contents acknowledgements introduction first learning goal second learning · pdf...

© BELB Primary Numeracy Team 2005

CONTENTS

Acknowledgements

Introduction

How to use the materials

First Learning Goal

Second Learning Goal

Third Learning Goal

Games

Resources


Acknowledgements

The Belfast Education and Library Board numeracy team would like to record their sincere appreciation to the principals of the schools involved for their willingness to participate in this project. The team would also like to thank all the teachers and children who have contributed to, and trialled, the ideas and materials in this book. The team in particular would like to thank the following;

Maire MacDermott St Peter’s Primary School, BelfastGeraldine McGlade St Peter’s Primary School, BelfastPauline Toner St Peter’s Primary School, BelfastRuth Graham Taughmonagh Primary School, BelfastAilsa Thom Mersey Street Primary School, BelfastRory Clenaghan St Matthew’s Primary School, BelfastGemma Falls St Matthew’s Primary School, BelfastLorna Keating Dundela Infants’ School, BelfastAnn O’Kane St Peter’s Primary School, BelfastMaureen McDonnell St Peter’s Primary School, BelfastTherese Searle St Peter’s Primary School, Belfast

We would also like to record our sincere appreciation to Eunice Pitt for her advice, guidance and support in the development and production of these materials.

T. AdairD. MartinL. CallaghanPrimary Numeracy Team


Introduction

On behalf of the numeracy team in Belfast Education and Library Board, I am delighted to introduce this new set of guidance materials for teachers. The ‘Ready for Calculating’ handbook has been produced by the team as the product of an action research project which was conducted in Belfast classrooms throughout the past two years. The handbook seeks to provide teachers with guidance on the development of number skills beyond the levels addressed in the early years’ handbook, Ready Set Go. In preparing ‘Ready for Calculating’, the team has availed of the advice and support of Eunice Pitt at each stage of development. This collaboration ensures that the approaches recommended here are entirely consistent with those already introduced in Ready Set Go.

I recognise that establishing a sound sense of number is essential to the further development of numeracy skills and it is my hope that this guidance will assist teachers in their objective of ensuring that children’s number skills are underpinned by sound understanding.

The handbook has an attractive, easy-to-use format and I trust that it will provide valuable support for teachers in this vital aspect of numeracy development.

Mary TorrensMathematics/Numeracy Adviser


How to use these materials

These materials have been produced to follow on from the activities in ‘Ready Set Go’. They are designed to provide teachers with a series of practical activities to support the development of the learning goals associated with mental calculation within 100. They follow a progression of sequenced activities and therefore mastery of each one is dependent on the acquisition of skills from the previous experience.

Children benefit from being aware of what they are learning and how this fits into mathematics and its applications in everyday life. Teachers can help the children gain confidence in these learning goals by explaining what they are going to learn, encouraging the children to reflect on their learning and by developing interactive approaches which encourage the children to share and explain their thinking. A number of games have also been included with the activities to provide a context for the children to ‘make sense’ of their learning.

The range of teaching and organisational approaches needs to be varied. Whole class teaching can set the learning context, while working with small groups can provide the opportunity to assess the children’s understanding. This approach supports the principles within the revised curriculum.

There are three main learning goals; composition of number within 10, mental calculation within 99 without bridging and mental calculation within 99 with bridging. Each learning goal follows a similar structure. Concrete/practical activities introduce the concept; pictorial/100 square activities reinforce the concept and the encouragement of mental responses takes the concept to an abstract stage. There are a number of assessment ideas to help the teacher identify whether or not the child has mastered the learning goal, and therefore ready to move on. If a child is showing difficulty at any stage, they would benefit from additional experiences from the previous activities to support their learning needs.

Children will be ready for these experiences once they are secure in all the ideas outlined in Ready Set Go.


Composition of number within

100

Mental calculation within 99 without

bridging

Mental calculation within 99 with

bridging

The Learning goals


A helpful cycle Abstract

Mental

Pictorial

Practical/concrete

Activities will follow the following stages;

COMMUNICATION

APPLICATION

3 – dimensional activities

Concrete stage

Use of 100 square Pictorial Stage

Mental Response Abstract stage

Giving children the opportunity to talk about their thinking enables teacher to assess their level of understanding and serves to

consolidate their learning.


First Learning Goal


Composition of Numberwithin 100

Children will:

• understand the composition of the ‘tens’ numbers – 10, 20, 30, 40, 50…….. 100 and talk about their practical arrangements.

• understand the composition of 2-digit numbers within 50/100 and talk about their practical arrangements.

• consolidate their understanding of 2-digit numbers within 50/100 and talk about their practical arrangements.

• explore the pattern of the numbered 50 array/100square.


Personal Notes


Children will understand the composition of the ‘tens’ numbers – 10, 20, 30, 40, 50……..100

They will talk about their practical arrangements.

Resources:Each child has a blank 50/100 array and access to counting objects such as beads, counter, cubes.

Concrete Stage

Teacher:

Choose one colour and use your cubes to fill the first

row of your grid/array.

Look at your cubes and tell me how many youneeded.

Child: 10

Teacher:

We can say,

One row of 10 is 10 cubes altogether. Let’s all say that together .

Ask the children to put out another row of 10, and we can say,

Two rows of ten is 20 cubes altogether.‘Let’s all say that together…..

Children respond initially by chanting together and later individually.

Continue in this way so that children discover

three rows of 10 is 30 cubes

four rows of 10 is 40 cubes

five rows of ten is 50 cubes.

Children should continue with this activity until they are confident in filling the rows and talkingabout their arrangements without counting individual objects.


Teacher:Put out 2 rows of cubes, how manyhave you altogether?Add another row – what can you tellme now?

Child: 20 and 10 makes 30

Further Ideas

Teacher:

You have three rows of 10, takeaway one row.What can you tell me?

Child: 30 take away 10 leaves 20

There is benefit in encouraging the children to put out other materials alongside their 50 grid. If

unifix or multilink is made up in rods of 10, children can use these rods as a further representation of

the number they are working with. If Cuisenaire is available this provides a further option. The more

variety in the children’s experiences the more secure their understanding.

50 Grid/array Unifix Multilink Cuisenaire


Children will understand the composition of 2-digit numbers within 50/100.


This activity is an extension of the previous activity. It is again good for the children

to use several different representations as they explore these 2-digit numbers.

Resources:

Blank 50 array for each child and cubes (or similar objects).

Rods of ten and singles, Cuisenaire (if available).

Concrete Stage

Teacher:

Count out 23 cubes.Put the cubes on your array filling therows from the top.

How many whole rows of 10 have you?

How many more?

Child: I have two whole rows of 10 and 3more

Teacher:

We say 23 is the same as 2 rows of 10 and 3 ones.

Initially children chant together, later they respond individually.

Children should continue with this activity until they are confident in filling in the rows and talkingabout their arrangements without counting individual objects.


Teacher:Now use your rods of 10 to make 23.

Children put out 2 rods of 10 and 3 singles with multilink/unifix,

and Cuisenaire rods if available.

Teacher:We say,23 is the same as 2 rods of 10 and 3 ones (looking at rods) 23 is the same as 2 rows of 10 and 3 ones (looking at grid)

Children should explore various numbers within 50 in this way until they show confidence in their

understanding of these numbers.

Comment

It is important to include the teens in these experiences in order to help the

children make further sense of these difficult numbers. (pp146 – 152 Ready Set Go)

It is sometimes the case that children gain fresh insight into the teens as a by

product of their growing understanding of the 20s and the 30s.

Abstract Stage

Teacher can show how this would be recorded horizontally.

Example:

23 = 10 + 10 + 3

23 = 20 + 3


Children will consolidate their understanding of 2-digit numbers within 50/100.


In this activity the children use a single marker to indicate the position of numbers

on their blank grid. This is a valuable activity to enable children to demonstrate

their understanding of the previous activities with the 50 array/100 square.

Resources

Blank 50 array/100 square for each child

Cube as a marker for each child

Pictorial Stage

Teacher:Put your marker on the space for 1.Move it to the space for 10.How do you know that is the space for 10?

Move your marker to the space for 20 – how do you know?

Move to 30, 40, 50 – what do you notice?

Teacher:Put your marker on 10, now move it to 9 – what did you notice?

Put your marker on 20, now move it to 19 – what did you notice?

Explore 30-29, 40-39, 50-49……. 100- 99

Teacher:Put your marker on 20, now move it to 21 (children will need to be careful)

Tell me what you did.

Extend these activities until the children can place their marker on any given

number and explain what they have done.


Game

Teacher calls out a series of numbers and the children place their markers in the squares. The result

from the example below is a letter.

Put markers on the following numbers to find the hidden letter

3, 16, 25, 46, 33, 6, 24, 23, 36, 13, 26, 43

Now make up another letter for your partner.


Children will explore the pattern of the numbered 50 array/100 square in order to build up a mental picture of these numbers.

Resources

Transparent or opaque counters

Numbered 50 array/100 square

Transparent counters allow children to see the number below. Solid counters

conceal the numbers. There is value in using both.

Pictorial Stage

1. Children explore the rows of the numbered 50array/100 square.

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

Teacher:

What is the last number in the secondrow?What is the first number in the secondrow?What pattern can you see in thesenumbers?

Children can explore other rows in a similar way.

2. Children explore the columns of the 50 array/100 square.

Teacher:Cover the numbers in the first column.

What is the first number in the first column?

Tell me all the numbers in the first column.

What pattern do you notice?

Children can explore other columns in a similar way.

.


.

Check: Mental response

As children gain confidence in these activities they should be able to respond mentally to questions such as;

What are the numbers in the first/second/ fifth/last row?

What are the numbers in the first /third/sixth/last column?

What is the first/last number in the fourth row?

‘What is the first/last number in the seventh column?

3. Children explore the pattern of even and odd numbers.

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

Teacher:Let’s count in twos. Put counters onthese numbers. What pattern do yousee?

We call these the even numbers.

The numbers that are not coveredare called the odd numbers.

Tell me the odd numbers. Move yourcounters to cover the odd numbers.What pattern do you see?


Personal Notes


Second Learning Goal


Mental Calculation within 99 without bridging

Children will:

• add 10 to multiples of ten, and talk about their thinking.

• subtract 10 from multiples of ten and talk about their

thinking.

• add 10 to any 2-digit number and talk about their thinking.

• subtract 10 from any 2-digit number and talk about their

thinking.

• add multiples of 10 to multiples of 10.

• subtract multiples of 10 from multiples of 10 and talk about

their thinking.

• add multiples of 10 to any 2-digit number and talk about

their thinking.

• subtract multiples of 10 from any 2-digit number and talk

about their thinking.

• add a single digit number to a 2-digit number without

bridging, and talk about their thinking.

• subtract a single digit number from a 2-digit number without

bridging, and talk about their thinking.

• use their knowledge of a ‘basic fact’ within 10 for more

difficult calculations and explain their thinking in both

addition and subtraction.

• add two 2-digit numbers within 99 (without bridging) and

explain their thinking.

• subtract a 2-digit number from a 2-digit number within 99

(without bridging) and explain their thinking.


Children will naturally gain confidence in this learning goal through experience of the preceding activities. They will benefit from following the same structure ie.concrete activities, 100 square activities leading towards a confident mental response.

Readiness Check

Children are ready to undertake the following activities when;

�� they have quick recall of the basic facts within 10,

�� they appreciate the commutative aspect of addition, e.g. 3 + 4 is the same as 4 + 3,

�� they appreciate the inverse relationship between addition and subtraction,

�� they understand the composition of 2-digit numbers.

IT IS GOOD TO DEVELOP THE SKILLS OF ADDITION AND SUBTRACTION IN PARALLEL

WHEREVER POSSIBLE. This helps children to consolidate and use their appreciation of the

relationship between these operations.

Equipment

Rods of ten and singles made with multilink, unifix or similar equipment from the

classroom.

Cuisenaire

100 square

Markers or counters, transparent and opaque

Scrap materials such as lollipop sticks.


Personal Notes


Children will add 10 to multiples of 10, (30 + 10, 10 + 30)

Children will subtract 10 from multiples of ten, (40 – 10)

Children will talk about their thinking, gradually working

towards a mental response.

Children should continue with these practical activities until they can respond

mentally.

Concrete stage/using rods of 10

Teacher:Use your rods to put out 30.How many rods do you need for 30? Why?Now I want you to add on 10. Tell me what you did. What is your answer? We say30 add 10 is 40. (Children chant together).You have 4 rods of 10 on the table – that’s 40 altogether.I want you to take away 10. Tell me what you did. What is your answer? We say40 take away 10 is 30. (Children chant together).’

Pictorial stage/using 100square 1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

Teacher:Look at your 100 square.Put your marker on 40. Add 10.Initially children may count on if necessary. What is your answer? Tell me how you move your marker to add 10 on your 100 square.

Our marker is on 40. Subtract 10.What is your answer? (NB if children need to count back in ones care must be taken when they reach 31).Tell me how you move your marker to subtract 10 on your 100 square.We say 30 add 10 is 40. 40 subtract 10 is 30.


Comment

Rods are used first as a thoroughly 3-dimensional experience to establish sound

understandings. Transferring the learning to the 100 square provides the step

between totally practical activities and the mental response.

Abstract stage/mental response

Children respond mentally when adding or subtracting 10 to or from any multiple of 10.

Comment

It is worth taking time on this learning goal until children are secure. It forms a firm

base for future activities.

Things to consider

��making connections between all the stages

��practical work is not an end in itself.


Children will add 10 to any 2-digit number.

Children will subtract 10 from any 2-digit number.

They will talk about their thinking.

Initially children will achieve these goals practically, then mentally.

Concrete stage/using rods of 10

Teacher:Put out rods and singles of multilink or cuisenaireto represent 24.

Add 10.Tell me what you did. Where did you place your extra 10 rod? What is your answer?We say24 add 10 is 34.

You have 34 on the table. Take away 10. Tell me what you did. What is your answer? We say24 add 10 is 34. 34 subtract 10 is 24.

Pictorial Stage/using 100 square

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23

TeacherPut your marker on 24.Add 10. What is your answer? Tell me how you moved your marker.

A similar approach can be used for subtraction.

24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100



Children respond mentally when adding 10 to any 2-digit number. Children respond mentallywhen subtracting 10 from any 2-digit number.

GameChildren can play ‘Ladder Race’ to reinforce these skills.


Children will add multiples of 10 to multiples of 10.

Children will subtract multiples of 10 from multiples of 10.


Concrete stage/ using rods of 10

TeacherPut out rods to represent 30.We want to add 20, what will we do?

Tell me your answer.We say 30 + 20 = 50.


Children should begin to see the benefit of grouping their tens together.

Pictorial Stage/using 100 square 1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

Teacher

Put your marker on 30.What do we need to do to add 20. Canyou show me.

We say 30 + 20 = 50



Abstract Stage/mental response

Children respond mentally when adding multiples of 10 to multiples of 10.Children respond mentally when subtracting multiples of 10 from a multiple of 10.


Children will add multiples of 10 to any 2-digit number.

Children will subtract multiples of 10 from any 2-digit number.


Concrete Stage/using rods of 10

Teacher:Put out 35 with rods of 10 and singles.Add 20. Tell me what you did. What is your answer? We say 35 add 20 is 55.

You have 55 on your table. Take away 20.Tell me what you did.What is your answer? We say55 take away 20 is 35.


1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

Teacher:

Put your marker on 35.What shall we do to add 20?Can you show me? Tell me what you did.

We say 35 + 20 + 55



By this time children should have begun to

display a good measure of confidence in

managing numbers mentally within 99 and

demonstrate this by explaining their thinking.

Readiness Check

Children who have achieved the previous learning goals demonstrate their readiness to extend

their learning through further guided activities with the 100 square.


Children respond mentally when adding multiples of 10 to any 2-digit number. Children respond

mentally when subtracting multiples of 10 from a 2-digit number.


Children will add a single digit number to a 2-digit number.

Children will subtract a single digit number from a 2-digit

number. They will talk about their thinking. Children will use

their knowledge of a ‘basic fact’ within 10 for more difficult

calculations and explain their thinking in both addition and

subtraction.

If children still need theuse of concrete materials for this

learning goal then theyare not ready.


1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

Tell me the number.14 add 3 is 17.Children continue this pattern down to the last row.‘What pattern have you made with your markers?’ Let’s all say 4 add 3 is 7…….14 add 3 is 17……. 24 add 3 is 27………… 94 add 3 is 97.

Teacher:Put a marker on 4.Add on 3. Now put a marker on youranswer.Tell me the number.We say 4 add 3 is 7 Now put a marker on 14Add on 3 and put a marker on your answer.

Teacher can show how this can be recorded on the board.

Eg. 4 + 3 = 7

14 + 3 = 17


Comment

Children will enjoy working through a variety of examples in this way (in each case

the ‘basic fact’ is less than 10). They should be encouraged to talk about the visual

patterns between the columns and connect this to the number patterns.

As children gain confidence in adding in this way the related subtraction facts

should also be explored.

Initially children will probably count on/back in ones. Once they have discovered

the pattern of the columns they should be encouraged to work mentally. They

learn to use two important ideas:

I. Quick response to the basic fact

II. Their understanding of the pattern of columns.

Children should be given TIME to become fully confident in this use of the

100square.


Children will use their knowledge of a ‘basic fact’ within 10 for more difficult calculations.e.g. 4 + 5………………34+5

Teacher:Put a marker on 4 Add on 5 (mentally) and put a marker on your answer.We all know 4 add 5 is 9. Let’s use this to help us with the next question.

Now place a marker on 34 We want to add on 5.Who can tell without counting?How do you know?

Children should do a variety of this type of calculation until they are confident. As previously,subtraction should be included as well.



Teacher:

Tell me 52 +5

Child:

2 + 5 is 7 so 52 + 5 is 57


Children respond mentally when adding a single digit number to a 2-digit number without

bridging.

Children respond mentally when subtracting a single digit number from a 2-digit number.

By now, children should havedeveloped thestrategy of spottingthe ‘easy fact’ in thecalculation and adding on extra tens.

GameChildren can play ‘Make the Target’ to reinforce these skills.


Children will add two2-digit numbers within 99 (without bridging)

and explain their thinking.

Children will subtract a 2-digit number from a 2-digit number within 99

(without bridging) and explain their thinking.

Comment

Children will naturally gain confidence in this learning goal through the experience

of the proceeding activities. They will benefit from following the same structure in

concrete activities, 100 square activities leading towards a confident mental

response.

Comment

Children will naturally gain confidence in this learning goal through the experience of

the preceding activites. They will benefit from following the same structure ie. concrete

activites, 100 square activities leading towards a confident mental response.


Personal Notes


ThirdLearning Goal


Mental Calculation within 99 with bridging

This mental skill can be broken down into a number of gentle steps. A helpful sequence of learning goals is recorded below. Each is supported by a specific example to make the text more easily understood. The reader may get the impression that this approach is unwieldy and complicated. Experience has shown, however, that children who are guided through these steps and given time to gain confidence in each are well able to master them. Such mental competence provides them with an excellent tool for all future mental calculation. In the guidance that follows addition and subtraction are considered separately. There is merit, however, in teaching related ideas simultaneously.

Readiness checkChildren are ready for these activities when they are competent in adding and subtracting mentally without bridging.

Children will add two 2-digit numbers with bridging and explain their thinking. The following activities will develop the ability to (a) jump on from any 2-digit number to the nearest ten e.g. 35 + = 40

(b) add on a single digit number by partitioning it to create two ‘jumps’ e.g. 35 + 8 = (35 + 5) + 3

(c) add two 2-digit numbers method 1 – by partitioning second number only and adding on the ‘tens’ first


e.g. 35 + 28 = 35 + 20 + 8 method 2 – by partitioning both numbers to combine the ‘tens’ and ‘ones’ e.g. 35 + 28 = 30 + 20 +5 + 8

Children will subtract two 2-digit numbers with bridging and explain their thinking. The following activities will develop the ability to (a) jump back from any 2-digit number to the nearest ‘ten’ e.g. 52 – = 50

(b) subtract a partitioned single digit number to create two ‘jumps’ (7 is the same as 2 and 5) e.g. 52 – 7 is the same as 52 – 2 then 50 – 5 = 45

(c) subtract two 2-digit numbers by partitioning the second number e.g. 52 – 27 is the same as 52 – 20 = 32, then 32 – 7 (32 – 2, 30 – 5) = 25 Comment

Children will have developed these skills in their earlier experiences but games or similar activities which reinforce them would provide valuable backup as they extend their mental capacity. If children can recall readily these simple facts it releases them to concentrate on the important new ideas that are being promoted. Experience shows that if mistakes are made it is more likely to be in the simple ‘basic facts’.


Personal Notes


Children will jump forward from any 2-digit number to the next ‘ten’.

Children will jump backwards from any 2-digit number to the nearest

ten.

They will explain their thinking.

Pictorial stage/ using the 100 square and the number line.

These aids should be seen as valuable tools to help children visualise their thinking. Initially theremay be a little counting in ones for reassurance, but this should not continue.

AdditionA few easy calculations during the warm up, will ease the children into the following activities.

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

What about 35 and how many make 40? (no clues given)

29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

Teacher can carry on with these early ideas to ensure that the children are proficient.

Teacher:7 and how many make 10?

3 and how many make 10?

23 and how many make 30?

What do 43 and 7 make?

Children use their knowledge of ‘easyfacts’ to help with more difficult ideas.


Subtraction

A few easy calculations during the warm up will ease the children into the new ideas.

100 squares and number lines should be made available.

37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

Teacher:

47 and how many to get back to 40? How can you tell? (no clues given)



Abstract Stage

Children respond mentally when adding on to the next multiple of ten.

Children respond mentally when subtracting back to the next multiple of ten.


Children will add on a single digit number by partitioning it to create two ‘jumps’.

Children will subtract a single digit number by partitioning it to create two ‘jumps’.


Comment

If the children at this stage are relying on counting on in ones, they would benefit

by going back to the concrete stage.

The examples that follow suggest prompts and questions to be asked by the

teacher and indicate the type of interaction that should be developed between

teacher and children.

Pictorial stage/ using number line

Addition

Teacher:

35 + 8, what will the answer be roughly?

Will it be in the thirties, forties or fifties?

How can you tell?

The answer would be in the forties.

It is difficult to work it out exactly in one jump, so let’s try two jumps.

A good number to ‘land on’ for the first jump would be 40.

How many to get from 35 to 40?

Child: 5

Teacher:

We have added on 5, but we want to add 8 altogether, how many more do we need to add?

Child: 3

Teacher:

Can you tell me why?

Child:

8 is the same as 5 and 3

35 add 5 is 40

40 and 3 is 43

35 + 8 is 43

Children should be given a number of examples to allow them to become confident in this

process.


Subtraction

Teacher:

What is 52 – 7 ?

What will the answer be roughly?

Will it be in the fifties, forties or thirties?

How can you tell?

The answer is in the forties. It is quite difficult to do it in one jump.

Let’s try two jumps. A good number to ‘land on’ would be 50.

39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

How many to get from 52 to 50?

Child: 2

Teacher:

We have subtracted 2 and we want to subtract 7 altogether, how many more do we need to

take away?

Child: 5

Teacher:

We had 52 and we subtracted 2 and landed on 50, Then 5 more and where have we landed?

Child: 45

Teacher:

Can you tell me why?

Child:

7 is the same as 2 and 5.

52 subtract 2 is 50

50 subtract 5 is 45

52 – 7 is 45

As above, the children should be given time to become confident in this process.

Some children may prefer to use the 100 square for this process.

GameChildren can play ‘Fill the Square’ to reinforce these partitioning skills.



As the children’s confidence in this process develops, they should progress gradually towards a mental response.

Assessment

Examples should be varied to include those without and with bridging within 99. Children should

demonstrate their understanding by using appropriate strategies for those varied examples and

explaining their thinking.


Personal Notes


Children will add any two 2-digit numbers with bridging.

Children will subtract any 2-digit number from a 2-digit number.


This learning goal is a simple extension of the previous one and involves no new

strategies. Children who have progressed successfully through the sequence of

activities in this development should move readily to a mental response.


Addition

45 + 27

Teacher:

How would we add these two numbers? (children suggest ways)

What would the answer be roughly?

Method 1- partitioning the second number

45 + 27 is 45 + 20 + 7

which is 65 + 7

which is 65 + 5 + 2

which is 70 + 2

which is 72

Method 2 – combining ‘tens’ and combining ‘ones’

45 + 27 is 40 + 20 + 5 + 7

which is 60 + 12

which is 70 + 2

which is 72


Comment

Children should be introduced to both methods and encouraged to chose the

one they prefer.

Subtraction

64 – 35

Teacher:

How can do this?

Where might the answer be roughly?

We can subtract 35 from 64 by partitioning the 35.

64 – 35 is 64 – 30 – 5

which is 34 – 5

which is 34 – 4 and 30 – 1

which is 29

Children should be given time to become confident in this process.

Assessment

Children use appropriate strategies to calculate mentally within 99. They can attempt the full

range of possibilities – single and 2-digit examples, without bridging and with bridging.

They can explain their thinking.

GameChildren can play ‘How can you make?’ to reinforce these skills.


Ladder Race

Children are asked to reach the top of the ladder by keeping a running total.

All players start with the same number, e.g. 7, which they can write in the bottom rung of the ladder.

Start number can be any from 1 – 10.

Each player takes it in turn to lift a card and add the number to his total.

He then writes his new total on the next rung.

The game finishes when all players reach the top of the ladder. The winner is the player with the highest total.


Player 1 Player 2 Player 3

Ladder Race


Game one – addition

Photocopy and cut out as many sets as is needed.

Blank cards are for other variations.

Add10

Add1

Add1

Add1

Add1

Add1

Add10

Add10

Add10

Add10

Game two – subtraction

Subtract10

Subtract10

Subtract10

Subtract1

Subtract1

Subtract1


Make the target

Children are asked to make the target number inside the square.

They must use the numbers from either circle to make this number.

Addition or subtraction can be used.

If they can make the target number, they must call out the entire solution,

e.g. 9 add 2 is 11.

Only one circle will have the correct solution.


Make the target

+ -1

11

11

+ -2

9

11

Make the target

+ - + -

Make a target


Fill the square

EquipmentBlank 100 square for each playerCuisenaire rodsTwo dice

Children are asked to throw both dice. They can create a number by adding or subtracting the numbers on the dice, e.g. if 4 and 5 are thrown 4 + 5 = 9 or 5 – 4 = 1.

Children then take the corresponding rod from the box of cuisenaire and place it on the 100 square.

The square needs to be completed consecutively.

They may have to exchange a rod for two smaller rods to fit along the rows.

The winner is the first to reach 100 exactly. Children will have to make decisions about the size of the number they can create.


1

100

Fill the square


How can you make?

Children are asked to make the number in the square by using the numbers from one circle.

Only one circle will give the correct response.

Addition or subtraction may be used.

If they can make the target number, they must call out the entire response eg. 25 take away 8 is 17 or 25 substract 8 equals 17.

The page is folded below the large square so that the correct response cannot be seen.


8

25

17

6

26

25 –

8 =

17


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31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

50 Array

Blank 50 Array


60 Array

Blank 60 Array

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12

34

56

78

910

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Bla

nk

60

Arr

ay


Blank 100 square


100 square

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Digit cards

1 2

4 5

7 8

121110

9

6

3

Digit cards


Digit cards

Digit cards

13 14

16 17

19 20

242322

21

18

15


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727170

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848382

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75


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Digit cards

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99

contents acknowledgements introduction first learning goal second learning · pdf...

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