Progression In Calculations at Lyndhurst First School.

Addition and Subtraction

Mathematical Calculations in School Today.This document is designed to help you to understand the calculation

methods your child will be taught in school. When supporting your child at home with Maths work it would be helpful if you could

reinforce these methods rather than teach them the way that you were taught. The methods are levelled according to ability and you

would need to speak to you child’s teacher to find out which methods would currently be the most appropriate for your child to

practice at home.Remember each child progresses at their own pace.

Understanding Addition. (EY/1C/1B)

Explanation The physical act of counting out a set number of objects, and combining

two groups, is an important step for children to explore. This is best done in a practical play based context as much as possible.

Understanding addition as combining two groups

Children need to experience counting out a set of objects and combining them with another set of objects to make a total amount. Initially this needs to be adding 1 more.

Eg. 4 plus 1 makes 5.

Count out a set of 4 and another set of 1. Then count them altogether to reach a total of 5

Explore 1 more through simple songs and rhymes, for example ‘1 man went to mo’ or ‘1, 2, 3, 4, 5, once I caught a fish alive’.

Use a Numicon shape and add on the 1 shape... What number do you have now? Find the new Numicon shape to cover over the top.

Key Questions/VocabularyMore, more than, one more, after, add, plus, count, total, equals, makesWhat is the number after 6?How will you find out how many there are in total?Can you show me how you worked out 1 more than....?

Success criteria• I can add one to a small group of

objects up to a total of 10 and explain what I am doing.

• I can count out 1p coins to pay for 2 items totalling up to 10p.

Understanding Subtraction. (EY/1C/1B)

Explanation The physical act of counting out a set number of objects and taking some

away is an important step for children to explore. This is best done in a practical play based context as much as possible.

Explore 1 less through simple songs and rhymes, for example ’10 green bottles’ or ‘5 little speckled frogs’.

Count out a given number of objects and take away 1 of them... How many do you have now?

Key Questions/VocabularyLess, less than, one less, before, take away, subtract, leaves, equalsWhat is the number before 5?How many different ways can you show me that 8 subtract 1 is 7?Can you show me how you worked out 1 less than.....?

Success criteria• I can use objects to take away 1

from any number up to 10.• I can work out how much I have

left from an amount up to 10p when I buy a sweet costing 1p (using 1p coins to work practically).

Understanding subtraction as taking away

Children need to experience counting out a set number of objects and then removing/taking away a certain number from that group. Initially this needs to be taking away 1 from a set.

Eg. 7 take away 1 leaves 6

Count out 7 objects. Then remove 1 from that set and count the objects that are left over.

Using a Number Track for Addition. (1B/1A)

Key Questions/VocabularyCount on, add, more, more than, equals,

totals, makes Find the number that is one more than...? 4 more than...?Count on 3 places from 15, where do you

land?How many is 5 more than 8?

Explanation Number tracks can be

used for children to locate a number, learn the order of numbers, and to begin to add one and then more than one to a given number.

1 2 3 4 5 6 7 8 9 10

One more than four is five

Success criteria• I can use a number track to

count on and find the answer to an addition sum up to 10 and then to 20.

Children need to be able to understand the order of numbers remains the same and that as we count on the numbers get bigger by 1. They need plenty of practise in counting objects and by rote... Count the stairs as you go up to bed... Count your footsteps as you walk across a room.... Write the numbers to 10 on separate pieces of paper and get your child to put them into order, counting to check., then progress to ordering numbers to 20.

Order Numicon 1 – 10 set, place a shape on top of the next one, noticing how there is a difference of 1.

Begin to recall all pairs of numbers that total 10.Begin to know doubles up to double 5.

Simple Jottings/Mark Making for Addition. (1B/1A)

Key Questions/VocabularyCount, count on, more, add, plus,

sum, altogether, total, equalsHow many altogether?Find the number that is five more than...?Count on 6 more from 13, what

number do you get to?

ExplanationSimple mark making is the first stage of children’s independent jottings to help them solve additions. They draw or make the appropriate number of marks under each number then count

them up to reach the total. It is not necessary to draw the number of

marks under the answer. Children can also use objects, such as

counters, sweets, beads, to create groups to combine to find the total of

an addition.

13 + 2 = 15

Success criteria• I can use simple

jottings to support the addition of two numbers up to a total of 10, then 20.

• I can begin to select appropriate apparatus to support addition.

Children need to begin to see that addition produces the same answer which ever way round it is solved eg 8 + 2=10 and 2+8=10. It is COMMUTATIVE. Lay the 8 and 2 Numicon shapes together and place another 2 then 8 on top to see it is the same. Encourage children to see that it is easier and quicker to count on from the largest number.

Using a Number Track for Subtraction. (1B/1A)

Key Questions/VocabularyCount back, take away, subtract, less than,

leaves, equalsFind the number that is one less than ....? Five

less than....?Count back 4 places from 8, where do you land?How many is 5 less than 9?

Explanation Number tracks can be used for

children to locate a number, learn the order of numbers, and to begin to find out one less and then a few less than a given number.

1 2 3 4 5 6 7 8 9 10

One less than nine is eight

Success criteria• I can use a number track to

count back and find the answer to a given question starting from numbers up to 10, then up to 20.

Children need to be able to understand the order of numbers remains the same and that when counting back the numbers get smaller by 1. They need lots of practice in counting backwards... Count back as you go down the stairs.... Do a countdown from 10 or 20 before you leave the house....Write the numbers to 10 on separate pieces of paper and get your child to order them in reverse, then try from 20.

Order Numicon 1 – 10 set, note the difference between two shapes next to each other is 1.

Simple Jottings/Mark Making for Subtraction (1B/1A)

Key Question/VocabularyCount, count back, subtract, take away, cross offDifference between, leaves, equalsHow many are left over?Find the number that is 6 less than...?Count back 5 from 16, what number do you get

to?

ExplanationSimple mark making is the first stage of children’s independent jottings to help them solve

subtractions. They draw the initial number of objects and then cross off the number it says to take away and count the ones left over. Children can also use objects, such as counters, sweets, beads, to

create the initial group and then physically take away

the right number to find the answer to the

subtraction.

12 - 3 = 9

Success criteria• I can use simple

jottings to support the subtraction of two numbers starting from numbers up to 10, then 20.

• I can begin to select appropriate apparatus to support subtraction.

At this level, children need to see that when doing subtraction the biggest number needs to be first and you take away the smaller number.

Using a Blank Number Line for Addition. (1A/2C)

Key Questions/VocabularyCount on, count on in ones, add, plus, more than,

total,equals, makesWhich number are you going to start your line

with?How many ones jumps do you need to do?What number have you reached?

ExplanationBlank number lines are used to enable children to count on and back with more than one jump. Children are taught to draw their own number line and start with the biggest number. There is no need to write +1 in each jump. Children learn to use ones jumps, adding single digit numbers and working within a range up to about 20. It is only necessary to record where they start and where they end up after adding on. They can then progress to using this method of single jumps when adding ‘teen’ numbers and working within numbers to about 30. Remember to jump on from the biggest number!

15 18 17 21

15 + 3 = 18 4 + 17 = 21

Success criteria• I can use number lines

to support the addition of two numbers starting from numbers up to 20, then 30.

• I can use a number line to help me solve addition problems involving money , up to 30p, and measures, up to a similar amount.

Children can use Deines (one blocks) to place in the jumps and support the visual image of how many they need to add on.

Rapidly recall all pairs of numbers that have a total of 10.Know doubles to double 5 and begin to know doubles up to double 10.

Using a Blank Number Line for Subtraction. (1A/2C)

Key Questions/VocabularyCount back, count back in ones, less than, take

away, Subtract, leaves, equalsWhere are you going to start your number line?Which number are you starting with?How many jumps back do you need to do?What number have you reached?

ExplanationBlank number lines are used to enable children to count on and back with more than one jump. Children are taught to draw their own blank number lines, enabling them to do calculations within any range of numbers. There is no need to write -1 in each jump. Children learn to use ones jumps, subtracting single digit numbers and working within a range up to about 20, then 30. Their recording methods should be the same as for addition, except that with subtraction they start at the right hand end of the line and jump back.

5 9 8 14

9 – 4 = 5 14 – 6 = 8

Success criteria• I can use number lines

to support the subtraction of two numbers starting from numbers up to 20, then 30.

• I can use a number line to help me solve subtraction problems involving money , up to 30p, and measures, up to a similar amount.

Children can use Deines (one blocks) to place in the jumps and support the visual image of how many they need to count back.

Developing use of Number Lines, Adding Tens and Ones. (2B)

Key Questions/VocabularyAddition, add, plus, more, more than, ten more, count in tens, one more, count

in ones, total, equals, altogetherHow many tens jumps do you need to

do? How many ones jumps?Inverse (children need to know at this stage that addition and subtraction are inverse operations, they undo each

other)

ExplanationWhen children understand that 15 is made up of one ten and five

ones, they can learn a more efficient method of using a number line

than just doing 15 single jumps. When confident adding on ‘teen’

numbers, progress to adding numbers with more than one ten.

26p + 12p = 38p

26p 36p 38p

+10

33 + 21 = 54

33 43 53 54

+10 +10

Children need to understand the place value of each digit in order to partition 2-digit numbers into tens and ones.

Success criteria• I can use number

lines more efficiently to add on 2-digit numbers by adding on the tens and then the ones.

Recall all + and – facts for each number to at least 10.Know doubles up to double 10 and their corresponding halves.

Developing use of Number Lines, Subtracting Tens and Ones. (2B)

Key Questions/VocabularySubtract, take away, minus, less than, ten less, count back in tens, one less, count back in ones, leaves, equals, Difference between (we find the difference between when the

numbers are close together and it is easier and quicker to count up than back. Eg 53 – 47, it is easier to count on

from 47 to find the difference between the two numbers than count back 47

places.)

ExplanationSubtracting tens and ones is the same as

for addition. Jottings are set out as shown, with

a record of where you have reached kept

under the line and the jumps done recorded over

the line. There is no need to write +1 or -1 in

the small jumps, this would be inefficient. When confident adding on ‘teen’ numbers,

progress toadding numbers with more than one ten.

48g – 13g = 35g

35g 38g 48g

-10

116 – 24 = 92

92 96 106 116

-10 -10

Children need to understand the place value of each digit in order to partition 2-digit numbers into tens and ones.

Success criteria• I can use

number lines more efficiently to subtract a 2-digit number by counting back the tens jumps and then the ones jumps.

Add or subtract 9 or 11 by Compensation (2B/2A)

Key Questions/Vocabulary

Add, plus, more than, sum

Subtract, take away, minus, less thanEquals, leaves, totalsadjust

ExplanationWhen adding or taking away 9,

children are taught that it as quicker to add /subtract ten and then adjust by one accordingly. This is why it is

important that children recognise number patterns to count on and back in

tens from any number.

25 + 9 = 34

25 34 35

+10

To add 9, + 10 then -1 To subtract 9, -10 and then +1

146 – 9 = 137

136 137 146

-10

Success Criteria• I can quickly add or

subtract 9 from any 2 or 3 digit number by adding or subtracting 10 first and then adjusting by 1.

• I can quickly add or subtract 11 from any 2 or 3 digit number by adding or subtracting 10 first and then adjusting by 1.

To add 11, + 10 then + 1 To subtract 11, -10 then - 1

117 + 11 = 128 85 – 11 = 74

117 127 128

74 75 85

+10 -10

Practical exploration with money, using 10p and 1p coins can help to support the understanding of which way to compensate.

Partition and Recombine. (2B/2A)

Key Questions/VocabularyTens digit, ones digit, unitsPartition, split, recombineHow many tens? How many

ones?How many altogether?

ExplanationSome children find this strategy a quick and easy method for addition,

that they soon are able to do it mentally. Initially it is important to give calculations where the ones digits do not total more than 10, (we say

they don’t cross the tens boundary). Once they are confident in this

method they can progress to partition and recombining 2-digit numbers where

the ones do cross the tens boundary, eg 37 + 26. So 30+20=50, 7+6=13 Then 50 +13=63

23 + 35

50 + 8 = 58

To add 23 and 35....First add the number of tens,

so 20 + 30 = 50

Then add the number of ones, so 3 + 5 = 8

Finally combine the answers to give the total,

so 50 + 8 = 58

Success Criteria• I can do

addition more efficiently by partitioning numbers into tens and ones and then recombining them.

Confidently recall + and – facts to 10 then 20 (eg, 9 + 6, 13 – 7, 15 + 4)Know all + and – facts for multiples of 10 to 100 (eg, 30 + 50, 90 – 20)

Develop Efficient Use of Number Lines. (3C/3B)

Key Questions/VocabularyAddition, add, plus, more, more

thanSubtract, take away, minus, less

thanTen more, ten less, count in tensOne more, one less, count in onesDifference between, inverseEquals, leaves, altogether

ExplanationOnce children are confident and accurate in the use of tens and ones jumps, they can progress to

using multiple of tens jumps. Encourage children to use their knowledge of number bonds to bridge to the

nearest multiple of 10 to make counting easier (as in the second eg). Make sure they keep a record in their

jumps of what they are doing so that they can check they have + or – the correct number.

74 + 43 = 117

74 114 117

+40

152 – 68 = 96

84 90 150 152

-60

+3

-2

Success Criteria• I can add and subtract

chunks of tens and ones to make my calculations more efficient.

• I can bridge through the nearest multiple of ten.

-6

Use mental recall of + and – facts to 20 and apply to problems.Know all the + and –facts for multiples of 5 to 100 (eg 35 + 45, 80 – 55).Derive rapidly all number pairs that total 100 (eg 61 + 39, 22 + 78)

Partition and Recombine. (3C/3B)

Key Questions/VocabularyHundreds digit, tens digit, ones digit, Partition, split, recombineHow many hundreds? tens?

ones?How many altogether?

ExplanationAt this phase. Children can

partition and recombine numbers that may cross the tens or hundreds boundary. They will also be able to use

this method with 3-digit numbers.

346 + 38

300 + 70 + 14

300 + 80 + 4 = 384

137 + 389

400 + 110 + 16

500 + 20 + 6 = 526

Deines can be used to create a clear visual image of the place value of each digit and supports the understanding when the tens or hundreds boundaries are crossed.

Success Criteria• I can add 3 digit

numbers by partitioning them into hundreds, tens and ones, adding them and then recombining to reach the total.