Early level 1 plan (term 1)

Planning notes
This plan is a starting point for planning a mathematics and statistics teaching programme for a term. The resources listed cover about 50% of your teaching time. Further resources need to be added to meet the specific learning needs of your class, to support your local curriculum and to provide sufficient teaching for a full term.
Resource logo
Level One
Integrated
Units of Work
This unit provides you with a range of opportunities to assess the entry level of achievement of your students.
  • Use groupings to efficiently count the number of objects in a set.
  • Create picture graphs about category data and discuss patterns in the data.
  • Create and follow instructions to make a model made with shapes.
  • Order a set of objects by mass (weight).
  • Create a sequential pattern and predict...
Resource logo
Level One
Number and Algebra
Units of Work
In this unit students investigate the different number pairs that numbers can be broken into, using the context of frogs in ponds. They list all possible combinations for a given number, working with numbers up to 9.
  • Give many names for the same number, using the strategies of drawing a picture, acting it out or using equipment.
  • Use the mental image of a given number to work out a missing number in a number pair.
  • Separate a set of up to 9 objects into two or more parts.
Resource logo
Level One
Geometry and Measurement
Units of Work
In this unit the students use a small plastic dinosaur as the unit with which to measure the capacity of containers. They apply their counting strategies and discover that a number of different shaped containers can contain the same number of dinosaurs.
  • Use non standard units to measure the volume of a container.
  • Accurately count a set of up to 20 objects.
Resource logo
Level One
Geometry and Measurement
Units of Work
In this unit students use the traditional tale of the gingerbread man as a context for ordering and comparing lengths. A “sessions” approach is used, with five related but not sequential activities.
  • Compare the length of two objects directly.
  • Order three or more objects by length.
  • Select objects that are the same length as a given object.
Resource logo
Level One
Geometry and Measurement
Units of Work
In this unit students explore movement and position using the popular Lynley Dodd character Hairy MacLary. Students explore the language of position in describing where an object is located and in giving and following sequences of movement instructions. They will move themselves and objects along...
  • Describes the position of an object.
  • Follow and give directions involving 1/2 and 1/4 turns.
  • Follow and give a sequence of instructions related to movement and position.
Source URL: https://nzmaths.co.nz/user/75803/planning-space/early-level-1-plan-term-1

All about us

Purpose

This unit provides you with a range of opportunities to assess the entry level of achievement of your students.

Specific Learning Outcomes
  • Use groupings to efficiently count the number of objects in a set.
  • Create picture graphs about category data and discuss patterns in the data.
  • Create and follow instructions to make a model made with shapes.
  • Order a set of objects by mass (weight).
  • Create a sequential pattern and predict further members of the pattern.
Opportunities for Adaptation and Differentiation

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:

  • having a range of different sized objects in containers for session 1.  Use larger objects for students who are beginning to count one-to-one and smaller objects for those who are more confident
  • reducing the number of activities covered in a session so that more time can be spent on the earlier ideas.  For example in session 5, ensure students are confident about identifying the next element in the pattern before connecting the pattern to ordinal positions.
  • using a class recording book instead of the individual records that are suggested as part of each session.

The context for this unit can be adapted to suit the interests and experiences of your students. For example:

  • In session 1 use counting objects that can be found locally (shells, pebbles, sticks, leaves).
  • In session 2 use activities/sports that students in your class engage in. 
  • In session 5 create patterns using native birds as an alternative to farm animals.
Required Resource Materials
  • Digital camera to record students’ work.
  • Session One – Countable objects, e.g. counters, cubes, toy animals.
  • Session Two – Scissors, glue sticks, plastic containers (2L icecream if possible), large sheets of paper, copies of Copymaster 1 and Copymaster 2.
  • Session Three – sets of geometric shapes, e.g. pattern or logic blocks, pieces of card for labels.
  • Session Four – balance scales (if available) or make balances from coathangers, string and pegs (to hold items), extra cheap healthy lunch items like apples, carrots, oranges, packets of raisins, muesli bars, etc, kitchen scales, preferably digital, that are sensitive to about 500g (optional).
  • Session Five – objects to form patterns, e.g. natural materials like acorns, shells, stones, or toy animals, geometric shapes, blocks, copies of Copymaster 3 to make pattern strips.
Activity

Prior Experience

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

Session One

  1. Talk to your students about the purpose of the unit which is to find out some information about them, so you can help them with their mathematics. In the first session students explore an activity called ‘Handfuls” which was first developed by Ann Gervasoni from Monash University, Melbourne. Handfuls should become a regular part of lessons during the year.
     
  2. Model taking a handful of objects from a container. Use smaller objects for Year 2 students and larger objects for New Entrants or Year one students. Place the collection on the mat in a disorganised arrangement.
     
  3. Estimate how many things I got in my handful (You may need to explain that an estimate is an educated guess).
     
  4. Ask your students to write the number on the palm of their hand 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 are there?
     
  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 ‘left overs’ when a composite is not complete, e.g. counting in fives below. 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 the handfuls in at least two different ways. Try to take digital photographs of the handfuls for use in the group discussion.
     
  8. Watch 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 digital photographs on the Interactive Whiteboard 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 trying 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.

  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 the data are 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.
     
  6. 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. The strips are about favourite fruit, fast food, pet, vegetable, way to travel to school, and after school pastime.
     
  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 vegetables like tomatoes.

Session Three

In this session you students use the language of two-dimensional shapes to provide instructions to other students. “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.

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.

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 features does the shape 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 circle is below
    the square.
    The circle is in front
    of the square.

    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.
     
  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 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 digital 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 (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. Create two cards with the words light and heavy.
     
  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 student heft the objects to see if there is a consistent judgement.
    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. Make 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 heaver 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 place on a continuum give the students a personal task.
    I want you to put the items in your lunchbox 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.
    Many students have an extraordinary number of items in their lunchbox but be aware that some students may have no lunch. Ensure you have a collection of healthy foods they can use and consume afterwards.
     
  8. Let the students order their lunch 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. Apples and metal spoons are good items to illustrate the point that 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. Play the patterns video, which contains four repeating patterns. Pause the video at the end of each pattern progression and 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. Note that patterns 3 and 4 have two variables and the sequence is different for those variables.
     
  3. In pattern 3 the colour variable has a yellow, red, yellow, red, … sequence while shape has a circle, hexagon, rectangle, circle, hexagon, rectangle, … sequence.
     
  4. In pattern 4 the animal variable has a goat, cat, cow, dog, … sequence while orientation has a right, left, right, left,… sequence.
     
  5. Provide students with a range of materials to form sequential patterns with. The items might include bottletops, corks, blocks, toy plastic animals, pens and pencils, 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).
     
  6. 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 16th object.
       
  7. Take digital 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.
     
  8. 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.

Frogs in Ponds

Purpose

In this unit students investigate the different number pairs that numbers can be broken into, using the context of frogs in ponds.   They list all possible combinations for a given number, working with numbers up to 9.

Achievement Objectives
NA1-3: Know groupings with five, within ten, and with ten.
Specific Learning Outcomes
  • Give many names for the same number, using the strategies of drawing a picture, acting it out or using equipment.
  • Use the mental image of a given number to work out a missing number in a number pair.
  • Separate a set of up to 9 objects into two or more parts.
Description of Mathematics

This unit is all about how numbers are made up of other, smaller numbers, an essential concept underlying addition and subtraction.  The unit helps develop two ideas:

  • there are a finite number of number pairs for a given number (for example 5 can be thought of as 0 and 5, 1 and 4, 2 and 3 and no other pairs can be found)
  • numbers are uniquely paired (if 2 is one of the parts of 5, the other part must be 3).

Students need to investigate these relationships many times.  Once students believe that 2 and 3 is always 5 they see a real reason to remember it.  

Students working on this unit will be using the strategy of count all, or counting from one, to solve simple addition and subtraction problems.  Students at this stage have a counting unit of one and given a joining or separating problem they represent all objects in both sets, then count all the objects to find an answer.  Objects may be represented by materials, or later, in their mind as an image. 

From this stage of counting all, students will move to counting on, a stage where they realise that a number can represent a completed count that can be built on.

Opportunities for Adaptation and Differentiation

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. As this is an early level 1 unit the numbers may need to be extended beyond 10 for some students. 

The frogs and pond context for this unit can be adapted to suit the interests and experiences of your students. For example: cars in/out of a parking building, eels hiding/swimming in a river, kererū flying/perched in tree.

Required Resource Materials
  • Copymaster of the problems.
  • Frogs: up to nine for each group of students. These can be plastic models or photocopied using the frogs copymaster.
  • Equipment to use as a pond to hide the frogs: pieces of blue fabric or paper would be appropriate, alternatively ice-cream containers could be used.
  • Paper for students to record their solutions.
  • Materials for making a wall chart or big book in the final session. Alternatives include paint, crayon and dye, glue, paper, scissors etc.
Activity

Getting Started

  1. Introduce the problem:

    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.)
     

  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 or a flip-fold page.
     

  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.  

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.
Attachments

Dino Cylinders

Purpose

In this unit the students use a small plastic dinosaur as the unit with which to measure the capacity of containers. They apply their counting strategies and discover that a number of different shaped containers can contain the same number of dinosaurs.  

Achievement Objectives
GM1-1: Order and compare objects or events by length, area, volume and capacity, weight (mass), turn (angle), temperature, and time by direct comparison and/or counting whole numbers of units.
Specific Learning Outcomes
  • Use non standard units to measure the volume of a container.
  • Accurately count a set of up to 20 objects.
Description of Mathematics

Measurement provides a context for the further development and reinforcement of number skills.   Students can measure without the use of number up to the stage of indirect comparison.  However as soon as they repeatedly use a unit to measure an object they need numbers to keep track of the repetitions.  

This unit is also designed to allow students to practice their one-to-one counting as they calculate the capacity of containers filled with plastic dinosaurs.

Opportunities for Adaptation and Differentiation

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:

  • ensuring that the rectangles provided in session 2 hold exactly 10 objects.  Alternatively the task could be made more complex by providing some rectangles that were too large and needed to be cut to size by the students
  • splitting the digits used in sessions 3-4 into two “hats”, one for digits 1-10 and the other for digits 11-20.  Direct students who are less confident with their numbers to 20 to select from the 1-10 “hat”.

The objects used as measuring units can be taken from your local environment (e.g. shells, pebbles) or adapted to to match the interests of your students (toy cars, small teddy bears, toy unicorns, marbles).  It is important though that the objects used are identical or very similar in size.

Required Resource Materials
  • Small plastic dinosaurs of the same size (or teddy bears or cubes).
  • A number of small containers (that hold up to 20 dinosaurs).
  • Light weight cardboard or heavy paper
  • Paper
  • Scissors
  • Tape
  • Recording Sheet
Activity

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 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.

  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 you 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 the exactly the same?
    What do you think that a cylinder for 20 dinosaurs would look like....rua tekau dinosaurs...lua sefulu dinosaurs?
  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 sequence of numbers.

  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 we each make 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.Diagram

The Gingerbread Man

Purpose

In this unit students use the traditional tale of the gingerbread man as a context for ordering and comparing lengths. A “sessions” approach is used, with five related but not sequential activities.

Achievement Objectives
GM1-1: Order and compare objects or events by length, area, volume and capacity, weight (mass), turn (angle), temperature, and time by direct comparison and/or counting whole numbers of units.
Specific Learning Outcomes
  • Compare the length of two objects directly.
  • Order three or more objects by length.
  • Select objects that are the same length as a given object.
Description of Mathematics

Early length experiences must develop an awareness of what length is, and a vocabulary that can be used to discuss length. Young students usually begin by describing the size of objects as big and small. They gradually learn to discriminate in what way an object is big or small and use more specific terms. The use of words such as long, short, wide, close, near, far, deep, shallow, high, low and close, focus attention on the attribute of length.

This unit focuses on students comparing lengths. Although comparing is at the early stages of the measurement learning framework adults will often measure things without using measurement units.

In mathematics it is often useful to have an estimate of the size of an answer to ensure the accuracy of calculations that have been used. The comparisons of lengths in this unit lay the foundation for estimates in area and volume, and for estimates generally.

In comparing three lengths, students implicitly realise the transitive nature of length. Hence if gingerbread man A is taller than gingerbread man B and gingerbread man B is taller than gingerbread man C, then gingerbread man A is automatically taller than gingerbread man C. There is no need to check the heights of A and C. The difference in height follows from the first two comparisons. This ordering ability is a valuable property of numbers and has many uses throughout mathematics. When it is not present, it causes some difficulties. 

Opportunities for Adaptation and Differentiation

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:

  • beginning the unit by comparing the heights of a pair of students and asking the remaining students deciding who is the tallest.  Choose pairs of clearly different heights
  • working with individual students to confirm that when comparing lengths they know to line up the starting points of the objects being compared
  • providing multiple opportunities throughout the school day to directly compare the length of objects (e.g. pencils, width of books, skipping ropes, sticks).

While this unit is firmly focused on the story of the gingerbread man and a river crossing, it is possible to adapt to use other fictional characters that the students have been reading about or are interested in.

Required Resource Materials
  • Scissors, glue, crayons or similar, sellotape, glue, pencils
  • Session One: copies of the gingerbread family (Copymaster One), large sheets of black paper.
  • Session Two: copies of the gingerbread man template and the recording sheet (Copymaster Two and Copymaster Three) for each student.
  • Session Three: large sheet of paper with river drawn or painted on, cardboard, small blocks to support bridges.
  • Session Four: strips of paper of varying lengths.
  • Session Five: one gingerbread man per student (Copymaster Two), variety of coloured paper for clothes (e.g. wrapping paper), wool for hair.
Activity

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 re-tell the story, or parts of the story, throughout the week to help maintain the focus for the activity sessions.

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.

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 One).

  • 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.

Session Three: Building Bridges

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

  1. Provide each student with a gingerbread man template (Copymaster Two) 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 Three) 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 found 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 the 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. diagram.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 then compare the lengths of their chains.

  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.

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 Two) 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?
  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 gluing on wool for hair.

Scatter Cat!

Purpose

In this unit students explore movement and position using the popular Lynley Dodd character Hairy MacLary. Students explore the language of position in describing where an object is located and in giving and following sequences of movement instructions. They will move themselves and objects along paths and will describe the movement of others.

Achievement Objectives
GM1-3: Give and follow instructions for movement that involve distances, directions, and half or quarter turns.
GM1-4: Describe their position relative to a person or object.
Specific Learning Outcomes
  • Describes the position of an object.
  • Follow and give directions involving 1/2 and 1/4 turns.
  • Follow and give a sequence of instructions related to movement and position.
Description of Mathematics

This unit is about building up students' vocabulary relating to position. Hence the emphasis on ‘in’, ‘on’, ‘under’ and so on, as well as various turns and left and right. This is an important step before more complex geometry is introduced.  The words used in this lesson are important as much in every day life as in school.

Opportunities for Adaptation and Differentiation

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:

  • providing direct teacher support to some children while those able to work more independently work with a partner.

While the sessions in this unit are centred on the storyline of Scatter Cat the context for session 3 could be readily adapted to include two characters from a favourite story.  Session 4 could be adapted to take place outside in an area  surrounded by “landmarks” that the students are familiar with (e.g. the school office, the playground, a memorial, a tree, a feature of the landscape).

Required Resource Materials
  • "Hairy MacLary, Scatter Cat!" by Lynley Dodd, text or video
  • Pictures of Hairy MacLary drawn onto card
  • Cardboard cut out puppets of Hairy MacLary and the cats
  • Blocks
Activity

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.
    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.

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. The teacher roves to 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?

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 of 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.

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. 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.

  1. 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 instruction do you need to give to make sure he does?
  2. 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.
  3. In pairs the students give and follow sequences of instructions including turning. They could also use the Hairy MacLary cut outs for this.

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 or wall display made in Session 1.
  6. How Can I Get to 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.

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