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.

Students need to simultaneously develop proficiency with number sequences forward 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 synchronous to, their need to apply it, so students who can count collections up to ten should be learning number sequences beyond ten.

Session 1: Hundreds board

Count by ones on a hundreds board, both forwards and backwards, and ask questions which help students connect numerals to spoken words. For example,
Can you find the number 8 without counting up or down?
What number comes after eight?
What number comes before eight?

Variations

Have students work in pairs. They take turns drawing a numeral card out of a container, then work together to find the number on a hundreds board and make a set which contains the number they have drawn, for example a set of eight counters.

First work with numbers 1–10 (tahi to tekau), and extend the range as needed to increase the challenge.

Session 2: Slavonic abacus

Count by ones on a Slavonic abacus, both forwards and backwards. While you count, say the numbers out loud with students as you move the beads. This supports them to connect the spoken word and the quantity. 
Can you find the bead for number 7?
What number comes after seven?
What number comes before seven?
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).

Variations
Have students work in pairs. They take turns to draw a numeral card out of a container, and challenge their partner to find the number on the Slavonic abacus. If needed, they can count the beads together to check that the right bead has been identified.

First work with numbers 1–10, and extend the range as needed to increase the challenge.

Session 3: Frogs in a bucket

1. Link the number after and before 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?
2. 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…
   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…

Variations

If needed, link explicitly to the number sequence by referring to a hundreds board.

Extend the problems to two more/less, three more/less and beyond as students’ understanding and control of sequences grows.

Have students work in pairs, with one student putting objects into a container, and the other student listening and counting how many.

Session 4: What’s changed?

1. Begin with a set of objects in a readily subitised arrangement. For example, begin with a set of six cars.
2. Tell the students: Take a photograph of the collection and stash it in your mind.
   Now close your eyes, and I’m going to change something.
   Try to hold the picture in your mind.
3. Change the objects for a different kind – vary shape, colour and size to add more challenge. For example, change the cars for teddies.
   
4. Now open your eyes. 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 because it has been the last few times, without necessarily accepting that number is conserved. Introduce the one more/one less principle with this activity. Vary the number of new objects by one while still retaining the original layout and 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.

Have the students work on the activity Odd one out in pairs, using Copymaster 1:

Students work with sets of three cards, and identify one difference between each card and the other two cards in the set. For example, possible answers for the cards with teddies are: the top card is different from the other two because the teddies are sitting down; the middle card is different from the other two because there are different amounts of teddies in each row, and the bottom card is different from the other two because there are 9 teddies.

Session 5: Is there the same number? 

1. Lay out two collections one above the other, with items aligned. 
   Have a look at this collection. Are there more blue teddies, more green teddies or are there the same number? Encourage your students to equate the length of a collection with the quantity of items.
2. Tell the students: Take a photograph of this collection and stash it in your mind.
   Now close your eyes, and I’m going to change something.
3. Change the spatial layout of the objects, by spreading out one of the collections.
   
4. Now open your eyes. Are there more blue teddies, more green teddies or are there the same number?

Variations

Vary the spatial arrangement of sets. Begin with a set of objects with some similar characteristics so that students can easily recall the objects that are present. For example, Take a photograph in your mind of the collection. Close your eyes and tell me what you see. Encourage students to pay attention to structure and the organisation of the set, with responses such as “There were two of each animal”, “The animals were on a hexagon”, and “Two on the top, two in the middle, two on the bottom.”

Now I’m going to change something. Vary the spatial layout of the objects, particularly expanding or contracting the length or area of the collection, or rearranging the layout.

Now open your eyes. Are there still the same number of objects? How do you 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.

Have students work on the activity Domino Count in pairs. This task encourages students to trust the count in the face of different spatial arrangements.

Working with at least one set of dominoes, students sort the dominoes into groups that have the same number of dots, in total. Each group can be labelled with a numeral card, or students could make their own labels. For example:

Once the dominoes have all been grouped, students can arrange the dominoes in a pattern and write the number fact for each domino. For example,

Session 6: Counting dots 

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 it helps them to realise that numbers are ideas.

Messages

Play the game Messages as a class:

Students sit in pairs, back to back, with one student from each pair facing the teacher. The teacher shows a pattern card from Copymaster 2 for a short time. The students turn around and gently tap the number of dots they saw on their partner’s back. The partner shows how many taps they felt by holding up that many fingers. Both players turn around to check whether the number of fingers matches the number of dots on the pattern card. Alternatively, a digit card can be held up instead of a pattern card.

Pattern memory match

Students play pattern match in groups of three or four. Each group needs a set of pattern cards (Copymaster 2) and a set of digit cards.

The pattern cards are spread out individually, face down on. The digit cards are shuffled and put in a pack, face down, in the centre. Players take turns to turn over the top digit card then 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.

After the game, talk with students about how they recognised 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.”