number without counting

Session 2

SLOs:

• To quickly recognise how many more are needed to make five.
• To record an expression, using ‘and’, the symbol + and 0.

Activity 1

Have students play Snap in pairs with fives frames cards. Each student has their own pile of cards upside-down in front of them. As they turn over each card they say the number of dots they can see and say snap if it’s the same number that their partner has just laid down.

Activity 2

1. Show the fives frames cards. Discuss with the students the empty spaces and how many more counters are needed to make five. Show five frames in a random order to the class. Have the students show with their fingers how many more counters are needed to make five and write the numeral with their finger on the mat in front of them.
        
    
2. Model recording the combinations, using ‘and’ and introducing the + symbol, for example 2 and 3, 1 + 4. Introduce 0 and model the example of 5 and 0 and 5 + 0. Write the meaning and synonyms, ‘plus’, and ‘and’.
    
3. Students work in pairs (tuakana/teina) with fives frames, counters and recording materials. A time limit is set (eg. while a favourite waiata is played or a timer is used) and students record combinations as they turn over the five frames cards, adding counters as appropriate.
   This can be varied and made a little more abstract with the use of a dice. If a six is rolled, the student just writes 6. For every other roll the student records combinations to five.
   For example if a three is rolled the student writes 3 (the dots seen) and 2 (the number of dots needed) or 3 + 2.
    

4. Introduce playing cards 1 (ace) – 5 or large digit cards 1-5. Discuss that the queen will be used as zero (she has no number) and model how a 5 and a queen is another way to show 5 + 0 = 5. Students work in pairs and play Memory Pairs to five. (Note: you could also use Numeral cards to make a set of digit cards for this game.) 
   The students spread out the cards between them face down and take turns to find matching pairs of cards which together make five.

   

   
   The students keep the digit pairs (for example 4 + 1, 2 + 3, 5 + 0) that make five and count these at the end of the game.

Session 3

SLOs:

• To use the equals (=) symbol and understand that it means ‘is the same as.’
• To record word stories that describe a situation. To record equations using + and = that match the word stories.

1. Organise students into groups of five. If there is an incomplete group, have these students help to record equations. Ask for 2 students in the first group to stand while 3 remain seated.
    
2. Write, for example: “In Kailani’s group two children are standing and three children are sitting down. There are five children in Kailani's group.” Underline the number words in the story.
    
3. Ask who can write this in another way. Accept all suggestions, including ‘two and three is the same as five.’ This should result finally in recording 2 + 3 = 5. Emphasise the connection between the words and the symbols. Highlight the fact that the group has five, so 2 + 3 is another way of showing 5. It is the same as five. Use both ‘is the same as’ and ‘equals’ as the equations are read together. Repeat this with other combinations to five using the other groups of students sitting and standing.
    
4. Have the students work in pairs to draw pictures of different combinations of bears (or similar) sitting on fives frames and record equations for these.
      
   Have the students read what they have written and display their work.

Session 4

SLOs:

• To connect word stories with mathematical equations involving unknowns.
• To record an unknown using ☐ in addition equations.

Activity 1

1. Show picture cards of numbers of items up to five.
   
   Discuss stories that could be written about these. For example: “There are three dinosaurs. How many more do I need to make five? Three and what is the same as five?”
    
2. Model recording “three and what is the same as five”: 3 + ☐ = 5. Read this together aloud.
    
3. Distribute assorted picture cards to the students. Have them record their own ‘and what’ equations, show the pictures and read their equations to a buddy. Have their buddies answer the ‘and what?’ question.

Activity 2

1. Model writing equations with the unknown in different places, for example ☐ + 1 = 5, 5 + ☐= 5, 2 + 3 = ☐. Write these in word sentences and read aloud both the word sentences and the equations together. Collaborate (mahi tahi) to answer what would go in the box (i.e. identify the unknown quantity).
    
2. Have the students draw pictures and write words and equations using equations with unknowns.

Session 5

SLOs:

• To record word stories which describe a subtraction situation.
• To record equations using - and = that match the word stories.

1. Ask five students to stand in front of the class. Tell four students from the group to return to their place on the mat, while one student remains standing. Record a word story for this. “Five children were standing. Four went away and sat down. One person is still standing.” Read the word story together and ask how this might be recorded just using numerals and symbols. Accept all suggestions and discuss.
    
2. Ask the five students to return and repeat the actions, recording the equation 5 – 4 = 1 as they do so. Emphasise the words ‘went away’. Introduce and write the words ‘subtract’ and ‘minus’. Read the equation several times, substituting the words and emphasising that they mean the same thing.
    
3. Model with students again, writing the word story and recording and reading and the equation in different ways.
    
4. Make "waka" by cutting compartments from a standard egg carton. Have students work in pairs with a fives egg carton bus and 5 plastic teddies (or similar). One student puts up to five teddies in the waka, rows it to the next island and has some teddies get off. Their partner writes or says a word story and an equation to describe what has happened. Have them complete 2 word stories and equations each then read what they have written with another pair of students.
    
5. Write equations using an unknown and read these together. 5 - 3 = ☐ , 5 - ☐ = 0. Together talk about what will ‘go in the box’ and complete these together.

Session 1

SLO: To recognise and describe a group of five in multiple representations of numbers within and to ten.

Activity 1

1. Make paper, crayons/felts, pencils, counters (or similar mathematics equipment) available to the students. Set a time limit as appropriate. Have the students write, draw and show you everything they know about five. This, and the next step, could be done in pairs to encourage tuakana-teina.
    
2. Have the students pair share their work.
    
3. Write the words ‘five’ and rima, and the numeral '5' on a paper chart, whiteboard, or in a modeling book. Collect and record the important ideas that the students have generated. Be sure to use words, symbols and drawings of equations, stories or materials.

Activity 2

1. Show tens frame for 5. 
   
   Describe it in words: ‘There are five dots filling up one column (or side) of the tens frame’. Or, ‘There are five dots. They fill up half of the tens frame'. Or, ‘There are five dots filling one side of the tens frame and five empty spaces on the other.’ Have the students describe to a partner what they see. Hide the tens frame. Have the student repeat their description to their partner of what they see in their mind.
    
2. Show the tens frames for 6, 7, 8, 9, 10. 
             
   For each say the number of dots and repeat 1 above. Encourage participation and accuracy in the oral descriptions including saying how many empty spaces. For example: ‘Seven. Five dots and two dots and there are three empty spaces.’
    
3. Show the tens frames in random order and have the students say the number, make it on their fingers and show a partner.
    
4. Include all tens frames and repeat above, this time with say, show, and write (make writing materials available, or have them use a ‘magic finger’ to write on the surface in front of them or in the air.)
                        

Activity 3

1. Introduce a 20 beads frame and animal strips. Discuss the similarities of the representations, model descriptions then have the students describe what they see.
   For example: ‘Seven. There are five white beads and two red ones.’
   For example: ‘Seven. There are five dolphins and two more dolphins after the dotted line.’
   Repeat with the beads or animal strips hidden. Have the students describe a number image to a partner, then show it to them to check to see if they are correct.
    
2. Distribute writing materials. Show numeral cards to 10 in random order and have them draw a matching image (using dots or beads). Emphasise the need for their drawing to show a group of five for numbers 6 – 10. Display the students’ work.

Session 2

SLO: To apply and record the operation of addition for groupings within ten.

Activity 1

1. Show the children a dice. Discuss, record and read the dot combinations for four.
   4 = 2 + 2, ‘Four is the same as two and two.’ 
   1 + 3 = 4 , ‘One plus three equals four.’
    
2. Show the students other dice faces and have them write and share equations for these. Encourage students to record equations both ways as above. Use the language ‘equals’ and ‘is the same as’.
    
3. Hide the dice, say one of the numbers and ask the students to draw it. Repeat.

Activity 2

1. Repeat Activity 1 above with tens frames cards 5 – 10.
    
2. Have the students work in pairs to play Scoring a Tri. (Purpose: to quickly recognise representations of the numbers 5 – 10).
   Make the link for the students between tri and three, for example: tricycle (3 wheels), triangle (3 sides and corners).
   Each pair has three shuffled piles of cards turned upside down between them:
   • pile 1: tens frames 5 - 10
   • pile 2: digit cards 5 – 10
   • pile 3: equation cards 5 + 1 to 5 + 5 (Copymaster 1).
     
     Compete to see who can ‘score a tri’ by turning over 3 matching cards. For example:
   •      
      
3. Students can repeat the game using animal strips, number word cards (instead of digit cards) and expressions. The winner is the person with the most sets.

Activity 3

1. Show an 8 tens frame. Pose the question “Is 5 + 3 the only way of writing something that is the same as 8?” Discuss and chart the multiple combinations that are the same as 8.
    
2. Distribute a tens frame (5 – 9) to each student and have them each write different combinations for the number of dots depicted.
    
3. Have each student share with a partner what they have done and ask, ‘Have I got them all?’
    
4. Conclude by revisiting the quinary (fives based) equipment used so far and reminding the students of how useful “5 and” is.

Activity 4

Play Murtles 5 and... (MM 5-9) (Purpose: to practice and know 5 + addition facts to 9)

Session 3

SLO: To understand the language of subtraction and apply the operation of subtraction to groupings within ten.

Activity 1

1. Tell and write with the students a subtraction story about someone in the class. For example: Erika was sharing her carrot sticks with Sadie. She had eight and gave three to Sadie. How many did Erika have for herself? Ask the students to record what happened using numbers and have them share their recording.
    
2. Model 8 – 3 = 5 on chart paper or in a modelling book (to keep and refer to later). Draw a box around 8 and highlight this is what Erika started with. Talk about how many she gave away and how many were left. Brainstorm and record words for the – subtraction sign. These should include ‘give away, take away, subtract, minus, less’. Read 8 – 3 = 5 several times using all of the words. Emphasise that they mean the same thing.
    
3. Explain that 8 – 3 = 5 is known as an equation because it has the equals sign which means that 8 - 3 is the same as 5. Make the link between the word equals and the word equation.
    
4. Ask the students which is the biggest number in the equation. Ask them why it comes first. Have them model with equipment to understand that you can’t subtract a smaller number from a bigger number (we are not discussing negative numbers here)
    
5. Record the important points discussed on the chart paper.

Activity 2

1. Distribute a card with a subtraction expression (Copymaster 2) to each student. Have them make a silent decision whether or not the result of the subtraction will be 5. Have them form two groups, a ‘Yes’ group and a ‘No’ group.
    
2. Have them take turns modelling their equation on the 20 beads (with 10 of the beads covered as they are not needed here) to show and explain why they are correct.
    
3. Ask the students whether knowing about the tens frames helped. With reference to the 20 beads frame, model the connection between 5 + 3 = 8 and 8 – 3 = 5.
    
4. In Attachment 1 there are three expressions, 5 – 7, 5 – 8, and 5 – 9 that are included to provoke discussion about why the big number comes first in subtraction equations. Refer to the chart made in 1 above to emphasise this point.

Activity 3

Have the students work in pairs to play Murtles 5 and... (MM 5-9) in reverse. (Purpose: to practice and know subtraction facts that make 5).

Each student covers all the numbers with see-through counters. They take turns to roll the dice. 

If the number rolled can be subtracted from a covered number to leave a result of five, the counter can be removed. The aim of the game is to be the first to lighten Murtle Turtle’s load by clearing all the counters.

Session 4

SLO: To make connections between the operations of addition and subtraction and develop an understanding of the relationships underpinning the family of facts.

Activity 1

1. With reference to the 20 beads frame, model the connection between 5 + 3 = 8 and 8 – 3 = 5. Talk about and record these equations and what the students notice about them, in particular that they have the same three numbers. Emphasise that these numbers have a special relationship and that this relationship sometimes means that we talk about “families” of numbers that are related.
    
2. With the group (or class) place a number strip where all the students can see it. Ask what they notice about it (That it is coloured in groups of five). Connect this to the other quinary materials you have been using. 
3. Have students model with see-through counters on the number strip and record 5 + 3 = 8 and 8 – 3 = 5. Ask if there is something else they can see with these numbers. Encourage them to see: 3 + 5 = 8 and 8 – 5 = 3. Together, model and record all four equations using another number up to 10. Model the same equation on a tens frame. Discuss what is the same about the representations. Emphasise the inverse relationship between addition and subtraction and the phrase : ‘If I know this (eg. 5 + 3 = 8) then I know this (eg. 8 – 3 = 5).’
4. Explain the class is making a display of ‘number families’, sometimes called ‘families of facts’. Ask, ‘What is a fact?’ Emphasise that a fact is a true statement.
5. Distribute number strips, blank tens frames and counters to pairs of students. Have them make, draw and record in pairs ‘families of facts’ associated with some of the numbers 5 – 10. They can choose to use number strips, tens frames or both. Encourage the students to record the families of different combinations, not just those of ‘5 and’ such as 5 + 3 = 8 (5 + 3 = 8, 3 + 5 = 8, 8 – 5 = 3, 8 – 3 = 5) but also 6 + 2 = 8 (6 + 2 = 8, 2 + 6 = 8, 8 – 2 = 6, 8 – 6 = 2).
6. Discuss and display the students’ work.

Activity 2

Have the students in pairs play ‘Go Fish’ or ‘Happy Families’ Copymaster 3 (Purpose: to identify all members of families of facts)

5 + 4 = 9 4 + 5 = 9 9 – 5 = 4 9 – 4 = 5

The aim of the game is to make the greatest number of complete families of facts. To play:

• The Family of Fact cards are shuffled and placed face down. Each player takes seven cards.
• The players sort their cards in their hand into ‘families’, identifying complete families and placing these face up in front of them.
• Each player takes turns to ask their partner for missing family members. If their partner cannot supply the card, they are told to ‘Go fish’. They take a card from the pile.

The game is played till all the cards are used and the winner is the person with the most complete families.

Session 5

SLO : To know and apply addition and subtraction facts within ten.

1. Show selected tens frames, 20 beads frame and animal strips modelling example equations such as "7 and 2". Have students model these with their fingers and talk about the related addition and subtraction equations.
2. Explain that they will be playing some games just working with numbers, but that they might like to picture fingers, tens frames, bead frames or animals to help them if they need to.
3. Explain the purpose of the activities is to practice what they know.
4. In pairs play the following games, using playing cards with Kings, Jacks and tens removed, and using the Queen as a zero:
   
   ‘Snap’ for a chosen number to 9 (Purpose: to practice and know addition and subtraction facts to 9): 
   Students draw a number from the pile, for example 7. This becomes the chosen number they must make. 
   One card is turned over to begin the game. 
   Students take turns to turn over a card from the pack, placing the turned card on top of the card before. If the turned card can combine in some way with the previous card to make the chosen number, the student says ‘Snap’, states the equation and collects the pile of cards. 
   The game begins again with the same chosen number. 
   For example, for the chosen number 7: if 9 is turned, followed by a 2, 9 – 2 = 7 is stated and the pile of cards is collected, or if 3 is turned, followed by 4, 3 + 4 = 7 is stated and the pile is collected.
   
   ‘Memory’ for a chosen number to 9 (Purpose: to practice and know addition and subtraction facts to 9): 
   Cards are turned down and spread out in front of the students. A chosen number is turned over and identified. 
   Students take turns to draw pairs. If the cards can make the chosen number, using either addition or subtraction, the pair is kept by the player. For example: 4 is turned over and identified as the chosen card. A player draws a 6 and a 2, and states 6 – 2 = 4 and keeps the pair, or a player draws 1 and 3 and states 1 + 3 = 4 and keeps the pair. 
   The game continues until all cards are used up. 
   The winner is the person with the most pairs.
   
   ‘Dice pairs’ for a chosen number to 9 (Purpose: to practice and know addition and subtraction facts to 9 and family of facts members): 
   Each player has a blank tens frame and ten counters to place one at a time on the frame to record their score. The winner is the first one to fill their frame. 
   Players roll two dice, combine these to identify a chosen number of 9 or less. If the combination is more than 9 they roll again. 
   Players take turns to roll the two dice to make the identified number. Each time they are successful and can state an equation and the other 3 members of the family of facts, they score by placing one counter on their tens frame. For example: If 8 is the chosen number. A player rolls a 2 and a 6 and states 6 + 2 = 8, 2 + 6 = 8, 8 – 2 = 6, 8 – 6 = 2. They are correct and place one counter on their tens frame.
   
   Have students each make puzzle cards for the class to use. (Purpose: to depict a context for a family of facts and record these): 
   Make available cards marked in 3 sections as shown below, felts/crayons and scissors. Have the students draw pictures of equations, write them, then cut into two puzzle pieces to match. When several have been created, students can play memory match, by turning the pieces upside down and trying to find pictures and matching equations.
5. 

Read ‘How Maui slowed the sun’. Discuss aspects from the story with ākonga.

For example; Why were Maui and his whanau angry at the sun? How do you think you would feel if you lived with his whanau? What are our days like now? Do you think this story is true? Why or why not? (Maui’s story is a traditional Maori story told to explain the length of days).

Session 1: Time on a line

In this activity we sequence events which occur within a school day.

• String and pegs to hang pictures
• Paper
• Crayons

1. Brainstorm with the ākonga all the things that they do in a school day, for example, reading, newsboard, playtime, mathematics, lunchtime, writing, hometime.
2. Ask ākonga to draw a picture of something that they do every day at school. Work with ākonga to write captions for their pictures.
3. Bring ākonga together to pin their events on the line of string.
4. As each student pegs their picture on the line, ask them to explain where it goes. If more than one student has drawn the same event, tape them together.
   Where does your picture go?
   What happens before your picture?

5. When everyone has pegged their picture to the line, discuss the order of events and ask them to decide where new events belong. 

   Where would I put playtime?
   Where would I put your parents coming to collect you from school?
   Which are morning events?
   Which events happen in the afternoon?

Session 2: My day

In this activity we sequence the events in our day from when we wake up until when we go to bed. We make these into a wrap-around-book.

• A strip of paper divided into 5 sections

1. Begin by asking ākonga to tell you about the first thing they do when they wake up.
   The first thing I do is look out the window.
   What do you do?
2. Get them to draw the first thing that they do on the first segment of the strip. Share the drawings.
3. Ask the ākonga to think about the last thing that they do each day. (In bed asleep)
4. Draw this on the last segment.
5. Now ask the ākonga to think about the other things that they do during the day.
6. Tell your friend about the things you do.
7. Fill in the other pictures on your day chart.
8. Join the ends of the strip to make a wrap-around-book.
9. Share the "My day books".

Session 3

In this activity we sequence days of the week. The activity works best if it can be developed over a week, taking a couple of minutes a day. The learning in this session could be complemented with singing a song about the days of the week (in English and other relevant languages).

• Paper strips with the days of the week written on each strip in English and in te reo Māori. Use 2 colours - one colour for the weekdays and one colour for the weekend.
• Staples or cellotape

1. On Monday give each student a strip of paper with Monday written in both English and Māori.
2. Ask the ākonga to tell you events that happen on Monday – list these on a chart.
   On Monday I ….go to ballet, visit Grandpa etc
   Ask each student to write one thing that happens on Monday on their strip. They can copy one from the class chart if they prefer.
3. Help ākonga join the ends of their paper strip to form a loop.
4. On Tuesday repeat the process, linking the Tuesday loop to Monday’s loop.
5. Repeat this for Wednesday, Thursday and Friday.
6. On Friday ask ākonga:
   On what day does the chain start?
   How many days are in the chain? Can you say them in English? In Māori?
   What day was it yesterday?
   What day is it today?
   What day is it tomorrow?
7. Add loops for Saturday and Sunday.
8. In the following weeks loops can be added to a class chain to develop the idea of repetition of days of the week.
   

Session 4 : Fast and Slow

In this activity we discuss things that move quickly and slowly. We begin by reading the story of the hare and the tortoise.

• Paper

1. Begin the activity by exploring fast and slow actions.
   Let’s wave our hands quickly…now slowly
   Let’s clap quickly…slowly
   Let’s blink quickly…slowly
2. Ask ākonga to share their ideas for other fast and slow actions.
   What other things can we do quickly and then slowly? Make links to relevant learning from other curriculum areas, where possible (e.g. we can beat the drum quickly, we can write letters slowly).
3. Discuss things that ākonga know that go fast or slow. List these ideas on a chart of slow and fast things.
4. Ask ākonga to think of their favourite fast thing and their favourite slow thing. Draw these onto a piece of paper.
5. Share the pictures of fast and slow things.

Session 5: Ages

In this activity we begin by looking at pictures of people of varying ages. Alternatively, use photos of you, the teacher, at various ages from birth until your present age.

• Pictures of people of varying ages, images from the internet, photos from magazine, or family photos
• Magazines

1. Gather ākonga on the mat to show them the pictures. Begin with the picture of a baby. (If it is a photo of you, get the ākonga to guess who they think it is.)
   How old do you think the baby is?
   Do you know any babies? Who?
2. Show two more pictures of ākonga.
   Who do you think is older?
   How can you tell?
   How old do you think that student might be?
   Is that older or younger than you?
3. Before you show the next picture ask ākonga to guess who it might be a picture of (mother, grandmothera, kuia, toua)
   What picture do you think I am going to show you next? Why did you guess that?
4. As you discuss the pictures display them on a line in order of age.
5. Ask ākonga to either cut from magazines or draw 4 pictures of people of different ages.
6. Give the sets to other ākonga to order.
7. Share the strips of pictures.

Session 1: Tricky bags

In this activity we investigate bags that look the same, but one is empty and the others are filled with books.

1. Display the bags for ākonga to see.
   Are these bags the same or different?
   How do you know?
   Are you sure?
2. If no one suggests looking in the bags or lifting them, ask for two ākonga to lift a bag each and describe what they feel. List the words that they use on the board.
3. Let other ākonga lift the bags and give their description.
4. Give pairs of ākonga two supermarket bags and ask them to make up their own 'tricky bags'.
5. Let ākonga share their tricky bags with other pairs of ākonga. Remind them to describe what the bag feels like when they lift it.
   Can you guess by just looking, which is heavy?

Session 2: Push and Pull

In this activity we push and pull objects to see which feels heavier.

1. Show ākonga two large cartons. Each carton should be filled with heavy blocks or books that ākonga can't lift easily - they should all vary in mass. 
   Are these cartons the same or different?
   How do you know?
   Are you sure?
   How could you find out?
2. If this activity has followed from the tricky bags activity you would expect ākonga to suggest that they lift the cartons. Tell ākonga that the cartons are too large to lift, and ask if they could think of another way of comparing them.
   The cartons are too large for you to lift safely. Can you think of another way of finding out how heavy they are?
3. Let ākonga take turns pushing or pulling the cartons.
   Do you think they are the same?
   Why? Why not?
   Which carton is heavier? How do you know?
4. Discuss objects that ākonga have seen being pushed or pulled rather than lifted. For example: beds, tables, couches, pianos, vehicles that have broken down, objects at construction sites.
5. Ask ākonga to draw a picture of one of these objects. Attach them to a chart of 'Pushing and Pulling'.

Session 3: Popcorn containers

In this activity we make popcorn containers for the Three Bears. Any other picture book that describes a quantity of something (e.g. an amount of food) could be used in this session. 

1. Read or tell the story "Goldilocks and Three Bears" to ākonga. When you have finished, tell ākonga that the bears are going to the movies and want to buy some popcorn.
   What size popcorn would Father Bear want?
   What size popcorn would Mother Bear want?
   What size popcorn would Baby Bear want?
2. Tell ākonga that they are going to make popcorn containers for the bears' popcorn. Show ākonga how to make popcorn cones by rolling a piece of paper or light card. Ākonga could decorate the paper before rolling it up to make a container.
3. Ask ākonga to make containers for the three bears' popcorn.
4. As a class, look at the popcorn cones made.
   How could we check if Father Bear's cone holds the most?
5. Give ākonga popcorn to pour between the containers to check.

Session 4: Fill it up

In this activity we pour water (or beans) between containers and guess how high up the water or beans will go.

1. Show the class a cup full of beans or water and an empty ice-cream container.
   What do you think will happen if I pour the beans into the ice-cream container?
   How far will it fill up?
2. Check and discuss.
   Did you guess correctly?
   Is the container full?
   Is it empty?
3. Give each ākonga a cup full of beans. Put several containers of varying sizes around the room. Ask the ākonga to pour their beans into the containers, first guessing how high up they think the beans will go. Alternatively this station could be set up outside on a water tray with various containers for ākonga to guess and fill. 

Session 5: Book corner

In this activity we look at some picture books that could be read to ākonga or enjoyed independently by ākonga, to reinforce measuring language associated with volume and mass.

1. Who Sank the Boat? Pamela Allen. (1996). This is also available in te reo Māori - Nā Wai Te Waka I Totohu?
2. Goldilocks and the Three Bears
3. Mr Archimedes' Bath.  Allen, P. (2020).
4. Watch Out! Big Bros Coming! Alborough, J. (1997).
5. The Bad Tempered Ladybird. Carl, Eric. (1977).

More titles and measurement specific activities are available on the Level 1 Measurement Picture Books page.

Session 1

Here we share the story and construct a pattern grid from the story. This pattern grid will be used throughout the sessions. It could be created with paper or with the use of digital tools (e.g. Google Slides).

1. Share “Ten in the Bed”.
2. With the help of the class, rewrite the poem so that the initial character is calling others to bed. There was one (tahi) in the bed and the little one said,
   “Come to bed, come to bed”
   There were two (rua) in the bed and the little one said
   “Come to bed, come to bed.”
3. As the poem is compiled, record what is happening in pictorial form and also record the total number of children in bed each time on the pattern grid (see one completed under step 8 below). For example:
   
4. Encourage the students to predict the next number each time. Students might use counters to demonstrate the addition of each new person. 
   What is happening?
   Who can see a pattern in the pictures?
   What is that pattern?
   Who can see a pattern in the numbers?
   What is that pattern?
5. As a class, continue to construct the grid up to five in the bed. As you record the poem encourage students to predict and repeat the parts of the text that form the pattern. These can be highlighted in a particular colour for emphasis. What is the same about the next page? What words will need to change?
6. How many will be in the bed next?
   Students make predictions and are then asked to go and check their answers using paper and pencil or objects.
7. Students continue until there are 10 children in the bed.
8. Volunteers share their solutions.
   What did you do to find the answer?
   Did someone do it another way?

9. The chart and book are compiled up to ten and both are displayed for the students to explore further (See pattern grid below.)

   Number of jumps into bed	1	2	3	4	5	6	7	8	9	10
   Number of children	1	2	3	4	5	6	7	8	9	10

Session 2

Here we focus on the number of eyes in the bed to build up a pattern that goes up two at a time. If your students are confident using English and te reo Māori words for numbers, you could incorporate words for numbers from any other languages reflected in the makeup of your class. This should be appropriate for your learners, so as not to add too much additional cognitive loading.

1. Share the poem and the chart compiled in the previous session. Focus on the pattern and how the students knew what was coming next.
2. If there was one (tahi) person in the bed how many eyes would we see?
3. Select students to act out the problem.
4. If there were two (rua) people, how many eyes would there be?
   What did you do to work it out?
   Record the number of eyes the same way as in the previous session.
5. Continue the story up to four (wha) people in bed. Record what has happened on the chart.
6. What is happening on our chart?
   Look at the picture of the eyes. What is happening each time?
   Look at the numbers. What is happening here each time?
7. The students are asked to continue the pattern to find out how many eyes there would be in the bed if there were ten in the bed. They are able to use pencil and paper, counters, or cubes.
8. Students come back to the whole class setting to share their solutions.
   What did you do? Why did you do that? Did someone do it another way?

9. The class jointly completes the chart (See below.)
   

   Number of jumps into bed	1	2	3	4	5	6	7	8	9	10
   Number of eyes	2	4	6	8	10	12	14	16	18	20

Session 3

Here we explore a pattern that increases by five and record it on a pattern grid.

1. Reread the new version of “Ten in the Bed.”

2. Tell the class that each evening their mother comes in to give the children a goodnight kiss. She gives each child five kisses. Record this information for one child on a chart using pictures and numbers.

   Number of children kissed	1	2	3	4	5	6	7	8	9	10
   Number of kisses	5

   
    

3. How many kisses would mum give if there were two in the bed?
   How could we find out?
   Record the answer on the chart.
4. Repeat for three in the bed.
   How many kisses will mum give now?
5. Examine the chart.
   Can anyone see a pattern in the picture?
   Is there a pattern in the numbers?
   Can we use this pattern to work out how many kisses mum will need to give if there are five in the bed? Seven in the bed?
6. Students solve the problems then return to a whole class setting.
7. What answers did you find?
   What did you do to find the answer?
   Why did you do this?
   Could we do it another way?
   How did you use the pattern to help you find the answer?”
8. The class jointly completes the chart by first using the solutions the students already have and second by predicting and then confirming using the pattern that they have seen.

Session 4

The students explore patterns of ten using toes as a focus.

1. Read through previous days’ charts, drawing attention to the picture and number patterns. As a class, you could act, or use puppets, to demonstrate the patterns.
2. Today we are going to find out how many toes there might be in the bed.  If there was one child in the bed we know there would be ten toes.
   Does anyone know how many toes there would be if there were two children in the bed?
   How did you work that out?
3. Using equipment or pencil and paper the students explore patterns of ten until they are able to say how many toes there would be with up to ten children in the bed. Support students, who are not yet confident with writing numbers, as necessary.
4. Students share their thinking and solutions with the class.

Session 5

The students design questions around “Ten in the Bed” for their class to solve.

1. We have been exploring patterns from the poem "Ten in the Bed".
   We have looked at patterns of eyes, kisses and toes.
   Today you are going to make up your own questions about our story for the class to solve.
   (You may need to discuss this with them before they start on their own.)
2. Students write problems that involve exploring patterns in the poem. Consider the writing abilities of your students. It may be wise to provide sentence starters for some, or all, of your students (e.g. there were 10 tamariki in the playground…how many…?). Alternatively, you may write one story as a class, and then pair up students to write questions relating to this story. This story should be relevant to current learning from another curriculum area (e.g. learning about minibeasts), to the wider context of your class (e.g. a class trip to the museum), or to a collective interest demonstrated by your students (e.g. animals).
3. Students swap problems and solve each other's problems.
4. Students share their problems and solutions with the class.

Getting Started

Today we follow Māui and his brothers on their journey to Rā the sun. We will look at the people and things Māui and his brothers are likely to meet.

1. Read or tell the story of Māui and the Sun. 
   Discuss with ākonga the setting of Māui's journey. Encourage ākonga to share their ideas about the objects that could be found on the land and sea as Māui journeys to Rā the sun.
   1. Show a picture of a fern to the class. Ask: Do you think Māui will see a fern on his journey to Rā the sun?
      Peg/blu tack the picture of the fern beneath the word card "will".
2. Show a picture of a basketball to the class. Ask: Do you think Māui will see a basketball on his journey to Rā the sun?
   Display the picture beneath the word card "won’t".
3. Show a picture of a frog to the class. Ask: Do you think Māui will see a frog on his journey to Rā the sun? 
   Display the picture beneath the word card "might".
4. Show ākonga the rest of the pictures in the Māui and the Sun story pack. Let ākonga take turns placing the picture under a word card. Ask ākonga to justify their decision. Some ākonga may have differing opinions, you may need to facilitate this.

Exploring

Over the next 2 to 3 days, ākonga can look at the journeys of other characters in different stories and make decisions about who or what they might meet.

1. In pairs (tuakana/teina), let ākonga select one of the prepared story packets. A story packet contains 3 word cards and pictures of objects for ākonga to classify.
   Remind ākonga to peg the pictures beneath the word cards. Stories could be read to ākonga in a tuakana/teina model, retold by other ākonga, listened to on audio books or watched on youtube or other sources. 
2. As ākonga classify the cards, ask questions that encourage ākonga to explain their thinking.
   Tell me why you have put that there?
   Why do you think that …….. is impossible?
   Could you have put it with one of the other words? Why/Why not?
3. Ākonga can draw 3 new pictures on blank cards – one object for each word card in their story packet.
4. At the end of each day, give ākonga an opportunity to display and discuss where and why they have put the pictures under each word.
5. As ākonga share their decisions, encourage ākonga to use the language of probability.

Reflecting

1. We begin today’s session by asking ākonga to brainstorm a list of their favourite stories.
2. In pairs, ask ākonga to select a story for which they can make a story pack. Discuss what the contents of a story pack are (pictures and 3 word cards).
3. Allow the pairs time to talk about the people or things that the main character will, might or won’t see.
4. Share ideas to ensure that ākonga understand what they are doing.
5. Let ākonga decide on the 3 probability words that they are going to include in their story pack. These words can either be provided on cards or written on the board for the ākonga to copy.
6. As ākonga make their story packs, ask questions that focus on their use of probability words and their decisions about the likelihood of events.
7. Swap packs.

This unit includes several activities for each session. Choose 2-3 activities for a single session or spread each session over more than one day.

Session 1

SLOs:

• To understand that an amount or number of items can be represented with a single unique symbol.
• To correctly write numerals to five.
• To understand that written words and oral words can be represented with a single symbol.
• To recognise and match words and symbols with the amounts they represent.

Activity 1

Play Number Eye Spy.
(Purpose: To identify numbers of items in groups up to five.)
Explain that in the classroom, some things we see might be in groups of two, three, four or five. Give an example, such as a group of three computers at the back of the classroom. Explain that you could give a clue about the items by saying, “I spy with my little eye, three of something.” You might give directional clues as well to develop the vocabulary of movement and position, e.g., “The items are at the front of the room.” Numbers spoken in te reo Māori can be interchanged with English numbers.

Pose the problem of finding matching collections, by changing the number in the group from three. Have students look about the classroom to identify the group of items you have seen. The person who guesses correctly has the next turn. Take digital photographs so the class can make a display of pictures that match each number from one to five, or further if students show proficiency. Use items that have significance to the students, such as their artworks, cultural artifacts, or toys/mascots. Students might draw collections of objects for a given numeral, such as the number of siblings they have in their whānau or their pets at home.

Activity 2

1. Play Spot the Spots, using the red and green 1 to 5 dot cards from Copymaster 1a, or the 1 to 5 koru cards from Copymaster 1b.
   (Purpose: To subitise groups of up to five dots.)
   Shuffle the cards. Hold them up one at a time, so that the students can all see them. As each card is held up, have the students show how many dots they see, by holding up the same number of fingers. Students might be asked to represent the number in different ways, such as say the number in words, write the numeral in the air if they know it, or make a set of counters that match the number and layout.
   
2. Shuffle the cards and distribute (at least) one to each student. Going around the mat circle, ask the students to take turns to hold up their card for the others to see. The other students who have a card with the same number of dots hold up their cards too.
3. Distribute numeral cards to 5, or a number fan to each student. Repeat Step 2 above, but this time the students show the numeral (card) that matches each student’s dot card as it is shown.
4. The cards can also be used to develop subitising (instant recognition). To encourage imaging, make the card visible for a short time, and ask the student to name the number. 

Activity 3

1. On the class chart revise together how to correctly write numerals 1 to 5.
   Explain that they will be writing numerals. Discuss what numerals are used for in daily life. Students might suggest things like the number of people who live in a whare, the number of kaimoana on a plate, the number of chicks in a nest, etc.
2. As numerals are formed on the chart, have students practice forming them in the air, and on the mat in front of them. Have them feel and describe that correct form.
   Emphasise the correct directionality when forming 2, 3 and 5 in particular.
   Model forming each numeral with your back to the students and write the numerals large in the air. Ask students to copy your actions. Adjust your writing hand for students who are left-handed.
3. Have students return their dot cards from Step 2 by, one at a time, coming to the chart, showing their dot card, saying the number and forming the numeral. Watch for correct numeral formation. Students are likely to need plenty of practice. Students might enjoy writing on small whiteboards or blackboards.

Activity 4

1. Write numerals 1 to 5 on the class chart. Ask the students what you have written (numerals). Explain that there are words for these numerals that can be written and spoken. Show word cards, one to five, from page 1 of Copymaster 2. Te reo Māori versions are included.
   Hold up the word cards in order and read them aloud together several times. Show them out of order, having the students quickly reading them aloud.
2. (Using Blue Tac or similar), with assistance from the students, arrange the word cards correctly beside the numerals on the chart. Together check that they match.

Activity 5

Have students work in pairs, or groups of three, to play One, Two, Three, Snap.
(Purpose: To correctly match words, numerals and images of numbers 1 to 5)
Make available to each group, word cards to five (Copymaster 2), numeral cards to 5 (Copymaster 4) and dot or koru images images to 5 (Copymaster 1a or Copymaster 1b). Alternatively, the picture card images from Copymaster 3 can be used instead of the dots. 

Each pile is shuffled and placed face down in front of the group.
Explain that students in the group each take turns to take one card from each pile, placing them face up in front of themselves as they do so. If all cards show the same amount (symbol, word and image) they say “Snap!” and keep the set.

If not, the cards are returned to the bottom of each pile.
The winner is the person with the most sets of three at the end of the game.

Activity 6

Conclude the session with a game of Get Together.
(Purpose: To form groups of up to five in response to hearing a number word, a written number word, or to seeing a numeral or a number word.)
Choose a piece of fast-paced music that your students enjoy. 
Ask your students to stand. Explain that they are to move about the room in time to music. When the music stops, the teacher will either say a number or show numeral or word cards up to five. Students are to look at the teacher, listen for a number or look for a numeral and, as quickly as possible, make a group of that number, and sit down when the group is formed.

Session 2

SLOs:

• To recognise and match sets of items with written and spoken words and their symbols.
• To correctly write numerals to five.
• To recognise numbers within story contexts.

Activity 1

Ensure that numerals 1 to 5 can be seen by the students. Read them together. Begin by playing Spot the Spots from Session 1, Activity 2. Instead of holding up the same number of fingers, have students write numerals in the air and on the mat with their finger.

Activity 2
(Purpose: To accurately write numerals 1 to 5 in response to hearing number words within a story context.)

1. Make paper and pencils available to the students. Explain that you are going to read them a story (Copymaster 5) and they are to listen very carefully and write down any numbers that they hear in the story. They should write these numerals in order across the page. Alternatively, you could tell them a made up story that includes members of the class.
2. Introduce the task by reading the first two sentences of the story, show the dog pictures, explain and model what to do.
3. Read the story, having them complete the task.
4. Read the story again together, having students actively identify the number words as they are read, and writing the numerals on the class chart. Emphasise correct formation of the numerals.
5. Have students check each other’s recording.
6. Ask if students know of other stories with numbers and record their ideas. For example, The Three Little Pigs, Pukeko counts to ten, Counting for kiwi babies, or The great kiwi 1, 2, 3, book. Suggest that students listen and for numbers spoken or seen during the day.

Activity 3

1. Ensure that students can see number words and numerals.
   Make a think board template (Copymaster 6) and pencil available to each student. Have the students write their favourite number (between 1 and 5) in the centre of their think board. Have them draw a picture, write their own number “story” that includes their favourite number, show any numbers by drawing dots or pictures of equipment, and write any number words, encouraging English and Te Reo.
   You may need to support emerging writers by recording part or all of their story for them, and use digital platforms for students who find handwriting difficult.
2. Once completed, have student pairs share their thinkboards.

Activity 4

Make the cards from One, Two, Three, Snap (See Session 1, Activity 5) available to the students so they can play a Memory game as they finish their thinkboard. To play memory they should turn all the cards from three sets face down, mix them up and take turns to find matching trios.

Activity 5

Conclude the session with class sharing of thinkboards. Students could take these home to share their learning with their whānau.

Session 3

SLOs:

• To understand and use the addition symbol.
• To recognise and use the written and spoken words for addition, with the addition symbol.

Activity 1

1. Ask the students which numerals they have been learning to write. Extend students to write numerals for 6 – 10. Record these numerals on the class chart. Have students take turns to come and write other numerals that they know on the class chart. As they do so, discuss the numerals, highlighting their correct formation, particularly numerals 6, 7 and 9.
2. Show a selection of dot cards from 6 to 10 (Copymaster 7a) or koru cards from 6 to 10 (Copymaster 7b), asking students to say what they can see. The focus here is on seeing familiar groups of 1 to 5 dots within the larger group. Some may readily recognise immediately the larger (complete) groups, but this is not the purpose of this task.
3. Ask students to say the numbers they see in words. Some students may be able to write the words. For example:
   “I can see five and one.”
   “I can see five (across) and two (in the corners).”
   “I can see four and four.”
4. Ask, “Is there another way to write this, using numerals?”
   Guide the students to shared recording on the class chart:
   “I can see five and one” → 5 and 1 → 5 plus 1 → 5 + 1
   “I can see five and two” → 5 and 2 → 5 plus 2 → 5 + 2
   “I can see four and four” → 4 and 4 → 4 plus 4 → 4 + 4

Activity 2

Together, make a chart, or class dictionary page, about addition and its symbol, + , asking and recording what the students already know. Use items that students are familiar with to create stories that might be modelled by addition. For example, “Two weka were hunting for worms. Three more weka came along. How many weka were there then?” Record the stories using addition equations, e.g., 2 + 3 = 5 for the weka story.
Create a class book of addition problems that students make up, including a picture and written story. The equation can be written on the back of the page.
Discuss the addition symbol. Included in the ideas recorded, should be:
+ is a symbol or sign
+ shows that we are joining together two amounts or numbers
+ is an addition symbol
when we see the + sign we can read it as “and”, “plus” and “add”
+is a short way of writing “and”, “plus” and “add”.

Activity 3

1. Together, write a mathematics expression about at least two other dot cards and model several ways of reading what has been written:
   For example: 
   Write 5 + 3 and together read: ‘five plus three’, five and three’, ‘five add three’, ‘five and three more’. 
   You might also highlight that 3 + 5 and the matching statements could also be written.
2. Make paper and pencils, or, whiteboards and pens, available to the students.
   Distribute at least four dot cards to each child that show numbers of dots greater than 1.
   Have students write, talk or draw about their cards. Use their recording to add to the class chart or create a digital presentation. 

Activity 4

Ask the students work in pairs to play Read and Draw, using the cards from Copymaster 8,
(Purpose: To read a mathematical expression in at least two ways and to respond to a mathematical expression with a drawing.)
Tell the students the purpose of the Read and Draw task. Explain that they take turns to be the Reader and the Quick Draw person.
The Reader’s task is to read the mathematical expression in at least two ways to their partner. Studenrtsshould check their partner’s drawing before showing them the task card on which the expression is written. Their task is to check the accuracy of the drawing.
The Quick Draw person’s task is to listen carefully to the expression that is read, and to draw a diagram of what they hear, using simple shapes. For example: The Reader reads, 4 + 2: “four and two, four plus two,” and the Quick Draw person draws:

Students should have at least four turns each.

Activity 5

Conclude by playing the Hands Together game using two sets of expression cards from (Copymaster 8).
Each student makes a number of choice on one hand by showing that many fingers. For example:

Have them show their ‘number’ to a friend. (This is to avoid students changing the number of fingers when they see the expression.)
The teacher shows an expression, for example 5 + 3. Children who have made these numbers on their fingers must move to pair up, one student showing 5 fingers and the other showing three. The first pair to form and to show 5 + 3 collects a 5 + 3 expression card each. The game begins again. The game finishes when all cards are used up. Students take turns to read aloud to the class the cards they have ‘won’. Each student should read their cards in a different way from the student before them.
Ask students to bring a favourite small soft toy for Session 4. The teacher also needs to bring a small blanket.

Session 4

SLOs:

• To understand and use the subtraction symbol.
• To recognise and use subtraction written and spoken words, with the subtraction symbol.

Activity 1

Write this symbol on the class chart: +
Ask students to tell you addition words and give examples of how to use them. For example, “plus”, “I have five fingers on this hand plus five fingers on this hand.” Record these words.

Students might make a given addition expression with materials, like counters, and explain what they have made. Explicitly link the meaning of the numerals, and + and = symbols, with the models that are made.

Activity 2

1. Together, read the rhyme, “Ten in the Bed.” (Copymaster 9).
   You might choose a different scenario that is appropriate to the interests of your students, such as ruru in the kahikatea tree, or people in the waka.
   Arrange ten of the students’ soft toys in bed, using the blanket.   
2. Read the rhyme a second time and have the students ‘act out’ one toy falling out each time. Have students take turns to return the toys to the bed, one at a time, and as they do so record addition expressions.
   For example 1 + 1, 2 + 1, 3 + 1, reading these together. As you do so, focus on modeling the correct formation of numerals 6 to 9.
3. Write 10 and ten (symbol and word) on the class chart and discuss. Read the first verse of the rhyme once more. This time discuss how to use symbols to record what has happened. Write 10 – 1, introducing and recording this as ‘ten takeaway one.’ Continue to read the rhyme, verse by verse, writing each mathematical expression and recording the words each time. Introduce the alternative words for the subtraction symbol as you do so. For example 9 – 1, “nine minus one”; 8 – 1, “eight less one”; 7 – 1, “seven subtract one”.
4. Ask, “What happened to the number of toys in the bed?” (The number was getting less). Discuss that subtraction symbol, brainstorm and record the student’s ideas of what it is telling us.
   Read the expressions and words again and highlight the different ways we can read the subtraction symbol.

Activity 3

1. Make available to each student, paper, pencils, five plastic teddies and a tissue.
   Have them put their teddies to bed under the tissue, say the rhyme to themselves and each time a teddy falls out, record the expression, for example, 5 – 1. Those who complete this task quickly can write the addition expressions as they return the teddies to bed, or take more teddies and record expressions for 6 to 10.
2. Have students pair share, reading aloud their mathematical expressions. As they take turns, encourage the students to use the different language of subtraction, such as “Three take away one equals two.”

Activity 4

Conclude the session with a game of Musical Chairs (or cushions). Use music that is appropriate to the interests of your class, such as hip hop or a current fast-paced popular piece.
Set out the number of chairs for students in the group. Record the number on the chart. Play a favourite piece of music. When it stops all students sit down. Have them stand and ask a student to remove one chair then come to record the expression and read aloud what they have written.
For example 10 – 1, “ten chairs minus one chair.”
Explain that one student will not have a seat this time and that this person will get to write and read the next mathematical expression on the chart.
Continue the game till no chairs remain and subtraction expressions have been written for each action.

Session 5

SLO:

• To recognise and write addition and subtraction expressions from story contexts.

Activity 1

1. Using class charts from sessions 3 and 4, review the symbols for addition and subtraction.
2. Either read the short scenarios from Copymaster 10, exchanging the names of students in the class for those in the scenarios, or create your own. Have the students identify if the story tells of an addition or subtraction ‘event’ and together record these on the class chart as mathematical expressions.

Activity 2

Make pencils, paper, felt pens or crayons available to the students. Have them write at least two of their own scenarios and record the mathematical expressions that represent what is happening. You can motivate them by discussing everyday events in which items are added and subtracted. Contexts might include playing games like tag, using up household items like plates, groups of friends meeting, or birds or other creatures arriving or departing a location, such as penguins in a burrow. Students' illustrations should show what is happening in the scenario and expression.

Activity 3

Conclude the session by having the students pair share, then class share their work. Emphasise the importance of having them read their mathematical expressions in at least two ways.

Station 1: Worms

In this activity we roll play dough to make long and short worms. This could be linked to learning focused on Mini Beasts, native animals, ecosystems, and non-fiction genres of writing (e.g. fact files). Picture books such as Carl and the Meaning of Life by Deborah Freedman,  Wonderful Worms by Linda Glasers, Wiggling worms at work by Wendy Pfeffer and Superworm by Julia Donaldson could be used to engage students in this learning.

1. Give each student a ball of play dough and ask them to make a worm. Support students with their fine motor skills as necessary. You might model how to make a worm, and record key words such as “roll” and “stretch”.
2. Get the students to bring their worms to the mat.
3. Ask the students to describe their worms.
   My worm is long
   My worm is wide
   My worm is tiny
4. Now ask the students to make a worm that is short.
5. Look at and discuss the short worms.
   How do you know that your worm is short?
   Is your worm the same as everyone else's? Why?
6. Ask the students to think of other worms that could be made (long, wiggly, thin)
7. Choose a word and ask everyone to make a worm that fits the description.
8. Repeat with other descriptive words and create a word bank that is displayed with illustrations. 
9. Conclude by asking the students to draw their favourite worm and write a descriptive word for it.

Station Two: Near and Far

In this activity we build a town with blocks and then "drive" our cars around it.

1. Begin by discussing the buildings that you might find in a town. Write the ideas on blank cards (One for each student or pair of students).
2. Give a card to each student, or pair of students, and ask them to build the building out of blocks.
3. Put the buildings together onto the mat (or large sheet of paper with roads drawn) and the building cards into a container.
4. Give two students a car to "drive" around the town.
5. Tell the students to stop their cars after a short time.
6. Draw a card from the container. Ask the students to identify which car is closest to the building drawn.
7. Give the cars to another two drivers and repeat.
8. Use different words, for example: furthest, nearest, far away, nearby.
9. Repeat with other descriptive words and add to the word bank that is displayed with illustrations.

Station Three: Shaping Ourselves

In this activity we make ourselves tall (tāroaroa), short (poto), wide (whānui), narrow (whāiti), close (tata) and far (tawhiti).

1. Tell the students that we are going to play a game of sizes.

2. Ask the students to make themselves:

   As tall as they can.
   As short as they can.
   As wide as they can.
   As close to a table as they can be.
   As far from the door as they can be.
   Take up loads of space covering the mat (lie down).

3. You could extend the activity by asking for volunteers to give instructions for "body sizes".
4. You could also link to geometry by asking the students to form different shapes with their bodies, for example, circles or triangles. The students could describe the size of their shape.
5. Repeat with other descriptive words and add to the word bank that is displayed with illustrations.

Station Four: Wrapping Paper

In this activity we follow directions and colour in large and small objects on our "wrapping" paper (Copymaster 1). We then find an object to wrap in our paper.

1. Give each student a sheet of hearts (or koru patterned) wrapping paper.
2. Look at and discuss the hearts on the paper.
3. Ask the students to colour-in the small hearts.
   How did you decide which were small?
4. Now ask them to colour in the large hearts.
   How did you decide which were large?
   Which took the longest to colour? Why?
   Which were the quickest to colour? Why?
5. Ask the students to find something to wrap in their paper.
6. Bring the objects and wrapping paper to the mat.
7. Check to see if the objects will fit in the paper.
   Whose didn’t?
   Why not?

Station Five: Moa footprints

In this activity we look at some footprints and decide who they could belong to. In our discussion we focus on the use of language associated with area. This could be linked to learning about native and extinct animals, animal tracks, and non-fiction genres of writing (e.g. fact files).

1. Show the students the "moa" footprint from Copymaster 2.
   Who could this belong to?
   Why do you think that?
   Is your foot as big as the moa? How do you know? How could you check?
2. Let the students place their feet on top of the moa print.
3. Ask students to create different "prints", for example: a mouse, a dog, an albatross, a gecko, or find images of different prints online. Support the use of comparative words in their descriptions.
4. Ask the students to draw a giant’s footprint.
5. Share and discuss giant footprints in comparison to their own.
6. Record the words used to compare the prints, collect the descriptive words and add to the word bank that is displayed with illustrations.

Session 1

1. Talk with the class about ‘turning’.  This can be motivated by playing Simon Says, and asking them directions from their classroom to somewhere else in the kura.  Emphasise ‘turning’ by asking them what they do when they get to a corner. Ask ākonga what they have to do if they want to go left or right (they make a turn.) Start recording some of the vocabulary being generated by the discussion related to turns: corner, turn, spin, circle, left, right, around etc. Encourage bilingual and multilingual ākonga to share words for these terms from their home languages.
2. Demonstrate full, half and quarter turns. Draw a large circle on carpet or concrete.  Alternatively, your kura may already have some pre-painted circles in your playground. Have one ākonga come to the centre of the circle and put their arm straight out in front. Get another ākonga to place a marker on the edge of the circle showing where the ākonga is facing and their arm is pointing. Demonstrate the full turn as the ākonga slowly turns all the way around and ends up back at their beginning point. Have everyone trace the full turn on the ground with their finger.  Choose another ākonga to come to the centre of the circle, face the same starting point and demonstrate a half turn. How far will they need to go? Where should they stop? Emphasise the idea of ending up facing the opposite direction. Have an ākonga mark where, on the edge of the circle the half turn stops, and the ākonga ends up pointing. Get them to do another half turn. Where do they end up? So 2 half turns make 1 full turn? Have all ākonga trace a half turn on the ground with their finger. Repeat for a quarter turn, if your ākonga are ready. Otherwise wait until they have had some practice doing full and half turns. This activity could be repeated in pairs to reinforce learning. For each demonstration, document where the pointing arm ends up, which way the ākonga is now facing, and what part of the circle the ākonga has covered. This can also be recorded on smaller circles on whiteboards or in modelling books. 
3. Repeat the demonstration with a toy. Using a toy animal, for instance, each ākonga could show how to move the animal through a full, half and quarter turn.
4. Give ākonga time to act out and draw several examples of full, half and quarter turns.  This may be done by using objects from around the classroom, for example, cars, animals or teddy bears. Consider integrating contexts represented in other curriculum areas (e.g. dance) or texts you have recently read as a class.
5. Kaiako can support their ākonga as they complete these acts and drawings by checking they have the right concept of turns and correct any misconceptions.
6. Create stories involving turns such as: forgetting something on the way to kura when you would have to turn around and go back.  This means you would have to do a half turn. Model the turn with your toy car or stick figure on the paper, with the use of finger puppets, or with ākonga acting out the stories. Another idea could be pretending that your class is in a marching band and they are in a parade navigating the streets.

In the three sessions that follow, ākonga produce artwork that they can collect in their own ‘Turns Book' or display in the classroom.

Session 2

Prior to this session, tie pieces of string to enough crayons for each ākonga to have one each. Do this with a variety of colours. The string should be quite short (about 5cm long - although they can vary in length) so that the angles can fit on an A4 or A3 size piece of paper.

1. Provide each ākonga with a crayon with string attached. Show them how to fix one end of the string by using a drawing pin or the finger of one hand. Then show how they can make a quarter turn arc by sweeping the crayon through a quarter turn. You will need to draw their attention to the importance of keeping the end of the string still and maintaining tension on the string.
2. Ask ākonga to make several ‘quarter turns’ in the same colour.  Check that their turns are approximately correct. 
3. Having done quarter turns, ākonga choose a new colour and create half turn arcs. Draw their attention to the relationship between quarter and half turns.
4. Have ākonga choose a third colour and create some full turns. Draw their attention to the relationship between full, quarter and half turns.
5. Their crayon turn arc artwork could be displayed or created into a 'Turn Book' for each ākonga or the whole class. 

Session 3

This session is similar to session 2, except that the turns are made using ‘combs’ the ākonga make for themselves. As an alternative, you may prefer to have ākonga use crayons lying flat to create the same effect.

1. To produce combs, give ākonga cardboard rectangles and get them to cut out ‘teeth’ to make ‘comb’ shapes similar to the diagram below.
    
2. By holding one end fixed, ākonga should be able to rotate their ‘combs’ through quarter and half turns after dipping their combs in different coloured paint. The cardboard 'combs' can be wiped clean with a paper towel before changing colour paint. Alternatively, you could have a certain number of 'combs' at each paint colour and ākonga could move to the colour of choice.
3. Give ākonga the opportunity to make patterns with their ‘combs’ based on quarter and half turns.  
4. Ākonga could be encouraged to produce several pages of patterns. Let them choose the one that they like best for their 'Turns Book'. Alternatively, these could be displayed around the classroom.
5. While ākonga are involved in this activity, check that their ‘comb’ shapes do represent quarter and half turns. There is no need to measure their work precisely but their turns should be close to the right magnitude. 

Session 4

Corners of shapes can also be thought of as quarter turns. The purpose of this session is to find corners of shapes that are equivalent to quarter turns.

1. Draw (with chalk) a rectangle in the playground (or use a small rectangle in class). Have four ākonga stand on the corners of the rectangle (or put four toys on the small rectangle).
2. Have one ākonga face another one. What turn would Taika need to make in order to be looking at Jorge?
   Repeat for other examples.
3. Point out that we can think of the corners of a rectangle as being made up of quarter turns. What other shapes can you think of that have corners that are quarter turns?
4. Explore right-angled and other triangles as a class (mahi tahi model)
   Does this triangle (right angled) have any quarter turns? (yes)
   Are all the corners quarter turns? (no)
   Do all triangles have quarter turns (no, provide examples that don't)
5. Now look at shapes in the classroom that do and don't have quarter turn corners. Ākonga can work in pairs (tuakana/teina model could work well here) to find objects for both these categories. They could record their thinking by writing a list, drawing pictures or taking photos.
6. Ākonga can share their findings with the class. Ākonga can draw or stick in two printed photographs of objects from the classroom that have quarter turn corners and two that don’t, to add to their 'Turns Book'.

Session 5

1. Have ākonga work in pairs to guide each other around a course using instructions involving quarter, half and full turns to the left and to the right. A tuakana/teina model could work well here. The course could be outside, possibly following a line drawn on a court, or they could be in the classroom, moving around the furniture.  
2. Bring the class together to talk about full, quarter and half turns (mahi tahi model). 
   Use questions such as:
   What kinds of turns have we been talking about this week?
   How would you describe a quarter turn? A half turn?
   What objects do you know that have quarter turns?
   How many quarter turns make a half turn? How many half turns make a full turn?
3. Finish with a game of Whakarongo Mai Tamariki Mā (Simon Says) using quarter, half and full turns. If the kaiako says "Whakarongo mai tamariki mā quarter turn to your left" the ākonga do it, if the kaiako just says "Tamariki mā quarter turn to your left" the ākonga should remain still, otherwise they e noho.