Mental multiplication and division
Year 6 Spring 3
Recognise multiples of 2 to 10 up to the 10th multiple
Previous learning
Core for Year 5
Extension
Use, and read these words:
Use, read and begin to write these words:
Use, read and write these words:
times, multiply, multiplied by, product, multiple, …
divide, divided by, group, share, divides exactly by, factor,
divisor, divisible by, test of divisibility, …
double, halve, …
times, multiply, multiplied by, product, multiple, prime, …
divide, divided by, group, share, quotient, divides exactly by,
factor, divisor, divisible by, test of divisibility, …
double, halve, …
times, multiply, multiplied by, product, multiple, prime, …
divide, divided by, group, share, quotient, divides exactly by,
factor, divisor, divisible by, test of divisibility, …
double, halve, …
Recognise multiples of 2 to 10 up to the tenth multiple, e.g.
Recognise multiples of 2 to 10 up to the tenth multiple, e.g.
Recognise multiples of 2 to 10 beyond the 10th multiple, e.g.
• Chant and recognise sequences of multiples to the tenth
multiple, e.g. multiples of 6:
• Chant and recognise sequences of multiples to the tenth
multiple, e.g. multiples of 6:
• Chant and recognise sequences of multiples to at least the
tenth multiple, e.g.
6, 12, 18, 24, 30, … 60.
• Recognise that all multiples:
of 10 end in 0 and of 5 end in 0 or 5
of 2 end in 0, 2, 4, 6, 8
of 9 have a digit sum of 9
of 3 have a digit sum of 3, 6 or 9.
7, 14, 21, 28, 35, … 70, 77, 84, …
6, 12, 18, 24, 30, … 60.
• Recognise that the units digit in the sequence of multiples:
multiples of 5 and 6
of 10, is always 0;
of 5, alternates between 0 and 5
of 2, cycles through 2, 4, 6, 8, 0
of 4, cycles through 4, 8, 2, 6, 0
of 9, decreases by 1 each time
of 8, decreases by 2 each time
of 7, decreases by 3 each time
of 6, decreases by 4 each time.
Patterns of the
units digits
in multiples of 4
• Recognise patterns of multiples of 2 to 10 on a 100-square,
e.g.
• Investigate patterns of multiples on a multiplication square,
e.g. multiples of 4.
Multiples of 3 („)
Multiples of 4 („)
© 1 | Year 6 | Spring TS3 | Mental multiplication and division
• Investigate patterns in the sums of multiples, e.g.
5
10
15
20
25
30
35
40
45
50
6
12
18
24
30
36
42
48
54
60
11
22 33 44
multiples of 3 and 7
55
66
77
88
99
110
30
3
6
9
12
15
18
21
24
27
7
14
21
28
35
42
49
56
63
70
10
20
30
40
50
60
70
80
90
100
Predict the sequence of the sum of multiples of 7 and 8.
• Recognise patterns in the last two digits of multiples of
100, 50 or 25.
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Find common multiples
Previous learning
Core for Year 6
Extension
Recognise multiples of 2 to 10 up to the tenth multiple, e.g.
Find common multiples, e.g.
Identify common multiples, e.g.
• Chant and recognise sequences of multiples to the tenth
multiple, e.g. multiples of 6:
• Generate the sequences of multiples of 2 (top row) and
multiples of 3 (bottom row). Scan the sequences to identify
the numbers in common (i.e. the common multiples).
• Sort the multiples of two different number on a Venn
diagram to identify their common multiples, e.g.
6, 12, 18, 24, 30, … 60.
• Recognise patterns in the digits of sequences of multiples.
2
4
6
8
10
12
14
16
18
20
3
6
9
12
15
18
21
24
27
30
This diagram shows the set of numbers from 1 to 25.
6, 12 and 18 are common multiples of 2 and 3.
• Recognise patterns of multiples on a 100-square, and that:
multiples of 4 are also multiples of 2
multiples of 6 are also multiples of 3 and of 2
multiples of 8 are also multiples of 4 and of 2
multiples of 9 are also multiples of 3
multiples of 10 are also multiples of 5 and of 2
• Find the smallest number that is a common multiple of two
numbers such as:
8 and 12
12 and 16
6 and 15
Multiples of 4 („)and multiples of 8 („)
© 2 | Year 6 | Spring TS3 | Mental multiplication and division
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Know and apply tests of divisibility by 2, 3, 4, 5, 6, 9, 10, 25, 50, 100 and 1000
Previous learning
Core for Year 6
Extension
Know and use tests of divisibility by 2, 3, 5, 9, 10 and 100.
Know and use tests of divisibility by 2, 3, 4, 5, 6, 9 and 10,
and 25, 50, 100, 1000, e.g.
Test a larger number by applying a test of divisibility for each
of a pair of factors of the number, e.g.
• Count in 50s to 1000 and in 25s to 500, then back.
Write three different multiples of 50. Of 25.
How can you recognise multiples of 50? Of 25?
• Test a number for divisibility by 15 by testing it for
divisibility by 5 and divisibility by 3.
• Know that a whole number divides exactly by:
– 100 if it ends in 00
– 10 if it ends in 0
– 5 if it ends in 0 or 5
• Know that a whole number divides exactly by:
– 2 if it ends in 0, 2, 4, 6, 8
– 1000 if it ends in 000
– 9 if its digit sum is 9
– 100 if it ends in 00
– 3 if its digit sum is 3, 6 or 9.
– 25 if it ends in 00, 25, 50 or 75
Respond to questions such as:
– 10 if it ends in 0
• Ring the numbers which are divisible by 5:
– 5 if it ends in 0 or 5
15
35
• Test a number for divisibility by 75 by testing it for
divisibility by 25 and divisibility by 3.
52
55
59
95
– 2 if it ends in 0, 2, 4, 6, 8
– 9 if its digit sum is 9
– 3 if its digit sum is 3, 6 or 9.
• Know that a whole number divides exactly by 4 if the last
two digits are divisible by 4, or if half of it is an even
number (i.e. if half of the number is divisible by 2).
• Know that all multiples of 6 are multiples of 2 and multiples
of 3, so that to test for divisibility by 6, test for divisibility by
2 and for divisibility by 3.
© 3 | Year 6 | Spring TS3 | Mental multiplication and division
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Recognise prime numbers up to 20 and find all prime numbers less than 100
Previous learning
Core for Year 6
Extension
Find all the pairs of factors of any number to 30, e.g.
Recognise prime numbers up to 20 and find all prime
numbers less than 100, e.g.
Find the prime factors of any two-digit number, e.g.
• The factor pairs of factors of 12 are:
• Know that a prime number has only one pair of factors,
itself and 1, and that the first few prime numbers are:
Know that, for example:
1 and 12, 2 and 6, 3 and 4,
so 12 = 1 × 12 = 2 × 6 = 3 × 4
Understand that if 12 is a multiple of 2, then 2 is a factor of 12.
2, 3, 5, 7, 11, 13, 17, 19, …
• Test whether two-digit numbers are prime by
systematically using tests of divisibility by the prime
numbers 2, 3, 5, 7.
• Find the primes to 100 using the Sieve of Eratosthenes.
On a 100-square, shade 1, then the multiples of 2 greater
than 2, the multiples of 3 greater than 3, the multiples of 5
greater than 5, and the multiples of 7 greater than 7. The
unshaded numbers are the primes.
15 is not prime, but can be written as the product 3 × 5.
3 and 5 are prime numbers which are factors of 15.
They are called the prime factors of 15.
12 is not prime, but can be written as the product of its
prime factors:
12 = 2 × 2 × 3
Write a number as the product of its prime factors, e.g.
• To write 72 as the product of its prime factors, look for the
smallest prime factor of 72, which is 2.
Divide 72 by 2
72 ÷ 2 = 36
Repeat with the new number (36).
Look for the smallest prime factor of 36, which is 2.
Divide 36 by 2
36 ÷ 2 = 18
Repeat. Look for the smallest prime factor of 18, which is 2.
Divide 18 by 2
18 ÷ 2 = 9
2 is not a factor of 9, so pick the next smallest prime
number (3) to see if it is a factor of 9.
Non-prime numbers („)
© 4 | Year 6 | Spring TS3 | Mental multiplication and division
Divide 9 by 3
9÷3=3
Investigate problems such as:
Repeat with the new number (3).
• Find some prime numbers which, when their digits are
reversed, are also prime.
Divide 3 by 3
3÷3=1
So 72 = 2 × 2 × 2 × 3 × 3
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Use knowledge of multiplication facts and place value to multiply and divide decimals mentally, e.g. 0.8 × 7, 4.8 ÷ 6
Previous learning
Core for Year 6
Extension
Recall and use strategies to remember all multiplication and
division facts for tables 2–10, e.g.
Use knowledge of multiplication facts and place value to
multiply and divide decimals by a single-digit number, e.g.
Use knowledge of multiplication facts and place value to
multiply and divide decimals by a single-digit number, e.g.
• Use the inverse relationship between multiplication and
division, so if 7 × 9 = 63, then 63 ÷ 9 = 7.
• Use a known fact to work out the next one, e.g. if you know
6 eights are 48, then 7 eights are 48 + 8 = 56.
• Use relationships between tables, e.g. 8s are double 4s,
7s are 5s plus 2s.
Complete quickly questions such as:
5×7=…
… × 9 = 54
0.8 × 7 = (8 × 7) ÷ 10
= 56 ÷ 10
= 5.6
0.08 × 7 = (8 × 7) ÷ 100
= 56 ÷ 100
= 0.56
4.8 ÷ 6 = (48 ÷ 6) ÷ 10
= 8 ÷ 10
=0.8
0.48 ÷ 6 = (48 ÷ 6) ÷ 100
= 8 ÷ 100
= 0.08
Complete questions such as:
28 ÷ 4 = …
…÷5=8
0.5 × 7 = …
… × 9 = 5.4
Complete questions such as:
2.8 ÷ 4 = …
… ÷ 5 = 0.8
0.05 × 7 = …
… × 9 = 0.54
0.28 ÷ 4 = …
… ÷ 5 = 0.08
Revise multiplying two-digit numbers by single-digit numbers by partitioning, e.g. 47 × 6 = (40 × 6) + (7 × 6)
Previous learning
Core for Year 5
Extension
Multiply a number from 11 to 19 by 2, 3, 4 or 5 by partitioning
the teens number, e.g.
Revise multiplying a two-digit number by a single-digit
number by partitioning, e.g.
Multiply a three-digit by a single-digit number by partitioning
and using a grid, e.g.
• 17 × 3
• 47 × 6
• 238 × 4
Use jottings to record, support and explain the calculation.
Use jottings to record, support and explain the calculation.
17
10
+
7
30
+
21
×3
= 51
Estimate: 50 × 6 = 300
×
40
7
6
240
42
282
Estimate: 200 × 4 = 800
×
200
30
8
4
800
120
32
952
If necessary, record the addition vertically.
Answer: 282
800
120
+ 32
952
Answer: 51
Answer: 852
Solve problems such as:
Solve problems such as:
Solve problems such as:
• Calculate 13 × 3… Work out 18 × 5… Multiply 16 by 4.
• Calculate 28 × 3… Work out 32 × 5… Multiply 15 by 6
• Calculate 328 × 3… Work out 132 × 5… Multiply 236 by 4
• Josh washes some cars using 12 buckets of water.
Each bucket has 5 litres of water.
How many litres of water does he use altogether?
• It costs 35p for a child to go swimming.
How much does it cost for 4 children?
• A printer costs £245. What do three printers cost?
• A bus ticket costs 17p. How much do 5 tickets cost?
• Suzy has 11 stamps. Tim has three times as many stamps
as Suzy. How many stamps does Tim have?
© 5 | Year 6 | Spring TS3 | Mental multiplication and division
• Lollies cost 24p each. How much do 3 lollies cost?
• A cake recipe uses 135 g sugar. Jamie bakes four cakes.
How much sugar does he use?
• Mark has 24 stickers.
James has four stickers for every one of Mark’s.
How many stamps does James have?
• Amy has 317 stamps in his album.
Jade has two stamps for every one of Amy’s.
How many stamps does Jade have?
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Use brackets
Previous learning
Core for Year 6
Extension
Begin to know that brackets determine the order of
operations, and that their contents are worked out first, e.g.
Know there are rules that tell us which operations to do first.
Know there are rules that tell us which operations to do first.
• If brackets appear, work out the value of the expression in
the brackets first, e.g.
• Work out the operations in this order:
• If brackets appear, work out the value of the expression in
the brackets first, e.g.
5 × (4 + 3)
=5×7
= 35
Do the brackets first.
Then the multiplication.
Answer: 35.
(4 + 6) ÷ (5 – 3)
= 10 ÷ 2
=5
Do the brackets first.
Then the division.
Answer: 5
• If there are no brackets, do multiplication and division
before addition and subtraction no matter where they come
in an expression, e.g.
5+6×7
= 5 + 42
= 47
Do the multiplication first.
Then the addition.
Answer: 47
Brackets
2
Indices, which are powers of numbers, such as 5
Multiplication and division
Addition and subtraction
• If there are no brackets or indices, do multiplication and
division before addition and subtraction no matter where
they come in an expression.
• If an expression has only addition and subtraction then
work from left to right to work it out.
Interpret calculations involving brackets, using a calculator
where appropriate, e.g.
Interpret calculations involving brackets, using a calculator
where appropriate, e.g.
Interpret calculations involving brackets, using a calculator
where appropriate, e.g.
• Write what the two missing numbers could be.
• Calculate 1.2 × (1.3 + 1.4) × 1.5
• Write the correct sign >, < or = in each box.
(4 + …) × … = 100
• Write in the missing number.
100 – (22.75 + 19.08) = …
(10 + 5) – 9 … (10 + 9) – 5
3 × (4 + 5) … (3 × 4) + 5
(10 × 4) ÷ 2 … 10 × (4 ÷ 2)
© 6 | Year 6 | Spring TS3 | Mental multiplication and division
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999