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.

Level One

Geometry and Measurement

Units of Work

In this unit students participate in a variety of art based activities to develop their knowledge of 2-dimensional shapes. They use their own language to describe their works and the shapes they have used.

Level One

Number and Algebra

Units of Work

The purpose of this unit of sequenced lessons is to develop knowledge and understanding of the place value structure of the numbers from ten to twenty.

Level One

Geometry and Measurement

Units of Work

This unit involves the students directly comparing the weight (mass) of two or more objects.

Level One

Number and Algebra

Units of Work

This unit explores early multiplication where students are encouraged to skip count to solve story problems, rather than counting all. For example "John has 3 ponds and there are 2 fish in each pond. How many fish are there altogether?" Students will be encouraged to solve this problem by going 2, 4...

Level One

Number and Algebra

Units of Work

In this unit we explore linear patterns using snakes as the context. We examine, construct and record snakes of different patterns. We also put scarves on our snakes and ask others to predict what is hidden.

Printed from https://nzmaths.co.nz/user/75803/planning-space/late-level-1-plan-term-3 at 1:08pm on the 21st January 2022

## Arty Shapes

In this unit students participate in a variety of art based activities to develop their knowledge of 2-dimensional shapes. They use their own language to describe their works and the shapes they have used.

This unit begins an exploration of basic 2D shapes, their properties and the mathematical language associated with them. There is a progression from the way the students think of and see these objects to the more formal mathematical ideas and descriptions. In order to be able to communicate on any topic, there is a need for a common language. This unit takes the initial steps in the formulation of this common language.

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

The contexts for the geometric pictures used in this unit can be adapted to the interests and experiences of your students. In session 1 there is an opportunity for students to identify the object that they want to create from the available shapes. It is also possible to enrich the unit by identifying the shapes being investigated in the school and classroom environment.

Throughout each session encourage the students to talk about what they are making and the features of the shapes they are using. Discuss the similarities and differences in shapes and encourage a wide use of a range of terms. Counting the numbers of sides and the numbers of corners each shape has is also a good way to get students to focus on shapes.

Terms: sides, corners, curved and straight lines, edges, pointed

Questions to use:

Do you see any ways that these shapes that are alike? How are they alike?Can you see any shapes that are different? How are they different?What do these shapes have in common?What are some of the things you notice about the shapes you are using?Do you know what we call these shapes?What can you tell me about that shape?Why have you chosen to use that shape?Are all the sides the same? Are all the corners the same?## Session 1: Shape collage

## Session 2: String shapes with PVA

## Session 3: Shape stencils in crayon and dye

## Session 4: Shape mobiles

## Session 5

In this session students reflect on one of their art works made in the previous sessions, discuss and describe it and write about their work.

Their writing could then be published and displayed, either in a classroom display or in a large book for the book corner.

Family and whānau,

This week at school we are looking at different shapes and the ways they are used in art works. It would be great if you could walk around your home and discuss the pictures on the walls with your child. Encourage they to tell you about the shapes they see.

## Teen numbers (building with ten)

The purpose of this unit of sequenced lessons is to develop knowledge and understanding of the place value structure of the numbers from ten to twenty.

When students meet ten they meet a two-digit number for the first time. They begin to become aware that there are no more numerals to learn and we just ‘recycle’ them. This is their entry into the structural world of our tens based number system.

They are introduced to the language of digits, place and value. It is a considerable conceptual shift for children to move from a face value understanding that a numeral represents a number of units that can be counted, to a place value understanding in which a numeral can represent a group or a number of groups that are in themselves made up of units that can be counted. This is is a complex idea.

As children study teen numbers and their meaning and structure (rather than simply ‘saying’ them in a counting sequence), the focus is on developing the understanding that the value of a digit depends on its place. This is not trivial and it is made more challenging by the language of teen numbers.

Children often confuse the number names such as ‘fourteen’ and ‘forty’ because the adult enunciation of the word endings is often unclear. In hearing ‘fourteen’ children may expect to see the 4 appear first in the symbolic form because that is the number that comes first when they say it. Seeing 14 and hearing ‘four – teen’ therefore has the potential for confusion.

Children need many opportunities to make these numbers with materials. When using place value material for the first time, children need the opportunity to group single units to make one ten. By doing this they come to understand that ten

‘ones’or units do in fact comprise one 'ten'. The first equipment to use therefore is that which can be physically grouped, one by one, to make or compose one group of ten, or a ‘ten’, and be able to be unpacked or decomposed again into ten ones. When this is complemented by symbolic recording that accurately matches the representation of the number, understanding of two-digit notation is developed. Equipment in which the tens are already pre-grouped can be used once grouping to make ten is well understood.It is a considerable shift for children to then use materials in which the ten looks completely different from the ones (for example, money) and to trust the 'ten for one' trade. The greatest abstraction is of course the digits in our number system where the tens and ones look exactly the same but it is only their place that tells their value.

In depth exploration of place value with teen numbers is essential if our students are to work with real understanding of the numbers within our number system.

The activities suggested in this series of lessons can form the basis of independent practice tasks.

## Links to the Number Framework

Stages 2-4

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

Using the place value language structure within Te Reo Māori to develop and reinforce the understanding that teen numbers represent “ten and” is an adaptation that supports Te Reo, the identity and language of Māori students, and the conceptual understanding of teen numbers.

## Session 1

SLOs:

Activity 113

Repeat with several teen numbers.

teenin the word, practice saying it and hearing the final consonant, ‘n’. Make the connection between this ‘teen’ word and ‘ten’. Retain this chart to add to later.Activity 2Have the students work in pairs to play

Teen Pairs.(Purpose: to recognise and match teen number representations and the words ‘ ten and ____’)

Students place between them two piles of cards face down (Attachment 1). Pile 1. Tens frame teen number cards (showing two tens frames) , Pile 2. Word Ten and _____ cards.

Students take turns to turn over one tens frame teen number card and say the number of dots they see. They then turn over a word card and read the words aloud. If the tens frames and word card match they keep the matching pair and the winner is the student with the most pairs.

For example:

Activity 312 is ten and two

## Session 2

SLOs:

Activity 1Hold up the ten bundle and ask, “Do I still have ten sticks here?” (yes) “How many bundles of ten do I have?” (1). Record on the chart, for example, I have fifteen. 15 is ten and five. 15 is 1 ten and 5 ones. Discuss the language of ‘ones’ and that sometimes ‘ones’ can be called ‘units’.

Activity 2If available, have the students work in small groups or pairs to explore, find and display the four matching cards in the BSM 9-1-48 card game.

Alternatively have the students make a class puzzle matching game. Provide each student with card, pens and scissors. Have them make their own puzzle pieces which can then be combined with those made by their classmates and mixed up to make a matching pairs game.

Activity 3Teen Teams(purpose: to match word, pictorial and symbol representations of teen numbers).Students deal out 7 cards each. The remaining pile of cards is placed in the centre of the group. Students take turns to ask one other player for a card needed to complete a set of 5 teen family cards. If the other player does not have the card sought the requesting player takes one from the pile. As sets are complete, students place these in front of them.

The winner is the player with the most complete sets.

## Session 3

SLOs:

Activity 1NB. The container for the beans looks different from the ones, but can still be unpacked. This is a subtle and important shift. Also consider exploring together as a group or class the place value beans animation, available from https://e-ako.nzmaths.co.nz/modules/PVanimations/

Activity 2Students play

Go Teenin pairs.(Purpose: to use ten ones to make one group of ten when adding add two single-digit numbers.)

Students have playing cards (ace - 9), shuffled and face down between them. They have single beans and empty tens containers (or single nursery/ice block sticks and hair ties), single digit and tens arrow cards available.

The players take turns to turn over two playing cards. When the two numbers are added, if they make less than ten they return them face down to a discard pile.

If they make more than ten they keep their playing cards, take the total number of beans, group the materials showing the total as 1 ten and units. They also show the number with the arrow cards.

However, if the number has already been made by their partner, (the arrow cards for that number have been used) the student must simply return their playing cards to the discard pile.

The winner is the player with the most tens (containers with beans) when all the arrow cards have been used up.

## Session 4

SLOs:

Activity 1A problem is posed in which the number being subtracted requires the ten to be ‘unpacked’ or decomposed:

“Here are the beans Gardener Gavin is going to plant. He plants 9 in the first row. How many beans are left to plant in the second row? How can we work this out?”

The students discuss strategies for subtracting 9 and suggest what they can do with the materials. The teacher models this and one more example is explored together.

Activity 2First to twenty.(Purpose: to understand how to compose and decompose a ten.)

Students have beans and containers, numeral cards 11- 14, a set of playing cards 2 – 5, a dice with a + or – symbol marked on each of the six faces. Numeral cards are spread out face down.

Each student selects a card and makes that number using place value equipment.

Players take turns to roll the dice and turn over a playing card. They follow the instruction, either adding or subtracting from their materials. Each time the student has a turn they are required to write the equation.

The winner is the first student who has two containers of ten beans (twenty).

For example: a student turns over and models 13, rolls + and 3, and makes 16.

At their next turn the student may have to – 4, followed on the next turn by – 3. This will requires the student to decompose the ten.

The student will have recorded for the three turns so far:

13 + 3 = 16

16 – 4 = 12

12 – 3 = 9

placeof a numeral in a number tells us what it is worth or itsvalue.’’ Show the enlarged arrow cards drawing attention to the wordstensandones.Dear parents and whānau,

In class in maths this week we have been learning about teen numbers and how they are made of ten plus a single digit number. For example thirteen is 10 + 3. We have also been introduced to place value, learning that the 1 in 13 is in fact one group of ten.

You can help your child practice this very important idea by playing the game,

Teenager match.Cut up the attached page to make separate cards. Spread them face down on the table. Take turns to choose a pair of cards. If they match, keep the pair. The winner is the person with the most pairs.

[Include a copy of Copymaster 5]

## Seesaws

This unit involves the students directly comparing the weight (mass) of two or more objects.

Weight is a measure of the force of gravity on an object. Mass is the amount of matter in an object and a measure of the force needed to accelerate it. This means that the mass of the object on the moon is the same as its mass on earth, but its weight is lighter on the moon. For practical purposes, the mass and weight of an object on earth are the same and the terms are used interchangeably,

An important early goal in measurement is for students to understand the attribute they are going to measure. Comparison activities help students develop an understanding of the attribute that is being measured. In the case of mass, the most personal experience is comparing the weights of two objects by holding one in each hand and feeling which has the greatest downward pull. This personal experience can then be transferred to the use of balance and spring scales.

Young students are influenced by what they see. The shape or the size of an object can easily deceive them. For example, students who do not yet

conservethe property of mass will think that if the shape of an object changes then so does its mass. In one of the stations, in this unit, the students change the shape of a piece of plasticene and then weigh it to see that the weight has stayed the same.The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to provide more support include:

The objects weighed in unit can be selected to suit the interests and experiences of your students. For example, the students could bring small objects from home or objects that they can collect from around the school playground (e.g. stones, cones, berries or shells).

## Station One: See-saws

In this station we work with a partner to make a see-saw using a soft-drink can and a shoe box lid. We then use the see-saw to find objects that are the same weight.

Stop the soft drink can from rolling by fixing it to the table with tape or put plasticene rolls on each side.

How did you make your see-saw?What are some things you found that balance? Show me.

Have you ever been on a see-saw? What happens?

## Station Two: Weighing balls and worms

In this station the students, in pairs, experiment with plasticene or play dough to find that changes in an object’s shape does not change its weight.

Will your cats be the same weight? Why /Why not?Check on the balance scales.

Whose worm is longest?Whose worm is heaviest? Check?

Why are they the same weight?

Whose has made the most balls?Which ball is the heaviest? Check?

If you both put all your balls together on the seesaw what do you think will happen?

What do you notice? Why is the seesaw balanced?

## Station Three: What balances Freddy Frog?

In this station the students experiment to find items that balance Freddy Frog (or an alternative object). The students paste their solutions onto a class chart.

What happens on the scales when Freddy is heavier?

Do you think that this "car" will be lighter or heavier? Why do you think that? Were you right?

What are some of the things that you found that were the same weight as Freddy Frog?## Station Four

In this station we line objects up in order of weight so that we can work out who goes where in our "tower". We need to have the heaviest at the bottom and the lightest at the top.

Were your guesses correct?Tell me how you put the toys in order?

Did you find a lighter toy on your first guess?How did you check your guess?

## Station Five: Bungees

In this station students use a simple piece of elastic as a bungee and measure how far the elastic stretches to compare the weight of different objects.

Family and whānau,

This week we have been comparing the weight of objects using soft drink "see-saws" and bungee strings. We have been encouraging the children to use words such as heavier and lighter to compare the weight of objects.

At home you might like to make your own "see-saw" or bungee and then use it to compare the weights of small objects.

1. Make a see-saw using a soft-drink can, a shoe box lid and some tape.

2. Make a bungee by attaching a clip to hat elastic, which is suspended from string.

## Skip it to multiply it

This unit explores early multiplication where students are encouraged to skip count to solve story problems, rather than counting all. For example "John has 3 ponds and there are 2 fish in each pond. How many fish are there altogether?" Students will be encouraged to solve this problem by going 2, 4, 6. "There are 6 fish altogether."

This unit develops the skill of skip counting to find the total of several equal sets. At Level One students are expected to use a range of counting strategies such as counting on, counting back, skip counting, etc. Both conceptual understanding and procedural fluency are important to counting. Skip counting involves understanding that a set can be treated as a composite unit. The last number counted tells how many objects are in the set. Composites can be combined whether they are equal or not, but skip counting (e.g. 5, 10, 15, 20) can be used particularly when the sets are equal. The procedural fluency students need to enact skip counting is knowledge of the skip counting sequences. Ideally learning word and numeral sequences, like 2, 4, 6, 8… is learned in conjunction with quantity. That way students realise that the next number is the result of adding two more objects to what is already there.

As well as knowing skip counting sequences, students need fluency in tracking the number of counts. Initially they may use fingers to do that. For example, the fingers in four hands might be skip counted 5, 10, 15, 20, while the number of hands is tracked 1, 2, 3, 4.

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

The contexts for this skip patterns used in this unit can be adapted to suit the interests and experiences of your students. For example:

Each of the following sessions is designed to take 20 to 25 minutes. This series of session can be used in whole class or small group situations. The first session develops students’ ability to skip count in a variety of ways.

Session 1 – Skip CountingEncourage the students to continue counting while you record the numbers they are saying in a loud voice on the board. Then stop and talk about the number sequence and the patterns they can see.

What can you tell me about the big voice numbers?What patterns can you see?

Tie a weighted objectto a piece of string and swing it from side to side. Get the students to count as the pendulum swings. Then omit the odd numbers. This will enable the students to focus on counting in twos.backwardsin twos from 10. Animation 1E - 1H use the Hundreds Board and Slavonic Abacus to count backwards by twos and fives.Counting circles- put students in different sized groups of up to eight students. Each group sits in a circle. Students skip count around the circle. One or two students have an individual piece of paper. When the counting reaches them, they record the number they say as a numeral, e.g. 25. Students continue to count around the circle as far as they can. Get the students to bring their numbers back to share with the whole class. Place the numbers on the mat.What patterns did you see?What numbers are missing from the pattern?

Use puppets- have 2, 3, 4 or 5 puppets, students come to the front of the class and count using the puppets. E.g. Using 3 puppets - puppet 1 says 1, puppet 2 says 2, puppet 3 says 3, puppet 1 says 4, puppet 2 says 5, …What do you think puppet 2 is going to say when it his turn next?

What will she say the next turn?

## Session 2

–Horses and StablesHere are four horse stables.Place two horses under each stable.

There are two horses in each stable(uncovering the collections and hiding them sequentially).How many horses are there altogether?Try to record their responses e.g. Len thought 1, 2, 3, 4, 5, 6, 7, 8; Tom went 1 2, 3 4, 5 6, 7 8; Hemi went 2, 4, 6, 8; and Kelly went 4 + 4 = 8 (note that this is an additive, not counting, response).

For example, “Now there are

5stables at John’s farm down the road. He has5horses in each stable how many horses are there altogether?” Encourage students to explain how they got their answer.2horses under each of these stables. How many are there altogether?" Their partner then works out how many horses there are altogether.## Session 3 – Fish in Fishponds

How many fish are there altogether?How can we work it out without counting the fish one by one?

Did anyone do it a different way?Is there a quick way to work out how many fish there are left?What if someone (student) puts one more fish in each pond? How many fish will there be altogether, then?## Session 4 – Cartons and Eggs

How many eggs are there altogether?(You might have cubes, ping pong balls, or other objects as the make-believe eggs).Sixes are hard to count with, so we are going to use smaller packets today.I want you to make problems for each other using the same sized packets.

You might like to record your strategies using numbers. That is up to you.

Be ready to share your problem with the whole class at the end.## Session 5

How many legs would be on five goldfish?Do students still realise that the problem can be written and solved, 5 x 0 = 0?How many legs would be on 10, 50, 100 goldfish?” What is always true?How many legs would be on 10, 50, 100 1-legged kiwi? What is always true?Dear family and whānau,

At school this week we have been using skip-counting sequences to solve simple multiplication problems. At home this week we would like your child to practice skip-counting

forwardsandbackwardsin twos and fives. Try doing this with them by clapping a beat together or by following a number strip. Change the starting numbers for the sequences.Start from 2:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, …

Count down from 14:

4, 12, 10, 8, 6, 4, 2.

Start from 5:

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, …

Start from 15:

15, 20, 25, 30, 40, 45, 50, …

Count down from 45:

45, 40, 35, 30, 25, 20, 15, 10, 5.

## Snakes and Scarves

In this unit we explore linear patterns using snakes as the context. We examine, construct and record snakes of different patterns. We also put scarves on our snakes and ask others to predict what is hidden.

The main idea behind this unit is for students to develop basic concepts relating to pattern by exploring simple patterns in a novel situation. So they will use multi-link cubes masquerading as snakes. The snakes have patterned ‘skin’. The students play with a variety of snakes, both inventing their own and investigating other students’. In the process, they should begin to see that (i) patterns are made up of repeating sections of coloured cubes; (ii) they can continue a pattern by adding on more cubes of the right colours; and (ii) they can predict parts of a pattern that are missing.

Pattern is an important idea both in mathematics generally and as a precursor to algebra. For instance, discovering patterns enables us to predict events. By knowing how the tides work we can predict when high tide will be and when will be a good time to go fishing. This pattern concept generalises in secondary school to finding results that work again and again.

The snake context used in this unit could be adapted to use worms or eels, although it would require a little more imagination as neither are multi-coloured or patterned. The simple counts and primary colours used in the unit provide an opportunity to use te reo and Pasifika words alongside English.

## Getting Started

Today we investigate snakes with special patterns. We think about what would come next as we increase the length of our snakes. We also think about what happens when we cover part of our snake with a scarf.

This week we are going to investigate patterns. Does anyone know what a pattern is?Share ideas about patterns. Encourage the students to look around the classroom for examples of patterns.

I am going to make a snake for you out of these multi-link cubes. Watch carefully to see if you can guess what kind of snake I am making.[Make a snake with a blue, red, blue, red, blue pattern.]

Who knows what colour comes next in our snake?

How did you know?Who knows what colour comes next?

How did you know?What cubes are hidden?

How did you know?## Exploring

Over the next 2-3 days we examine, construct and record the patterns on our snakes. We cover parts of our snakes with scarves and play ‘guessing games’ with other students.

Can you ‘read’ me your snake?What colour cubes is your snake made of?

Can you see a pattern in your snake?

With all the students gathered together ask:

What cubes do you think are hidden under the scarf?How do you know?

## Reflecting

We conclude the unit by sharing the pattern snakes that we have made. We look for snakes that are alike.

How are they alike?Which snakes have the same pattern as this one?Dear parents and whānau,

This week in maths we have explored repeating patterns using snakes made of different coloured cubes. We have practised predicting what cubes have been hidden when the snake puts on a scarf.

Ask your child to tell you about the pattern of this snake and how the pattern could be continued.

Which cubes do you think are hidden under this scarf?

Can you and your child find some simple repeating patterns like this around your home? You could talk about them and play a game covering parts of them and saying what is hidden.