Download Brough Primary School Division Calculation Policy DIVISION STEPS

Brough Primary School
Division Calculation Policy
DIVISION STEPS EYFS
Early Learning Goal
Children develop an awareness of number names
through their enjoyment of action rhymes and
Children count reliably with numbers from one
songs that relate to their experience of
numbers.
to 20, place them in order and say which
Children need to :
number is one more or one less than a given
•Knows that numbers identify how many objects
number. Using quantities and objects, they add
are in a set.
and subtract two single-digit numbers and count
• Compares two groups of objects, saying when
on or back to find the answer. They solve
they have the same number.
problems, including doubling, halving and
• Create opportunities for children to separate
sharing.
objects into unequal groups as well as equal
groups.
BIG MATHS ‘Learn Its’
Term 1
1 + 1 = 2, 2 +2 = 4
Term 2
5 + 5 = 10, 4 + 4 = 8, 3 + 3 = 6
Term 3
2 + 1 = 3, 2 + 3 = 5
(to prepare for inverse – switchers)
Say multiples of 10
EYFS vocabulary
Twenty….nineteen…..eighteen ….to zero, hundred…ninety…..eighty….to zero, count, count back (from, to) count in ones, twos... tens..., how
many times? Even. Pair, pattern, estimate ,halve, sort, equal, sets of, share
DIVISION STEPS
Year 1
 Count on or back in ones, twos, fives and tens and use this knowledge to derive the multiples of 2, 5 and 10 to the tenth multiple
 Solve one step practical problems involving division of 2, 5 or 10 with support
Mental Methods
Practical Methods
Doubling and Halving
Find half of even numbers to 12, including it is hard to halve odd numbers
Begin to count in 2s, 5s, and 10s
Spider counts in tens (the ones stay the same)
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
Grouping
Begin to use visual and concrete arrays and ‘sets of’ objects to find the answers to such
questions as ‘How many towers of 3 can I make with twelve cubes?’
Sharing
Find half of even numbers by sharing
E.g. find half of 14 cubes by giving one each repeatedly to two children
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Key Vocabulary
problem, solution, calculate, calculation, number sentence, answer, method,
explain, money, coin, pence, penny, pound, pay, change, buy, sell, price, spend,
number sequences, count back (from, to) in ones, twos...fives….. tens...less, few,
many, odd, even, how many times? pair, multiple, half, halves, share
DIVISION STEPS
Year 2
 Count on or back in ones, twos, threes, fives and tens and use this knowledge to derive the multiples of 2,3, 5 and 10 to the tenth
multiple
 Solve problems involving division
 Calculate mathematical statements for division and write them using the ÷ and = signs
 Show that division of one number by another cannot be done in any order (commutative)
Mental Methods
Count in 2s, 5s and 10s
Practical/Written Methods
Say how many rows in a given array
e.g. How many rows of 5 are in an array of
3 × 5?
Doubling and Halving
Find half of numbers up to 40 realising that half of and odd number gives a
remainder of 1 or an answer containing a half
E.g. half of 11
Begin to count in 3s
Using fingers, say where a given number is in the 2s, 5s or 10s count
e.g. 8 is the fourth number when I count in 2s
Relate division to grouping
e.g. How many groups of 5 in 15?
Grouping
Relate division to multiplication by using arrays or towers of cubes to find
answers to division.
e.g. How many towers of five cubes can I make from fifteen cubes?
_ x 5 = 15 and also as 15 ÷ 5 = _
Begin to halve numbers to 40 and multiples of 10 to 100
Find 1/2, 1/3, 1/4 and 3/4 of a quantity of objects and of amounts
(whole number answers)
24 divided into groups (chunks) of 6.
There are 4 groups of 6 in 24.
Using Number Facts
Sharing
Begin to find a quarter of a quantity using sharing
Know half numbers to 24
Know x2, x5, x 10 division facts
Begin to know x3 division facts
÷ = signs and missing numbers
(Switchers and Fact Families- Big Maths)
6÷2=
=6÷2
6÷=3
3=6 ÷
÷2=3
3=÷2
÷=3
3=÷
2x3=6
3x2=6
e.g. find a quarter of 16 by sorting the piles into four piles
Find ½, ¼, ¾ of small quantities
Key Vocabulary (Y2)
calculate, calculation, inverse, answer, explain, method, sign, operation, symbol, number sentence, number line, mental calculation,
written calculation, informal method, jottings, diagrams, pictures, images, grouping, halve, share, share equally, one each, two each,
three each... group in pairs, threes... tens , equal groups of, ÷ sign, divide, divided by, divided into, left ,left over, remainders
DIVISION STEPS
Year 3
 Recall and use division facts for the 2, 3, 4, 5, 8 and 10 times-tables
 Divide two-digit numbers by one -digit numbers
 Solve problems, including missing number problems with positive integer scaling problems and correspondence problems which n
objects are connected to m objects
Mental Methods
Know by heart all the division facts
derived from the ×2, ×3, ×4, ×5, ×8 and
×10 tables
Written Methods
Perform divisions just above the 10th multiple using horizontal or vertical jottings and understanding
how to give a remainder as a whole number
e.g. 41 ÷ 4 = 10 r1
Divide whole numbers by 10 or 100 to give
whole number answers
+40
+1
10 groups
Recognise that division is not commutative
e.g. 16 ÷ 8 does not equal 8 ÷ 16
Use place value and number facts in
mental division
e.g. 84 ÷ 4 is half of 42
Divide larger numbers mentally by
subtracting the 10th multiple as
appropriate, including those with
remainders
e.g. 57 ÷ 3 is 10 + 9 as 10 × 3 = 30 and
9 × 3 = 27
Halve even numbers to 100, halve odd
numbers to 20
78
35
4
39
Use division facts to find unit fractions of quantities and begin to find non-unit fractions of quantities
e.g. ¾ of 48 is 3 x (48 ÷ 4)
Halve even numbers up to 50 and multiples of 10 to 100.
Perform divisions within the tables including those with remainders
e.g. 16 ÷ 3
0
3
6
9
12
15 16
Relate division to multiplication with missing digits
e.g.
x 5 = 30 is the same calculation as 30 ÷ 5 = ?
Key Vocabulary
problem, solution, calculate, calculation, inverse, answer, method, explain, predict, estimate, reason,
operation, symbol, number sentence, equation, mental calculation, written calculation, informal method,
jottings, number line, pound ( ), penny/pence (p), note, coin, units of measurement and their
abbreviations, share, share equally ,one each, two each, three each. group in pairs, threes... tens , equal
groups of ,÷ sign, divide, division , divided by, divided into, left, left over, remainder, inverse
DIVISION STEPS
Year 4
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

Recall and derive division facts up to 12 × 12
Use place value, known and derived facts to divide mentally, including x by 0 and 1
Recognise and use factor pairs and commutativity in mental calculations
Mental Methods
Know by heart all the division facts up to
144 ÷ 12
Divide whole numbers by 10, 100, to give
whole number answers or answers with 1
decimal place
Divide multiples of 100 by 1-digit numbers
using division facts
e.g. 3200 ÷ 8 = 400
Use place value and number facts in
mental division
e.g. 245 ÷ 20 is half of 245 ÷ 10
Divide larger numbers mentally by
subtracting the 10th or 20th multiple as
appropriate
e.g. 156 ÷ 6 is 20 + 6 as 20 × 6 = 120 and
6 × 6 = 36
Written Methods
Use a written method to divide a 2-digit or a 3-digit number by a 1-digit number
Numberline chunking e.g. 64 ÷ 4 =
10 groups of 4
0
Column Chunking
e.g. 64 ÷ 4 = 16
65
3
68
Begin to halve amounts of money
e.g. half of £52·40 is £26·20
40
1 group of 4 = 16 groups of 4
60
64
64
- 40 (10 groups of 4)
24
- 20 ( 5 groups of 4)
4
- 4 ( 1 group of 4)
0
Short division method 98 ÷ 7 = 14
53 ÷ 4 = 14 r 2 ( Give remainders as whole numbers)
Refer to
as a ‘chocolate box’ (There are 98 chocolates in a box to share between 7 people. How
many will they get each?)
e.g.
Find halves of even numbers to 200 and
beyond using partitioning
136
5 groups of 4
14
7 9 28
1 4r2
4 5 18
Begin to reduce fractions to their simplest forms e.g. 6/9
=
2
/3 or ¼
Find unit and non-unit fractions of larger amounts e.g. 7/8 of 56 is 7 x (56 ÷ 8)
Divide whole numbers by 10 and 100 to give whole number answers or answers with 1 decimal place
e.g. 643 ÷ 10 = 64.3
Find unit fractions of amounts e. g. 2/3 of 60 = 40
Key Vocabulary (Y4)
calculate, calculation, equation, operation, symbol, inverse, answer, method, explain, predict, reason, reasoning, pattern, relationship,
decimal, decimal point, decimal place, pound ( ), penny/pence (p), units of measurement and abbreviations, degrees Celsius
share, share equally ,halve, one each, two each, three each... group in pairs, threes... tens ,equal groups of, divide, division, divided by,
divided into, divisible by, remainder, factor, quotient, inverse
DIVISION STEPS
Year 5
 Identify multiples and factors
 Know and use vocabulary of prime numbers, prime factors and composite(non-prime number)
 Divide numbers mentally using known facts
 Divide numbers up to 4 digits by a 1-digit number using formal written method of short division and interpret remainders
appropriately for the context
 Divide whole numbers involving decimals by 10, 100 and 1000
 Solve ÷ problems using knowledge of factors and multiples, squares and cubes
 Solve ÷ problems including scaling by simple fractions and problems involving simple rates
Mental Methods
Know by heart all the division facts up to
144 ÷ 12
Divide whole numbers by 10, 100, 1000,
10 000 to give whole number answers or
answers with
1, 2 or 3 decimal places
Use doubling and halving as mental division
strategies
e.g. 34 ÷ 5 is (34 ÷ 10) × 2
Use knowledge of multiples and factors, as
well as tests for divisibility, in mental division
e.g. 246 ÷ 6 is 123 ÷ 3
e.g. We know that 525 divides by 25 and
by 3
Halve amounts of money by partitioning
e.g. 1/2 of £75·40 = 1/2 of £75 (£37·50) plus
half of 40p (20p) which is £37·70
Divide larger numbers mentally by
subtracting the 10th or 100th multiple as
appropriate
e.g. 96 ÷ 6 is 10 + 6, as 10 × 6 = 60 and
6 × 6 = 36
e.g. 312 ÷ 3 is 100 + 4 as 100 × 3 = 300 and
4 × 3 = 12
Know tests for divisibility by 2, 3, 4, 5, 6, 9
and 25
Written Methods
Short division of 3- and 4-digit numbers by 1-digit numbers
e.g. 145 ÷ 4
3 6r1
4 1 425
Give remainders as whole numbers or as fractions
Find non-unit fractions of large amounts
e.g. 3/5 of 265 is 3 x (265 ÷ 5) = 159
Choose the most efficient method in any given situation
Divide whole numbers by 10, 100 or 1000 to give answers with up to 1 decimal place
Use an efficient written method to divide numbers ≤ 1000 by 1-digit numbers
Know square numbers and cube numbers
Reduce fractions to their simplest form
Key Vocabulary (Y5)
calculate, calculation, equation, operation, symbol, inverse, answer, method, strategy, explain, predict, reason, reasoning, pattern,
relationship, decimal, decimal point, decimal place, estimate, approximate, pound ( ), penny/pence (p), units of measurement and
abbreviations, degrees Celsius
share, share equally , halve, one each, two each, three each... group in pairs, threes... tens, equal groups of, divide, divided by, divided
into, divisible by, remainder, factor, quotient, divisible by, inverse
DIVISION STEPS
Year 6
 Divide numbers up to 4 digits by a 2-digit whole number using formal method of long division or short division, and interpret
remainders as whole number remainders, fractions, or by rounding up or down appropriately
 Identify common factors, common multiples and prime numbers
 Use knowledge of the order of operations to carry out calculations involving the four operations
 Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
 Multiply simple pairs of proper fractions, writing the answer in the simplest form
 Divide numbers by 10, 100 and 1000 giving answers to 3 decimal places
 Divide proper fractions by a whole number
Mental Methods
Know by heart all the division facts up to
144 ÷ 12
Divide whole numbers by powers of 10 to give whole
number answers or answers with up to
3 decimal places
Identify common factors, common multiples and primes
numbers and use factors in mental division
e.g. 438 ÷ 6 is 219 ÷ 3 which is 73
Use tests for divisibility to aid mental calculation
Use doubling and halving as mental division strategies, for
example to divide by 2, 4, 8, 5, 20 and 25
e.g. 628 ÷ 8 is halved three times:
314, 157, 78·5
Divide 1- and 2-place decimals by numbers up to and
including 10 using place value
e.g. 2·4 ÷ 6 = 0·4
e.g. 0·65 ÷ 5 = 0·13
e.g. £6·33 ÷ 3 = £2·11
Halve decimal numbers with up to 2 places using
partitioning
e.g. Half of 36·86 is half of 36 (18) plus half of 0·86
(0·43)
Know and use equivalence between simple fractions,
decimals and percentages, including in different contexts
Recognise a given ratio and reduce a given ratio to its
lowest terms
Written Methods
Use short division to divide a number with up to 4 digits by a 1-digit or a 2-digit number
e.g. 145 ÷ 4
3 6r1
4 1 425
Use long division to divide 3-digit and 4-digit numbers by 2-digit numbers
e.g. 4176 ÷ 13
300 + 20 + 1, r1
4176 ÷ 13 = 321 r 3
13 4176
- 3900
276
- 260
16
-13
3
Give remainders as whole numbers or as fractions or as decimals
Use place value to divide a 1-place or a 2-place decimal number by a number ≤ 12 using
multiples of the divisors
e.g. 3· 65 ÷ 5 as (365 ÷ 5) ÷ 100 = 0·73
Divide proper fractions by whole numbers
Use an efficient written method, involving subtracting powers of 10 times the divisor, to
divide any number of up to 1000 by a number ≤ 12
e.g. 836 ÷ 11 as 836 – 770 (70 × 11) leaving 66 which is 6 × 11, giving the answer 76
Key Vocabulary (Y6)
calculate, calculation, equation, operation, symbol, inverse, answer, method, strategy, explain, predict, reason, reasoning, pattern,
relationship, decimal, decimal point, decimal place, estimate, approximate, pound ( ), penny/pence (p), units of measurement and
abbreviations, degrees Celsius, halve, share, share equally, one each, two each, three each... group in pairs, threes... tens, equal
groups of, divide, division, divided by, divided into, remainder, factor, quotient, divisible by, inverse, integer