Multiplication and division and word problems
Year 2 Spring 11
Use multiplication and division sentences to describe an array and repeated hops on a number line
Previous learning
Core for Year 2
Extension
Understand these words:
Understand and use these words
Understand and read these words:
lots of, groups of, …
lots of, groups of, times, multiply, divide, …
multiple, times table, …
groups of, times, multiply, multiplied by, divide, divided by,
product, … multiple, times table, …
and understand and use the × and ÷ signs.
and understand and use the × and ÷ signs.
Understand multiplication as repeated addition or hops along
a number line, or as describing an array:
Understand multiplication as repeated addition or as
describing an array, and that:
Understand multiplication as repeated addition, e.g.
2 + 2 + 2 + 2 + 2 = 5 lots of 2
+2
0
+2
2
+2
4
+2
6
+2
8
5 lots of 3 = 15 and 3 lots of 5 = 15
5 times 3 = 15 and 3 times 5 = 15
5 × 3 = 15 and 3 × 5 = 15
10
How many 5s make 15?
15 ÷ 5 = 3
3×5
5×3
3 × 5 means 3 multiplied by 5 (5 lots of 3)
3×5=3+3+3+3+3
5 × 3 means 5 multiplied by 3 (3 lots of 5)
5×3=5+5+5
Know that multiplication is commutative and can be done in
any order so:
3 multiplied by 5 = 5 multiplied by 3
How many 3s make 15?
15 ÷ 3 = 5
3×5=5×3
Know that division is not commutative and cannot be done in
any order, so:
35 ÷ 5 does not equal 5 ÷ 35.
Understand grouping as one model of division
Previous learning
Core for Year 2
Extension
Understand the idea of sharing equally: e.g.
Understand division as grouping (repeated subtraction), and
use the division sign (÷).
Understand division as grouping (repeated subtraction) or as
sharing (see the columns on the left), and use the division
sign (÷).
• 6 sweets are shared equally between 2 people.
How many sweets does each person get?
• There are 20 apples.
How many packs of 5 apples can you make?
Understand the relationship between multiplication and
division, e.g.
Know that if 5 threes or 3 fives are 15, then the answer to:
Share objects into two equal groups in a context.
Say ‘How many 5s make 20?’, and record 20 ÷ 5 = 4.
– ‘How many 3s make 15?’, or 15 ÷ 3, is 5
– ‘How many 5s make 15?’, or 15 ÷ 5, is 3.
© 1 | Year 2 | Spring TS11 | Multiplication and division and word problems
Examples adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Begin to understand that division can leave some left over
Previous learning
Core for Year 2
Extension
Say how many are left over after a simple division, e.g.
Give the remainder when one number is divided by another.
• Jill puts these strawberries on plates.
For example, work out that when 17 is divided by 5 (‘How
many 5s make 17?’) the answers is 3 with 2 left over.
17 ÷ 5 is 5 remainder 2, or 5 r 2.
She puts 5 strawberries on each plate.
How many strawberries are left over?
Respond to questions such as:
• A pen costs 5p. Amy has 53p. She buys as many pens as
she can. How much money does she have left?
Record 12 ÷ 5 = 2 and 2 left over.
Learn multiplication facts for the 2, 5 and 10 times tables
Previous learning
Core for Year 2
Extension
Count on in fives from 0 to at least 50, e.g.
Build up and begin to learn facts for 5 times table, e.g.
Build up and begin to learn facts for 4 times table, e.g.
• Count on from 0 in steps of 5 to 50.
Which fives number comes after 30? Before 50?
How can you work it out if you don’t know?
• Count on from 0 in steps of 5 to 50. Count back again to 0.
What is the multiple of 5 before 25? After 30?
How can you work it out?
• Count on from 0 in steps of 4 to 40. Count back again to 0.
What is the multiple of 4 before 40? After 24?
How can you work it out?
• Count along the line. Which numbers are missing?
• Count along the line. Which numbers are missing?
5
10
…
20
…
30
…
40
…
50
• What do you notice when you count from zero in:
tens
10
20
30
40
fives
5
10
15
20
(5s are halves of 10s)
• Build up and then recite the table of 5s, using the
relationship with the 10 times table, e.g.
zzzzz
zzzzz
zzzzz
1 five is 5
2 fives are 10
3 fives are 15, etc.
• Recognise that numbers in the 5 times table alternate
between ending in 5 and 0.
© 2 | Year 2 | Spring TS11 | Multiplication and division and word problems
4
8
…
16
…
24
…
32
…
40
• What do you notice when you count from zero in:
twos
2
4
6
8
fours
4
8
12
16
(4s are double 2s)
• Build up and recite the table of 4s, using:
– the relationship with the 2 times table;
– commutativity, e.g. 4 fives are 20 so 5 fours are 20.
zzzz
zzzz
zzzz
1 four is 3
2 fours are 8
3 fours are 12, etc.
Examples adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Previous learning
Core for Year 2
Extension
Begin to recognise multiples of 2, 5 and 10, e.g.
Know by heart multiplication facts for the 2, 5 and 10 times
tables.
Know by heart multiplication facts for 2, 3, 4, 5 and 10 times
tables.
Use strategies to remember tables facts, e.g.
Use strategies to remember tables facts, e.g.
• Recite tables, e.g.
1 two is 2, 2 twos are 4, etc.
• Recite tables, e.g.
1 three is 3, 2 threes are 6, etc.
• Chant the multiples of 2, 5, 10 to the tenth multiple,
recognising that:
• Chant the multiples of 2, 3, 4, 5, 10 to the tenth multiple.
• Count on in steps of 2, 5, 10 to the tenth multiple,
beginning to recognise that:
– multiples of 10 end in 0.
– multiples of 5 alternate between ending in 5 and 0;
– even numbers end in 0, 2, 4, 6 or 8.
– multiples of 10 end in 0.
– multiples of 5 alternate between ending in 5 and 0;
– multiples of 2 end in 0, 2, 4, 6 or 8.
• Recognise the relationship between the 2, 5 and 10 times
tables and counting in 2s, 5s and 10s.
• Recognise that 5s are half 10s, so if 7 tens are 70, then 7
fives are half of 70, or 35.
• Use the commutative law, e.g. if 4 fives are 20 then
5 fours are 20.
• Use a known fact to work out the next one, e.g. if you know
3 fours are 12, then 4 fours are 12 + 4 = 16.
• Recognise that 4s are double 2s.
• Recognise that 5s are half 10s, so if 7 tens are 70, then 7
fives are half of 70, or 35.
• Recognise that 3s are 2s plus 1s, so 6 threes are 6 twos
plus 6 ones, or 12 + 6 = 18.
• Recognise that the digit sum of multiples of 3 is 3, 6 or 9.
Decide what action is needed to solve a word problem and what calculation to do (multiplication or division)
Previous learning
Core for Year 2
Extension
Use counting in 2s, 5s or 10s to solve a practical problem
involving repeated addition, or halving or doubling, e.g.
Solve one- and two-step word problems involving
multiplication or division of numbers, money or measures,
choosing appropriate calculations and showing working, e.g.
Solve one- and two-step word problems involving
multiplication or division of numbers, money or measures,
choosing appropriate calculations and showing working, e.g.
One step problems
One step problems
One step problems
• There are 10 crayons in each box.
• There are 2 apples in each pack.
Rick buys 7 packs of apples.
How many apples does he buy?
• It costs 85p for a child to go swimming.
How much does it cost for 2 children?
How many crayons are there altogether?
• Sienna puts these coins in a box.
• How many pairs of socks
are there?
• A bag of potatoes weighs 6 kg.
What do 12 bags of potatoes weigh?
• There are 35 children. They get into teams of 5.
How many teams are there altogether?
How much does she put in the box altogether?
© 3 | Year 2 | Spring TS11 | Multiplication and division and word problems
Examples adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Previous learning
Core for Year 2
Extension
Problems with more than one step
Problems with more than one step
Problems with more than one step
• A chew costs 2p.
Sam buys 6 chews.
How much change does he get from 20p?
• A pencil costs 10p.
Anna has 54p. She buys as many pencils as she can.
How much money will she have left?
• Patrick bought three choc bars at 15p each.
How much change did he get from 50p?
• There are 12 cakes in a box.
Half of the cakes have been eaten.
How many cakes are left?
• Liam and Thomas share this money equally.
• John has 75 plums. He puts 10 plums in every box.
How many boxes does he fill?
How many plums are left over?
How much do they each get?
© 4 | Year 2 | Spring TS11 | Multiplication and division and word problems
Examples adapted from the Framework for teaching mathematics from Reception to Year 6, 1999