As promised at the Calculation evening, I have organised examples of the different strategies that we use at Redland to solve problems relating to the four operations. They are organised progressively for each operation. Please use these as a reference so that you can support your child’s learning at home. It is imperative that your child works on the strategy that best suits the stage that they are working at in Maths, rather than what you might think they should be working on for their age. As teachers, we do our utmost to ensure that what we teach your child develops their learning at an optimum rate so please support us by echoing this at home. If you have any questions about any of the methods, do come into school and arrange a mutually beneficial time to see your child’s teacher. Many thanks for your continued support, Miss Keates. Maths Subject Leader.
Transcript
As promised at the Calculation evening, I have organised examples of the different strategies that we
use at Redland to solve problems relating to the four operations. They are organised progressively for
each operation. Please use these as a reference so that you can support your child’s learning at home. It
is imperative that your child works on the strategy that best suits the stage that they are working at in
Maths, rather than what you might think they should be working on for their age. As teachers, we do
our utmost to ensure that what we teach your child develops their learning at an optimum rate so
please support us by echoing this at home.
If you have any questions about any of the methods, do come into school and arrange a mutually
beneficial time to see your child’s teacher.
Many thanks for your continued support,
Miss Keates.
Maths Subject Leader.
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Redland Primary School
Support for parents and carers.
Addition This document explains the methods that pupils at Redlands will use when solving problems involving addition. They are arranged in a progressive manner and may refer to mental strategies as well as written methods. Please remember that your child will be taught to use methods that suit the stage they are at in their mathematical development. These methods do not necessarily correlate with a particular year group. Please use this document as a point of reference when helping your child at home, but please support your child’s teacher by respecting their professionalism and mirroring that which they are teaching your child in school.
Vocabulary + Add, addition, plus, and, count on, more than, sum, total, altogether, increase, one more, ten more.
Early experiences ♦ Combine sets of objects practically, using cubes/counters etc.
♦ Verbalise number sentences.
♦ Practically partition numbers to 10.
♦ Use appropriate mathematical language verbally in practical situations: 5=3+2 2+2 +1=5
It is important that children have a good understanding of place value and partitioning using real objects, resources and visual images to support calculations
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Stage 1 Know by heart all pairs of numbers with a total of 10 and 20
Know that addition can be done in any order (Record on number line) Put the biggest number on the number line first and count on.
Add two single digit numbers that bridge 10
8 + 7 = 15
Add 3 or more single digit numbers
8 + 7 + 3 = It is essential that pupils are given opportunities to draw their own number lines as well as using those given to them, once they are becoming confident with the mathematics involved.
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Stage 2 Partition two digit numbers using tens and units.
Jump along marked and then empty number lines (start by counting on in 10s and then progress to multiples of 10), pupils should be given opportunities to draw their own number lines as well as using those created for them.
Stage 3 Mental addition of 2 digit numbers by partitioning needs to be secure.
48 + 36 = 48 + 30 = 78 78 + 6 = 84 Encourage estimation first then recording on a number line, it is essential that pupils are given opportunities to draw their own number lines.
48+36= 84
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Stage 4 Expanded method
48+36= 40 + 30 = 70 8 + 6 = 14 70 + 14 = 84
40+ 8 30+ 6 70+14 = 84
48 +36 70 14 84
Eventually this will lead to
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Stage 5 Expanded to compact standard This can now be extended to larger numbers It is far better that children work using the expanded method they understand rather than a more formal standard written method that they can not explain to you.
Stage 6 Children then use their chosen method to work with decimal numbers
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Redland Primary School Support for parents and carers.
Subtraction This document explains the methods that pupils at Redlands will use when solving problems involving subtraction. They are arranged in a progressive manner and may refer to mental strategies as well as written methods. Please remember that your child will be taught to use methods that suit the stage they are at in their mathematical development. These methods do not necessarily correlate with a particular year group. Please use this document as a point of reference when helping your child at home, but please support your child’s teacher by respecting their professionalism and mirroring that which they are teaching your child in school.
Vocabulary - Take away, how many left? How many fewer than? How many more to make" count back, less than, fewer, difference between, subtract, minus, subtraction, decrease.
Early experiences
♦ Begin to count backwards.
♦ Practical taking away from a set of objects
♦ Draw objects and cross out number taken away.
♦ Use vocabulary associated with subtraction in practical and real life situations.
♦ Group of cubes on a tray, part of them covered and need children visualise the calculation.
♦ Compare lengths of objects ready to find the difference
It is important that the children have a good understanding of place value and partitioning using real objects, resources and visual images to support calculation.
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Stage 1 Use the language ‘less than’ Stage 2 Count back in ones and then tens. Know by heart subtraction facts for numbers up to ten and 20.
Subtract single digit numbers often bridging through 10
Subtract multiples of 10 mentally but also show how to record using a number line. Begin to find the difference by comparing 2 lines Find a small difference by counting up from the smallest number
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Stage 3 Find the difference by counting on.
32 – 26 = 6 Extend the size of numbers Jump along the empty number line using boundary numbers or multiples of 10.
74-27= 47 aim for fewer jumps
NB Help children decide whether to count on or back depending on the size of the difference. E.g. 156 – 7" count back. 185 – 162" count on. It is essential that pupil have opportunities to create their own number lines as well as using those they have been provided with as this encourages independence.
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Stage 4 Expanded method Model how to take the numbers from the number line into vertical recording
+3 +40 +4
27 30 70 74
Progressing to recording vertically
Extending to (exceeding 100):
+3 +70 +4
27 30 100 174
Progressing to recording vertically
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Stage 5 Expanded to compact standard It is far better that children work using the expanded method they understand rather than a more formal standard, written method that they cannot explain to you.
This is dependent on a secure knowledge of place value and complements to 100 so this must be secure mentally first.
Optional Additional method (for children working in upper KS2 at level 3 and above) Leading to the most ‘recognisable’ vertical method, once pupils understand the concept of decomposition. This can also be used for larger numbers.
Stage 6 Children can choose their chosen method to work with decimal numbers,
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Redland Primary School Support for parents and carers.
Multiplication This document explains the methods that pupils at Redlands will use when solving problems involving multiplication. They are arranged in a progressive manner and may refer to mental strategies as well as written methods. Please remember that your child will be taught to use methods that suit the stage they are at in their mathematical development. These methods do not necessarily correlate with a particular year group. Please use this document as a point of reference when helping your child at home, but please support your child’s teacher by respecting their professionalism and mirroring that which they are teaching your child in school.
Stage 1 Counting in 2s, 5s and 10s Practical grouping of objects
Vocabulary X lots of, groups of, multiply, multiplication, multiple, product, once, twice, three times, array, row, column, double, repeated addition, times, 10 times as big/long/high etc.
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Stage 2
Repeated addition 4 lots of 2 make 8
Stage 3a
Multiplication as an array:
‘Five lots of three are fifteen’ 5 x 3 = 15
4 x 3
4, 3 times 4 multiplied by 3 3 groups of 4
Stage 3b Number line arrays (Pupils need opportunities to draw Their own number lines)
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Stage 4a Multiplying TU x U (one ten only) This depends on the ability to multiply by 10 mentally, having the understanding that when we multiply by 10 the digits move up one column so the number gets 10xbigger.
13 x 4 40 + 12 = 52 Stage 4b
Multiplying TU x U This depends on the ability to identify that 3 x 40 = 3 x 4 x 10 and then applying their understanding of place value (x by 10) and tables to solve this.
23 x 4 80 + 12 = 92
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Stage 5a Multiplying TU x TU 14 x 33
leads to
Stage 5b This is best when the numbers get bigger but the example shows 14x33 so that you can see where the numbers in the standard method come from.
Stage 6 Pupils must be highly secure in mental x and + (including decomposition) in order to be able to use this method. 14 X33 42 1 420
1 462
Stage 7 Pupils can extend a method (not necessarily the method shown in ‘Stage 6’) to multiplying 3 digit numbers by 2 digit numbers and multiplication of whole numbers by decimals.
14 X 33 12 30
120 300 462
(3 x 4) (3 x 10) (30 x 4) (30 x 10)
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Redland Primary School Support for parents and carers.
Division This document explains the methods that pupils at Redlands will use when solving problems involving division. They are arranged in a progressive manner and may refer to mental strategies as well as written methods. Please remember that your child will be taught to use methods that suit the stage they are at in their mathematical development. These methods do not necessarily correlate with a particular year group. Please use this document as a point of reference when helping your child at home, but please support your child’s teacher by respecting their professionalism and mirroring that which they are teaching your child in school.
Vocabulary ÷ lots of, equal groups of, shared equally, group, halve, half, divide, division, divided into, divided by, remainder, factor, quotient, divisible by, inverse, divisor. Avoid using the term ‘divided by’ until at least stage 3
Stage 1 Practical sharing of objects with vocabulary of sharing not grouping. This may include a ‘leftover’
Pictorial recording
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Stage 2 Understand division as grouping
Link grouping to arrays
Stage 3
Using a number line to record grouping up.
Include some remainders
19 ÷ 3 = 6 r 1
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Stage 4a Expanded method (allow time to ensure this stage is secure) TU ÷ U where the first ‘chunk’ is 10 lots of the divisor Use knowledge of multiples to ‘chunk’
This depends on the ability to recall multiples of 10 mentally
72 ÷ 5 = 10 lots 4 lots r2
0 50 70 72 Model how the line relates to the written method of recording. Children need to see these both together for a while. It may be useful, at this point, to count back on the number line, for some children, so that they can see the repeated subtraction on a number line relates to that when using the ‘chunking’ method.
Stage 4b
TU ÷ U but may need larger multiple for the first chunk
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Stage 5 Expanded to compact standard HTU ÷ U
518 ÷ 7
Stage 6 This can now be extended to larger numbers (HTU by TU) and decimals divided by a single digit.
