Revision 6: Multiplication and division
Year 6 Summer 6
Multiply and divide whole numbers and decimals mentally by 10, 100 or 1000
Previous learning
Core for Year 6
Extension
Understand, read and begin to write these words:
Understand, read and begin to write these words:
Understand, read and write these words:
times, multiply, multiplied by, product, …
divide, divided by, group, share, … double, halve, …
times, multiply, multiplied by, product, …
divide, divided by, group, share, quotient, … double, halve, …
times, multiply, multiplied by, product, …
divide, divided by, group, share, quotient, …double, halve, …
Multiply whole numbers by 10 or 100, and respond to oral
questions such as:
Multiply and divide whole numbers by 10, 100 or 1000,
including decimal answers for division, and respond to oral
questions such as:
Multiply and decimals by 10, 100 or 1000, and respond to oral
questions such as:
• Multiply thirty-one by ten.
• What is sixty-five multiplied by one hundred?
• What is nought point two five multiplied by one hundred?
• Divide three hundred by ten.
• Divide eight thousand four hundred by one hundred.
• What is six point two multiplied by one thousand?
• Divide nine hundred and twenty by ten.
• What is three thousand divided by twenty?
• What is seven point five divided by one hundred?
• What is four hundred divided by one hundred?
• Divide twenty-three by one hundred.
• Divide thirty-one point five by ten.
Multiply two-digit numbers, including decimals, by single-digit numbers, using mental methods, with jottings where appropriate
Previous learning
Core for Year 6
Extension
Recall and use strategies to remember all multiplication and
division facts for tables 2–10, e.g.
Multiply a two-digit number by a single-digit number by
partitioning, e.g.
Multiply a three-digit number by a single-digit number by
partitioning, e.g.
• Use the inverse relationship between multiplication and
division, so if 7 × 9 = 63, then 63 ÷ 9 = 7.
• 47 × 6
• 238 × 4
• 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.
Estimate: 50 × 6 = 300
Use jottings to show working and explain the calculation.
×
40
7
6
240
42
• Use relationships between tables, e.g. 8s are double 4s,
7s are 5s plus 2s.
282
Answer: 282
or 47 × 6 = (40 × 6) + (7 × 6) = 240 + 42 = 282
Use knowledge of multiplication facts and place value to:
Multiply a multiple of 10 to 90 by a single-digit number, e.g.
40 × 3 = 3 × 4 × 10 = 12 × 10 = 120
Multiply a multiple of 100 to 900 by a single-digit number, e.g.
400 × 3 = 3 × 4 × 100 = 12 × 100 = 1200
Multiply a pair of multiples of 10 to 90, e.g.
30 × 40 = 3 × 10 × 4 × 10 = 12 × 100 = 1200
© 1 | Year 6 | Summer TS6 | Revision 6: Multiplication and division
Estimate: 200 × 4 = 800
Use a grid to show working.
×
200
30
8
4
800
120
32
952
If necessary, record the addition vertically.
Answer: 952
Use knowledge of multiplication facts, place value and
partitioning to multiply decimals by a single-digit number, e.g.
Use knowledge of multiplication facts and place value to
multiply decimals by a single-digit number, e.g.
• 0.8 × 7 = (8 × 7) ÷ 10
= 56 ÷ 10
= 5.6
• 0.08 × 7 = (8 × 7) ÷ 100
= 56 ÷ 100
= 0.56
• 3.8 × 3 = (3 + 0.8) × 3
= (3 × 3) + (0.8 × 3)
= 9 + 2.4
= 11.4
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Previous learning
Core for Year 6
Extension
Respond to oral questions such as:
Respond to oral or written questions such as:
Respond to oral or written questions such as:
• Multiply six by seven.
• What is nought point eight multiplied by five?
• What is eight multiplied by seven?
• It costs 35p for a child to go swimming.
How much does it cost for 4 children?
• A book costs five pounds and ninety-nine pence.
What is the total cost of three of these books?
• What is nine times four?
• What is thirty multiplied by seven?
• What is nine multiplied by three hundred?
• What is thirty times forty times ten?
• Lollies cost 24p each. How much do 8 lollies cost?
• Oranges cost 15p each. I buy four oranges.
How much change do I get from a £2 coin?
• Divide six hundred by twenty.
• Mark has 24 stickers. James has four stickers for every
one of Mark’s. How many stamps does James have?
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 two-digit whole
numbers and decimals and derive corresponding halves, e.g.
• Double 67 = double 60 + double 7
= 120 + 14
= 134
• Use double 67 = 134 to work out:
double 670 = 1340
double 6.7 = 13.4
double 0.67 = 1.34
• Half of 56
• Use half of 56 = 28 to work out:
half of 560 = 280
half of 5.6 = 2.8
half of 0.56 = 0.28
= half of 50 + half of 6
= 25 + 3
= 28
Respond to oral questions such as:
Respond to oral questions such as:
• Multiply 91 by 2.
• Double 2.9.
• What is double 67?
• Multiply 8.7 by 2.
• Calculate half of 58.
• How much is half of £9.50?
© 2 | Year 6 | Summer TS6 | Revision 6: Multiplication and division
• A printer costs £245. What do three printers cost?
• A recipe for a cake uses 135 g sugar. Joe bakes 4 cakes.
How much sugar does he use?
• 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
Multiply three- and two-digit numbers by two- and single-digit numbers using written methods
Previous learning
Core for Year 6
Extension
Multiply a three-digit by a single-digit number, e.g.
Multiply a four-digit by a single-digit number, e.g.
Multiply a sum of money such as £6.38 by a single-digit
number, e.g.
• 238 × 4
• 2638 × 4
• £6.38 × 4
Estimate: 200 × 3 = 800
Use a grid to show working.
Estimate: 3000 × 4 = 12 000
Use a grid to show working.
×
200
30
8
4
800
120
32
952
If necessary, record the addition vertically.
Use a grid to show working.
×
2000
600
30
8
4
8000
2400
120
32
10552
Record the addition vertically.
800
120
+ 32
852
×
£6
30p
8p
4
£24
£1.20
32p
£25.52
If necessary, record the addition vertically.
8000
2400
120
+
32
10552
Answer: 852 (close to the estimate)
£.00
24.00
1.20
+ 0.32
25.52
Answer: 10 552 (close to the estimate)
Multiply a two-digit by a two-digit number, e.g.
Multiply a three-digit by a two-digit number, e.g.
• 27 × 32
• 126 × 23
Estimate: 30 × 30 = 900
Estimate: £6 × 4 = £24
Answer: £25.52 (close to the estimate)
Estimate: 100 × 20 = 2000
Use a grid to show working.
Use a grid to show working.
×
20
7
×
100
20
6
30
600
210
810
20
2000
400
120
2520
2
40
14
54
3
300
60
18
378
864
Answer: 864 (close to the estimate)
2898
Answer: 2898, which is fairly close to the estimate
Divide two-digit numbers, including decimals, by single-digit numbers, using mental methods, with jottings where appropriate
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
divide decimals by a single-digit number, e.g.
Use knowledge of multiplication facts and place value to
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.
4.8 ÷ 6 = (48 ÷ 6) ÷ 10
= 8 ÷ 10
=0.8
0.48 ÷ 6 = (48 ÷ 6) ÷ 100
= 8 ÷ 100
= 0.08
• Use relationships between tables, e.g. 8s are double 4s,
7s are 5s plus 2s.
© 3 | Year 6 | Summer TS6 | Revision 6: 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 6
Extension
Use knowledge of multiplication and division facts and place
value to respond to oral questions such as:
Use chunking on the ENL to divide two-digit numbers by
single-digit numbers, including those with a remainder, e.g.
Use chunking on the ENL to divide three-digit numbers by
single-digit numbers, including those with a remainder, e.g.
• How many sixes are there in forty-two?
• 58 ÷ 4
Estimate: 10 fours are 40 and 20 fours are 80, so 58 ÷ 4
lies between 10 and 20.
• 112 ÷ 4
Estimate: 20 fours are 80 and 30 fours are 120, so 112 ÷ 4
lies between 20 and 30.
• What must I multiply eight by to get seventy-two?
• What is fifty-six divided by eight?
• How many five pence coins do you get for forty-five pence?
• What is the remainder when thirty-two is divided by five?
58
–40
18
–16
2
• Divide three hundred by ten.
• How many sevens are there in six hundred and thirty?
• How many threes are there in two hundred and ten?
• How many forties are there in eight hundred?
112
–80
32
–32
0
10 fours
4 fours
14 fours
Answer: 58÷ 4 = 14 r 2, close to the estimate.
20 fours
8 fours
28 fours
Answer: 112 + 4 = 28, close to the estimate.
• Some friends share £96. They each get exactly £6.
How many friends share the money?
• A bottle of sauce holds 125 ml. A teaspoon holds 5 ml.
How many teaspoons of sauce are in the bottle?
• A box holds 4 cakes. 96 cakes are packed into boxes.
How many boxes are filled with cakes?
• A bag has 110 marbles in it. As many children as possible
take 8 marbles each. How many marbles are left over?
• A large box holds 75 biscuits. 1 biscuit in every 5 is ginger.
How many of the biscuits are ginger?
• David needs 126 balloons. The shop sells balloons in
packs of 7. How many packs does he need to buy.
Divide three- and two-digit numbers by two- and single-digit numbers using written methods
Previous learning
Core for Year 6
Extension
Divide a three-digit number by a one-digit number on an ENL,
extending to divisions with a remainder, e.g.
Divide a three-digit number by a two-digit number on an ENL,
e.g.
Use a column method to divide a three-digit number by a onedigit number, extending to divisions with a remainder, e.g.
• 138 ÷ 6
Estimate: 20 sixes are 120 and 30 sixes are 180, so there
are between 20 and 30 sixes in 140.
• 368 ÷ 16
Build up multiples of 16 and 160:
16 × 1 = 16
16 × 10 = 160
16 × 2 = 32
16 × 20 = 320
16 × 3 = 48
16 × 30 = 480
• 370 ÷ 16
Build up multiples of 16 and 160
Answer: 23
• 140 ÷ 6
Answer: 23 r 2
© 4 | Year 6 | Summer TS6 | Revision 6: Multiplication and division
Estimate: 20 sixteens are 320 and 30 sixteens are 480, so
there are between 20 and 30 sixteens in 370.
370
Estimate: 20 sixteens are 320 and 30 sixteens are 480, so
there are between 20 and 30 sixteens in 370.
Answer: 23
20
× 16
–48
3
× 16
2
23
–320
50
Answer: 23 r 2
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Choose mental, written or calculator methods to work out multiplication and division calculations, including solving word problems
Previous learning
Core for Year 6
Extension
Understand that once you have decided on the calculation to
do it can be worked out by any efficient method.
Understand that once you have decided on the calculation to
do it can be worked out by any efficient method.
When working without a calculator, decide how to work out
calculations such as:
When working without a calculator, decide how to work out
calculations such as:
When working without a calculator, decide how to work out
calculations such as:
423 × 4
50 × 60
2.1 × 4
132 ÷ 11
12000 ÷ 30
45 × 59
• 143 × 37
£4.27 × 3
58 × 6
£190 ÷ 5
£36.64 ÷ 8
504 ÷ 21
848 ÷ 16
• 900 ÷ (45 × 4)
72 ÷ 3
2000 ÷ 100
91 ÷ 7
924 ÷ 22
31.6 × 7
509 × 24
• 50 ÷ … = 2.5
When calculators are available, choose to use a calculator,
or a written or mental method to solve problems such as:
When calculators are available, choose to use a calculator,
or a written or mental method to solve problems such as:
When calculators are available, choose to use a calculator,
or a written or mental method to solve problems such as:
• A fruit pie costs 55p.
What is the cost of 8 fruit pies?
• A yogurt costs 45p.
How many yogurts can you buy for £5?
• Write in the missing number.
• Rachel saves £13.25 each week.
How much has she saved after 6 weeks?
• Suki pays £16.20 to travel to work each week.
She works for 45 weeks each year.
How much does she pay to travel to work each year?
• A DVD costs £12.45.
What do four of these DVDs cost?
• Jack has £50.
He buys 3 flowerpots at £12.75 each.
How much change does he get?
• There are 12 eggs in a box.
How many eggs are there in 26 boxes?
• There is space in the car park for 17 rows of 32 cars.
How many cars can park?
• A museum charges an entrance fee of £1.20.
60 people paid the entrance fee on Monday.
How much money is that altogether?
• A shop sells trees for £9 each.
Julian has £250.
He wants to buy as many trees as possible.
How many trees can he buy?
• The entrance fee for a car boot sale is 50p for adults and
30p for children.
100 adults and 80 children pay to go in.
How much money do they pay altogether?
• Trees cost £17 each. Louise has £250.
She wants to buy as many trees as possible.
How many trees can Louise buy?
• One shelf holds 32 books.
A library has 142 shelves filled with books.
How many books does the library have?
568.1 ÷ F = 24.7
• The cost for using a minibus is £1.36 for each kilometre.
8 friends go on a 114 kilometre journey.
They share the cost equally.
How much does each person pay?
• Write two decimals, each less than 1, which multiply to
make 0.1.
F × F = 0.1
• How much less than 1000 is 9.7 × 9.8 × 9.9?
• Find the multiple of 45 that is closest to 8000.
Show your method.
• Calculate:
• A box contains 125 matches.
How many matches are there in 24 boxes?
• A packet contains 1.5 kilograms of guinea pig food.
Ismat feeds her guinea pig 30 grams of food each day.
How many days does the packet of food last?
• Dan could buy a season ticket that would let him travel for
45 weeks each year. It would cost £630.
How much is that each week?
© 5 | Year 6 | Summer TS6 | Revision 6: Multiplication and division
49.3 × (2.06 + 8.5) = F
1.2 × (1.3 + 1.4) × 1.5
• Which two of these numbers, when multiplied together,
have the answer closest to 70?
7.4
8.1
9.4
10
• Leila knows that 65 × 3 = 195.
Explain how she can use this information to find the
answer to 165 × 3.
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Use division to check multiplication and multiplication to check division
Previous learning
Core for Year 6
Extension
Check the answer to an multiplication using division, e.g.
Use a calculator to check multiplication with division, e.g.
Use a calculator to check multiplication with division, e.g.
• Check 65 × 32 = 2080 with
2080 ÷ 32 = 65.
• Check 11.72 × 5 = 58.6 with
58.6 ÷ 5 = 11.72
• Check £67.86 × 5 = £339.30 with
£339.30 ÷ 5 = £67.86.
Check the answer to a division using multiplication, e.g.
Use a calculator to check division with multiplication, e.g.
Use a calculator to check division with multiplication, e.g.
• Check 456 ÷ 3 = 152 with
152 × 3 = 456.
• Check 897÷ 23 = 39 with
39 × 23 = 897
• Check £1488 ÷ 31 = £48 with
£48 × 31 = £1448.
© 6 | Year 6 | Summer TS6 | Revision 6: Multiplication and division
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999