Halves, quarters and doubles
Year 2 Spring 12
Find halves and quarters of 4, 8 or 12 by folding strips
Previous learning
Core for Year 2
Extension
Understand and use these words
Understand and begin to read these words
Understand and read these words:
half, whole, … halve, double, …
part, fraction, one whole, one half, one quarter, three
quarters, …., double, halve, …
part, fraction, one whole, one half, one quarter, three
quarters, one third, two thirds, one tenth, ….
double, halve, …
Read and write:
Read and write proper fractions such as:
Recognise that one whole can be split into two identical
halves.
1
2
,
1
4
1
2
Recognise that one whole can be split into two identical
halves or four identical quarters.
,
1
4
,
3
4
,
1
3
interpreting the denominator as the total number of parts of a
whole and the numerator as the number of parts, e.g.
• Write a fraction to show how much each person gets when
1 cake is shared equally among 4 people.
Find halves of even numbers to 10, initially by folding strips.
• Find
1
2
by folding paper strips of an even number up to 10
Find halves and quarters of numbers by folding strips.
• Find
1
2
,
1
4
by folding paper strips of 4 then 8 counters or
Find halves and quarters of numbers by folding strips.
• Find
1
2
,
1
4
,
3
4
by folding paper strips of 4 then 8 or 12
counters or pictures of objects, first an undivided strip:
pictures of objects, first an undivided strip:
counters or pictures of objects.
then a strip of squares to be counted before and after
folding:
then a strip of squares to be counted before and after
folding:
Later, use numbered strips.
Record, for example,
Record, for example,
1
2
of 8 = 4.
Record, for example,
1
4
of 12 = 3.
• Find
1
3
,
2
3
1
4
of 12 = 3.
by folding paper strips showing 3 or 6 or 12
counters, then numbered to 1 to 3 or 1 to 6 or 1 to 12.
Record, for example,
Recognise from folding paper strips that halving reverses
doubling and that doubling reverses halving.
half of 8 = 4 and double 4 = 8
© 1 | Year 2 | Spring TS12 | Halves, quarters and doubles
2
3
of 12 = 8.
Understand the relationship between halving and doubling.
Understand that doubling and halving reverse each other
(halving and doubling are inverse operations), e.g.
• Knowing a double such as 7 × 2 = 14 means that
half of 14 is 7, or 14 ÷ 2 = 7.
Examples adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Find one half of up to 20 objects by sharing them into two equal groups
1
2
,
1
4
,
3
4
,
1
3
,
2
3
of a set of objects, e.g.
Find one half of a set of up to 10 objects, e.g.
Find one half of a set of up to 20 objects, e.g.
Find one
• Holly ate half the cherries on the plate.
How many cherries did she eat?
• Mary eats half of these cherries. How many does she eat?
• Here are 15 apples. Put a ring around one third of them.
• Using up to 10 cubes, make a stick of cubes which is half
red and half blue.
• Using more than 10 cubes, make a stick of cubes which is
half red and half blue.
• Take 12 cubes. Make a shape which is
• Ring one half of this set of 6 apples.
• Ring one half of this set of 10 buttons.
• What fraction of these buttons is ringed?
1
2
red and
1
3
blue.
Find doubles up to double 15 and the corresponding halves
Previous learning
Core for Year 2
Extension
Find doubles of numbers 1 + 1 to 10 + 10 by pairing cubes,
e.g.
Know doubles of numbers 1 to 10, relating these to even
numbers to 20, e.g.
Use known facts and partitioning to derive doubles of
numbers 1 to 50.
7 + 7 = 14 and 7 × 2 = 14
Find doubles of numbers 11 to 15.
Use jottings to explain how to double a two-digit number by
doubling the tens and doubling the ones.
47
Use a paper strip of squares, with the central 20 squares in
one colour and the remaining two outside squares in another
colour. Fold it in half.
40
+
7
80
+
14
×2
= 94
Respond to questions such as:
10 + 1 = 11
• How many squares are there in half of the strip? [11]
• How many squares will there be in the whole strip?
[double 10 and double 1 = 20 + 2 = 22]
• Double 19… Double 43… Double 38… Two 43s.
• A pencil costs 48p. What do two pencils cost?
• Suzy has 27 stamps. Tim has twice as many stamps as
Suzy. How many stamps does Tim have?
Complete questions such as:
37 + 37 = …
© 2 | Year 2 | Spring TS12 | Halves, quarters and doubles
42 × 2 = …
… × 2 = 86
Examples adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Previous learning
Core for Year 2
Extension
Relate halving to sharing equally or folding into 2 equal parts,
e.g.
Relate halving to sharing equally or folding into 2 equal parts,
e.g.
1
2
Find halves of even numbers to 10 by folding paper strips, e.g.
• Half of 8 = 4
zzzz
{{{{
of 8 = 4
Know halves of even numbers to 20, e.g.
• Half of 14…
1
2
1
2
zzzzzzzz
{{{{{{{{
of 16 = 8
Find halves of numbers to 1 to 40.
Use jottings to halve the tens and halve the ones, e.g.
of 18
39
Find halves of even numbers from 22 to 30.
Use knowledge of doubles of 1 to 15 to find halves of even
numbers to 30, e.g.
30
• Find half of 39.
15
• Half of 22 = 11 because double 11 = 22.
Solve problems such as:
Solve problems such as:
• Zara spent half of her 24p pocket money.
How much did she spend?
• Harry has a set of 32 crayons.
He gives half of them to Tom.
How many crayons does Tom get?
• One half of a number is 8. What is the number?
• Jo’s box is 11 cm wide.
Mary’s box is twice as wide as Jo’s box.
How wide is Mary’s box?
+
9
+
4
halve
1
2
1
= 19 2
• What is half of £7?
• What is the next number in this halving sequence?
40
20
10
5
…
Find doubles of multiples of 5 up to double 50 and corresponding halves
Previous learning
Core for Year 2
Extension
Use knowledge of doubles of numbers 1 to 10 to double
multiples of 10 from 10 to 50, e.g.
Use knowledge of doubles of numbers 1 to 10 to double
multiples of 10 from 10 to 100, e.g.
• double 40 is 80 because double 4 is 8
• double 70 is 140 because double 7 is 14
Use known facts and partitioning to derive doubles of
multiples of 5 to 50.
Use known facts and partitioning to derive doubles of
numbers 1 to 50.
Use jottings to explain how to double a two-digit number by
doubling the tens and doubling the ones.
Use jottings to explain how to double a two-digit number by
doubling the tens and doubling the ones.
35
© 3 | Year 2 | Spring TS12 | Halves, quarters and doubles
47
30
+
5
60
+
10
×2
= 70
40
+
7
80
+
14
×2
= 94
Examples adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Previous learning
Core for Year 2
Extension
Respond to questions such as:
Respond to questions such as:
• Double 45… Two 25s.
• Double 19… Double 43… Double 38… Two 43s.
• A comic costs 35p.
Anna bought two comics. How much did she spend?
• A pencil costs 48p.
Anil bought two pencils. How much did he spend?
• Paul has 15 sweets.
Mark has twice as many sweets as Paul.
How many sweets does Mark have?
• Suzy has 27 stamps.
Tim has twice as many stamps as Suzy.
How many stamps does Tim have?
Complete questions such as:
Complete questions such as:
40 × 2 = …
35 + 35 = …
… × 2 = 30
42 × 2 = …
37 + 37 = …
… × 2 = 86
Use partitioning to derive halves of multiples of 10 to 100, e.g.
Use partitioning to derive halves of even numbers to 100, e.g.
• Find one half of 90
• Find one half of 76
half of 90 = half of 80 + half of 10
= 40 + 5
= 45
half of 76
= half of 70 + half of 6
= 35 + 3
= 38
76
70
+
6
÷2
35
50 ÷ 2 = …
© 4 | Year 2 | Spring TS12 | Halves, quarters and doubles
of 30
3
38
Complete questions such as:
Complete questions such as:
1
2
+
… ÷ 2 = 35
84 ÷ 2 = …
1
2
of 76
… ÷ 2 = 36
• Two pens cost 70p.
What does one pen cost?
• Two biros cost 52p.
What does one biro cost?
• When I doubled a number, the answer was 90.
Which number did I double?
• When I doubled a number, the answer was 78.
Which number did I double?
Examples adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Identify near doubles using doubles already known, e.g. 40 + 41
Previous learning
Core for Year 2
Extension
Find near doubles, using doubles already known.
Find near doubles, using doubles already known.
Find near doubles, using doubles already known.
For example, work out that:
For example, work out that:
For example, work out that:
• 5 + 6 = 11
explaining that it is double 5 add 1, or double 6 subtract 1.
• 6 + 7 = 13
explaining that it is double 6 add 1, or double 7 subtract 1
• 40 + 39 = 79
explaining that it is double 40 minus 1
• 36 + 35 = 71
explaining that it is double 35 add 1
© 5 | Year 2 | Spring TS12 | Halves, quarters and doubles
Examples adapted from the Framework for teaching mathematics from Reception to Year 6, 1999