Cliff Lane Primary School’s Calculation Policy
The following calculation policy has been devised to meet the needs of the National Curriculum 2014 for the teaching and learning of mathematics. The 2014 Mathematics Curriculum can be found at :- https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/335158/PRIMARY_national_curriculum_-_Mathematics_220714.pdf
The early learning in number and calculation in Reception follows the ‘Development Matters’ EYFS document and this calculation policy is designed to build progressively from the content and methods established in EYFS.
The first page for each year group shows the content taught during the year and the following pages show the methods used to teach the concepts.
KEY STAGE 1
Year 1
Place Value / Addition and Subtraction / Multiplication and Division· count to and across 100 forwards and backwards, beginning with 0 or 1, or from any given number.
· count, read and write numbers to 100 in numerals; count in multiples of 2,5 and 10 forwards.
· given a number identify one more or one less.
· identify and represent numbers using objects and pictorial representations including the number line , and use the language of: equal to, more than less than, fewer, most, least.
· read and write numbers 1-20 in numerals and words
· x and ÷ by 10 stressing on the patterns by moving digits NOT adding zeros / · read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs.
· Represent and use number bonds and related subtraction facts within 20 (9+7=16; 16-7=9; 7=16-9)
· add and subtract numbers using concrete objects, pictorial representations and mentally including one digit and two digit numbers to 20 (including 0)
· solve one step problems that involve addition and subtraction, using concrete objects and pictorial representations , and missing number problems such as 7 =0 -9.
(Problems should include the terms put together, add, all together, total, take away) / · solve one step problems involving multiplication and division by calculating the answer using concrete objects, pictorial representation and arrays.
(Grouping and sharing quantities, doubling and halving, make connections between arrays, number patterns, counting in twos, fives and tens)
Please refer to ‘units’ as ‘ones’ as this is the terminology used in the curriculum.
Year 1
Addition / Subtraction+ = signs and missing numbers
Children need to understand the concept of equality before using the ‘=’ sign. Calculations should be written either side of the equality sign so that the sign is not just interpreted as ‘the answer’.
2 = 1 + 1
2 + 3 = 4 + 1
Missing numbers need to be placed in all possible places.
3 + 4 = □ □ = 3 + 4
3 + □ = 7 7 = □ + 4
Counting and Combining sets of Objects
Combining two sets of objects (aggregation) which will progress onto adding on to a set (augmentation)
Understanding of counting on with a numbertrack.
Understanding of counting on with a number line(supported by models and images)
Vocabulary
Add, more, plus, and, make, altogether, total, equals to, count on, number line / - = signs and missing numbers
Missing number problems e.g. 7 = □ - 9; 20 - □ = 9; 15 – 9 = □; □ - □ = 11; 16 – 0 = □
Use concrete objects and pictorial representations. If appropriate, progress from using number lines with every number shown to number lines with significant numbers shown.
Understand subtraction as take-away:
-5
0 14 19
Understand subtraction as finding the difference:
The above model would be introduced with concrete objects which children can move (including cards with pictures) before progressing to pictorial representation.
The use of other images is also valuable for modelling subtraction e.g. Numicon, bundles of straws, Dienes apparatus, multi-link cubes, bead strings
Vocabulary
Equal to, take, take away, less, minus, subtract, leaves, distance between, difference between, how many more, how many fewer/ less than, most, least, count back, how many left, how much less is?
Year 1
Multiplication / DivisionUnderstand multiplication is related to doubling and combing groups of the same size (repeated addition)
Children must have secure counting skills- being able to confidently count in 2s, 5s and 10s.
Children should be given opportunities to reason about what they notice in number patterns.
Use washing lines, and other practical resources for counting. Concrete objects. Numicon; bundles of straws, bead strings
Children should be given the opportunity to problem solve with concrete objects (including money and measures)
Use Cuisenaire or similar apparatus to develop the vocabulary relating to ‘times’ –
Pick up five, 4 times
Use arrays to understand multiplication can be done in any order (commutative law)
2 groups of 4
0 2 4 6 8
4 groups of 2
0 2 4 6 8
Vocabulary
Groups of, lots of, times, array, altogether, multiply, count, double / Children must have secure counting skills- being able to confidently count in 2s, 5s and 10s.
Children should be given opportunities to reason about what they notice in number patterns.
Group AND share small quantities- understanding the difference between the two concepts.
Sharing
Develops importance of one-to-one correspondence.
Children should be taught to share using concrete apparatus.
Grouping
Children should apply their counting skills to develop some understanding of grouping.
Use of arrays as a pictorial representation for division. 15 ÷ 3 = 5 There are 5 groups of 3.
15 ÷ 5 = 3 There are 3 groups of 5.
Children should be able to find ½ and ¼ and simple fractions of objects, numbers and quantities.
Vocabulary
Share, share equally, one each, two each...... , group, groups of, lots of, array
Year 2
Place Value / Addition and Subtraction / Multiplication and Division· count, read and write numbers to 100 in numerals; count in multiples of 2, 3, 5 and 10 forwards and backwards and in 10s from any number.
· recognise the place value of any two-digit number T and O. (also need to partition numbers in different ways e.g. 23 = 20 + 3 and 23 = 10 + 13 and begin to recognise 0 as a place holder)
· compare and order numbers from 0 to 100; use > < and =.
· identify and represent and estimate numbers using objects and pictorial (different) representations, including the number line, and use the language of: equal to, more than, less than, fewer, most, least
· read and write numbers to at least to 100 in numerals and words.
· use place value and number facts to solve problems.
· x and ÷ by 10 stressing on the patterns by moving digits NOT adding zeros / · recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 (e.g. 7+3 = 10; 70+30=100; 100-30=70; 30=100-70)
· add and subtract numbers using concrete objects, pictorial representations, and mentally including one-digit and two-digit numbers to 20 (including zero), a two-digit number and ones; a two-digit number and tens; two two-digit numbers; three one-digit numbers.
· solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = 0- 9 including those involving numbers quantities and measures by applying their increasing knowledge of mental and written methods (Problems should include the terms put together, add, altogether, total, take-away,
· show that addition can be done in any order (commutative) and that subtraction cannot; recognise and use the inverse relationship to check calculations and solve missing number problems. / · solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays, repeated addition, mental methods, multiplication and division facts . (Grouping and sharing quantities, doubling and halving, make connections between arrays, number patterns, counting in twos, fives and tens)
· recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers.
· recall and use multiplication and division facts for the 9 times table- using fingers
· calculate mathematical statements for multiplication and division within the table and write them using the multiplication (x), division (÷) and equals (=) signs (inverse relationship)
· show that multiplication is commutative and division of one number by another isn’t.
Please refer to ‘units’ as ‘ones’ as this is the terminology used in the curriculum.
Year 2
Addition / SubtractionMissing number problems e.g 14 + 5 = 10 + □ 32 + □ + □ = 100 35 = 1 + □ + 5
It is valuable to use a range of representations (also see Y1). Continue to use number lines to develop understanding of:
Counting on in tens and ones
23 + 12 = 23 + 10 + 2
= 33 + 2
Partitioning and bridging through 10
The steps in addition often bridge through a multiple of 10
e.g. Children should be able to partition the 7 to relate adding the 2 and then the 5. Number bond knowledge is key!
8 + 7 = 15
Adding 9 or 11 by adding 10 and adjusting by 1 (Cheating)
e.g. Add 9 by adding 10 and adjusting by 1
+ 10
-1
35 44 45
35 + 9 = 44
Vocabulary:
Add, more, plus, and, make, together, total, equal to, equals, count on, number line, sum, tens, ones, partition, addition, column, tens boundary / Missing number problems e.g. 52 – 8 = □; □ – 20 = 25; 22 = □ – 21; 6 + □ + 3 = 11
It is valuable to use a range of representations (also see Y1). Continue to use number lines to model take-away and difference.
Counting back
37 – 12 =
-2 -10
25 27 37
Find the difference
46 – 28 =
+2 +10 +6
28 30 40 46
2+10+6= 18
Cheating
34 – 9 =
- 10
+1
24 25 34
Vocabulary
Equal to, take, take away, less, minus, subtract, leaves, distance between, how many more, how many fewer/ less than, most, least, count back, how many left, how much less is?, difference, count on, strategy, partition, tens, ones
Year 2
Multiplication / DivisionExpressing multiplication as a number sentence using x
Using understanding of the inverse and practical resources to solve missing number problems.
7 x 2 = □□ = 2 x 7
7 x □ = 14 14 = □ x 7
□ x 2 = 14 14 = 2 x □
□ x Ñ = 14 14 = □ x Ñ
Develop understanding of multiplication using arrays and number lines (see Year 1). Include multiplications not in the 2, 5 or 10 times tables.
Begin to develop understanding of multiplication as scaling (3 times bigger/taller)
Doubling numbers up to 10 + 10 Link with understanding scaling. Using known doubles to work out double 2d numbers (double 15 = double 10 + double 5
Towards written methods
Use jottings to develop an understanding of doubling two digit numbers.
Partition the number
Double the tens, double the ones
Recombine
16
10 6
x2 x2
20 12
Vocabulary
Groups of, lots of, times, array, altogether, multiply, count, multiplied by, repeated addition, column, row, commutative, sets of, equal groups, twice as big as, once, twice, three times, double, most / ÷ = signs and missing numbers
6 ÷ 2 = □□ = 6 ÷ 2
6 ÷ □ = 3 3 = 6 ÷ □
□ ÷ 2 = 3 3 = □ ÷ 2
□ ÷ Ñ = 3 3 = □ ÷ Ñ
Know and understand sharing and grouping- introducing children to the ÷ sign.
Children should continue to use grouping and sharing for division using practical apparatus, arrays and pictorial representations.
Grouping using a number line
Group from zero in jumps of the divisor to find out ‘how many groups of 3 are there in 15?’
15 ÷ 3 = 5
Continue work on arrays. Support children to understand how multiplication and division are inverse.
Vocabulary
Share, share equally, one each, two each...... , group, groups of, lots of, array, divide, divided by, divided into, division, grouping, number line, left, left over.
KEY STAGE 2
Year 3
Place Value / Addition and Subtraction / Multiplication and Division· count from 0 in multiples of 4, 8, 50 and 100 (still count in multiples of 2, 3, 5 and 10 too to build up from Year 2)
· find 10 or 100 more or less than a given number.
· recognise the place value of each digit in a 3-digit number (H+T+O) (e.g. 146 = 100+40+6 but also 146 = 100+30+16 and 140+6 or 130+16 etc)
· compare and order numbers up to 1000
· identify, represent and estimate numbers using different representations (including measures)
· read and write numbers up to 1000 in numerals and words
· solve number problems and practical problems using the above ideas
· x and ÷ by 10 and 100 stressing on the patterns by moving digits NOT adding zeros / · add and subtract numbers mentally, including a three-digit number and ones; a three-digit number and tens; a three-digit number and hundreds. (For mental calculations with two digit numbers, the answer could exceed 100)
· add and subtract numbers with up to three digits using formal written methods of columnar addition and subtraction. (Pupils will use their understanding of place value and partitioning and practice using column addition and subtraction with increasingly large numbers up to 3 digits to become fluent)
· estimate the answer to a calculation and use inverse operations to check answers.
· solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction. / · recall and use multiplication and division facts for the 3, 6, 4 and 8 multiplication tables. (through doubling connect the 2, 4 and 8 times tables and the 3 and 6 times tables)
· write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods. (mental methods using commutivity (e.g. 4 x 12 x 5 = 4 x 5 x 12 = 20 x 12 = 240) and associativity ((2 x 3) x 4 = 2 x (3 x 4 and inverse to derive related facts e.g. 3 x 2 = 6; 6 ÷ 3 = 2; 2 = 6 ÷ 3 30 x 2 = 60; 60 ÷ 3 = 20; 30 = 60 ÷ 2;(develop reliable written methods starting with calculations of two-digit numbers by one-digit numbers
· solve problems, including missing number problems, involving multiplication and division including positive integer scaling problems and corresponding problems in which n objects are connected to m objects. (scaling contexts – four times as high; eight times as long; correspondence problems – 3 hats and 4 coats, how many outfits? if 4 apples cost 20p, how much would 12 cost?
Please refer to ‘units’ as ‘ones’ as this is the terminology used in the curriculum.