Mental multiplication and division
Year 5 Summer 3
Recognise multiples of 6, 7, 8 and 9 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:
multiple, divides exactly by, …
multiple, divides exactly by, factor, divisor, divisible by, test of
divisibility, …
prime number, multiple, divides exactly by, factor, divisor,
divisible by, test of divisibility, …
Recognise multiples of 2, 3, 4, 5 and 10 to at least the tenth
multiple, e.g.
Recognise multiples of 6, 7, 8 and 9 up to the tenth multiple,
e.g.
Recognise multiples of 2 to 10, e.g.
• Chant and recognise sequences of multiples to at least the
tenth multiple, e.g. multiples of 4:
• 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.
4, 8, 12, 16, 20, … 40 …
• 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.
• Recognise the patterns of multiples of 2, 3, 4, 5 and 10 on
a 100-square.
7, 14, 21, 28, 35, … 70, 77, 84, …
6, 12, 18, 24, 30, … 60.
• Recognise that in the sequences of multiples:
of 9, the units digit decreases by 1 each time
of 8, the units digit decreases by 2 each time
of 7, the units digit decreases by 3 each time
of 6, the units digit decreases by 4 each time
• Recognise the patterns of multiples of 6, 7, 8 and 9 on a
100-square, and that:
• Look at patterns of digits,
e.g. the units digits
of multiples of 4.
• Investigate patterns of multiples on a multiplication square,
e.g. multiples of 4.
multiples of 9 are also multiples of 3
multiples of 6 are also multiples of 3 and of 2
multiples of 8 are also multiples of 4 and of 2
Multiples of 4 („)
Multiples of 3 („)
Multiples of 4 („)and multiples of 8 („)
© 1 | Year 5 | Summer TS3 | Mental multiplication and division
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Find factors of two-digit numbers
Previous learning
Core for Year 5
Extension
Know that factors occur in pairs, e.g.
Know that factors occur in pairs, e.g.
Know that:
Know that:
• A factor is a number that divides exactly into a bigger
number, e.g.
• Factors occur in pairs so that if 3, say, is a factor of the
number 24, then 24 ÷ 3 = 8 is also a factor of 24.
5 is a factor of 15
because 5 divides exactly 3 times into 15.
• If a number is a multiple of, say, 2, then 2 is a factor of the
number.
6 is not a factor of 15
because 6 does not divide exactly into 15.
• Factors occur in pairs, e.g. since 12 = 3 × 4, both 3 and 4
are factors of 12. The simplest factor pair of any number is
the number itself and 1.
Find factors of two-digit numbers, e.g.
Revise finding factors of two-digit numbers, e.g.
• Find the factor pairs of, say, 20 by arranging 20 counters in
the shape of different rectangles:
• Find the factor pairs of 36 by arranging 36 counters in the
shape of different rectangles.
20 × 1, 10 × 2, 5 × 4
The factor pairs of 36 are:
1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6
There are no other pairs of numbers which have a product
of 20.
The nine factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
So the six factors of 20 are 1, 2, 4, 5, 10 and 20.
• Make a ‘factor finder’.
By colouring factors on a grid, show for example that
factors of 6 are also factors of 12.
Recognise prime numbers up to 20 and find all prime
numbers less than 100, e.g.
• Know that a prime number has only one pair of factors,
itself and 1, and that the first few prime numbers are:
2, 3, 5, 7, 11, 13, 17, 19, …
© 2 | Year 5 | Summer TS3 | Mental multiplication and division
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Find common multiples, e.g. of 6 and 9
Previous learning
Core for Year 5
Extension
Find common multiples, e.g.
Identify common multiples, e.g.
• 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.
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.
• Colour multiples of 2 and of 3 in different colours on a 100square. Identify the common multiples (the squares shaded
in both colours). Identify these as multiples of 6.
• 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 2 („)and multiples of 3 („)
Double multiples of 10 to 1000 and multiples of 100 to 10 000, e.g. double 760, double 7600, and derive the corresponding halves
Previous learning
Core for Year 5
Extension
Use known facts and partitioning to derive doubles of
numbers 1 to 100, and derive corresponding halves, e.g.
Use patterns of similar calculations to double multiples of 10
to 500 or multiples of 100 to 5000, and derive corresponding
halves, e.g.
Use patterns of similar calculations to double multiples of 10
to 1000 or multiples of 100 to 10 000, and derive
corresponding halves, e.g.
• Double 38 = double 30 + double 8
= 60 + 16
= 76
• Use double 38 is 76 to work out:
double 380 is 760
double 3600 is 7600
• Use double 67 is 152 to work out:
double 760 is 1520
double 7600 is 15200
• Half of 94
• Use half of 94 is 47 to work out:
half of 940 is 470
half of 9400 is 4700
• Use half of 184 is 92 to work out:
half of 1840 is 920
half of 18400 is 9200
= half of 90 + half of 4
= 45 + 2
= 47
© 3 | Year 5 | Summer TS3 | Mental multiplication and division
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Previous learning
Core for Year 5
Extension
Respond to questions such as:
Respond to oral questions such as:
Respond to questions such as:
• Suzy has 67 stamps.
Tim has twice as many stamps as Suzy.
How many stamps does Tim have?
• What is half of 860?
• A CD costs £7.60. What do two CDs cost?
• A CD costs £4.60. What do two CDs cost?
• Two paperbacks cost £13.80p.
What does one paperback cost?
• Two paperbacks cost £7.80p.
What does one paperback cost?
• Two biros cost £1.52p.
What does one biro cost?
Multiply by 19 or 21 by multiplying by 20 and adjusting <I would recommend moving this to Y6>
Previous learning
Core for Year 5
Extension
Use knowledge of multiplication facts to multiply a single digit
number by a multiple of 10 to 90, e.g.
Multiply a number by 19 or 21, by multiplying it by 20 and
adding or subtracting the number, e.g.
To multiply a number by 49 or 51, multiply it by 50 and add or
subtract the number, e.g.
• 13 × 21 = (13 × 20) + 13
= (13 × 2 × 10) + 13
= 260 + 13
= 273
• 13 × 51 = (13 × 50) + 13
= (13 × 5 × 10) + 13
= 650 + 13
= 663
• 13 × 19 = (13 × 20) – 13
= (13 × 2 × 10) – 13
= 260 – 13
= 247
• 13 × 49 = (13 × 50) – 13
= (13 × 5 × 10) – 13
= 650 – 13
= 637
8 × 20 = 8 × 2 × 10
= 16 × 10
= 160
Complete questions such as:
9 × 50 = …
60 × … = 120
5 × … = 200
Multiply by 50 by multiplying by 100 and halving and by 25 by multiplying by 100 and dividing by 4
Previous learning
Core for Year 5
Extension
To multiply by 5, multiply by 10 and then halve, e.g.
To multiply by 50, multiply by 100 and then halve, e.g.
• 36 × 5 =36 × 10 ÷ 2
= 360 ÷ 2
= 180
• 36 × 50 = 36 × 100 ÷ 2
= 3600 ÷ 2
= 1800
To multiply by 25, multiply by 100, then divide by 4, e.g.
• 24 × 25 = 24 × 100 ÷ 4
= 2400 ÷ 4
= 600
© 4 | Year 5 | Summer TS3 | Mental multiplication and division
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999