Year-5-Spring-Term-Block-2 - Fractions-Fluency.pptx

Fluency Teaching Slides
Equivalent
Fractions
5

Activity
1
Equivalent Fractions
Take two pieces of paper of the same size.
Fold one piece into three equal
pieces. Fold the other into nine equal
pieces.
What equivalent fractions can you
find?
?
2
Fractions –
5
masterthecurriculum.co.uk

Activity
1
1
3
3
9
Take two pieces of paper of the same size.
Fold one piece into three equal
pieces. Fold the other into nine equal
pieces.
3
Fractions –
5

Activity
1
Use the models below to write equivalent fractions.
4
Fractions –
5

Activity
1
Use the models below to write equivalent fractions.
1
2
4
8
3
12
1
4
4
10
2
5
5
Fractions –
5

Activity
2
1
5
4
20
X 4
=
X 4
Rosie uses the models below and her multiplication
and division skills to find equivalent fractions.
Find the equivalent fractions of 2
, 3
, and 4
where the denominator is
30.
5 5
5
?
6
Fractions –
5

Activity
2
2
5
12
30
X 6
=
X 6
Rosie uses the models below and her multiplication
and division skills to find equivalent fractions.
3
5
18
30
X 6
=
X 6
4
5
24
30
X 6
=
X 6
7
Fractions –
5

Activity
3
4
=
28 7
9
=
15 5
15
=
27 9
Zach uses the same approach to find the
equivalent fractions of these
fractions.
How does his method
differ?
?
8
Fractions –
5

Activity
3
4
=
1
28 7
9
=
3
15 5
Zach uses the same approach to find the
equivalent fractions of these
fractions.
÷ 4
÷ 4 ÷ 3
÷ 3
15
=
5
27 9
÷ 3
÷ 3
9
Fractions –
5

Discus
s
What equivalent fractions can you find by folding a piece
of paper? How can you record these?
What are the similarities and differences about the
numerators and denominators in equivalent
fractions?
How does multiplication and division help you find
equivalent fractions? Where can you see this in your
model?
10
Fractions –
5

Improper to
Mixed
Numbers
5

Activity
1
Improper to Mixed
Numbers
4
Kate converts the improper fraction 15
into a
mixed number using cubes.
She groups the cubes into 4s, then has 3 left
over.
4
4
is the same
as
4
8
is the same
as
4
15
is the same as
Use Kate’s method to convert 13
, 13
, 13
, and 13
.
2
3
4
?
12
Fractions –
5

Activity
1
Improper to Mixed
Numbers
4
Kate converts the improper fraction 15
into a
mixed number using cubes.
She groups the cubes into 4s, then has 3 left
over.
1
2
3
4
4
is the same
as
4
8
is the same
as
4
15
is the same as
3
4 = 3 4 ; 5
13 = 6
1 ;
13 = 4
1 ;
134 1 13 = 2
3
2 2 3 3 5
13
Fractions –
5

Activity
2
Improper to Mixed
Numbers
4
4 2
7
2
7
7
Malachi converts the improper fraction 30
into a
mixed number using bar
models.
Use Malachi’s method to convert 20
, 38
, 38
, and 70
.
9
8
7
?
14
Fractions –
5

Activity
2
Improper to Mixed
Numbers
2 2
9
7
Malachi converts the improper fraction 30
into a
mixed number using bar
models.
4 6
8
11
4
6
5
3
7
5 3
7
114
6
4
6
8
2
2
9
20
9
38
8
38
7
70
6
15
Fractions –
5

Discus
s
How many parts are there in a whole?
What do you notice about the mixed number when
the denominator increases and the numerator remains the
same?
What happens when the numerator is a multiple
of the denominator?
Improper to Mixed
Numbers
16
Fractions –
5

Mixed Numbers
to Improper
5

Activity
1
Mixed Numbers to
Improper
1 whole is equal to
eighths.
3 wholes are equal to
eighths.
eighths + 3
eighths =
eighths.
8
Mia converts 33
into an improper fraction using
cubes.
Use Mia’s method to convert 2 3
, 3 3
, 4 5
, and 5 4
.
4
5
?
18
Fractions –
5

Activity
1
Mixed Numbers to
Improper
8
Mia converts 33
into an improper fraction using
cubes.
1 whole is equal to 8
eighths.
3 wholes are equal to 24
eighths.
24eighths + 3 eighths = 27
eighths.
4
2
3
→
quarters.
quarters.
8 quarters + 3 quarters =
11 quarters.
5
3
3
→
fifths.
fifths.
15 fifths + 3 fifths =
18 fifths.
6
4
5
→
sixths.
sixths.
24 sixths + 5 sixths =
29 sixths.
7
5
4
→ 19
Fractions –
5
sevenths.
sevenths.
35 sevenths + 4 sevenths
= 39 sevenths.

Activity
2
Mixed Numbers to
Improper
5
22
= wholes +
fifths
Tia uses bar models to help her convert mixed
numbers into improper fractions.
Use Tia’s method to convert 6 1
, 7 2
, 1 5
, and 2 3
.
7
5
?
2 wholes = fifths
fifths + fifths =
fifths
20
Fractions –
5

Activity
2
Mixed Numbers to
Improper
Tia uses bar models to help her convert mixed
numbers into improper fractions.
7
6
1
→
6 wholes + 1 seventh. 6 wholes = 42 sevenths.
42 sevenths + 1 seventh = 43 sevenths.
5
7
2
→
6
1
5
→
8
2
3
→
7 wholes + 2 fifths. 7 wholes = 35 fifths.
35 fifths + 2 fifths = 37 fifths.
1 whole + 5 sixths. 1 whole = 6 sixths.
6 sixths + 5 sixths = 11 sixths.
2 wholes + 3 eighths. 2 wholes = 16 eighths.
16 eighths + 3 eighths = 19 eighths.
5
21
Fractions –
5
22
= 2 wholes + 2 fifths
2 wholes = 10 fifths
10fifths + 2 fifths =12 fifths

Discus
s
How many quarters/halves/eighths are there in a whole?
How does multiplication support you in converting
mixed numbers to improper fractions?
Can you explain the steps in converting an improper
fraction to a mixed number?
Use the terms numerator, denominator, multiply, and add.
How would you use the previous bar model to help?
Mixed Numbers to
Improper
22
Fractions –
5

5
Fluency Teaching
Slides
Number
Sequences

Activity
1
Number Sequences
24
Fractions –
5
Use the counting stick to count up and down in these
fractions.
How do you figure out the numerator and denominator when you count up
or down? Does the denominator stay the same?
?
Start at 0 and count up in steps of
1
2
Start at 2 and count down in steps of
2
5
3
4

Activity
1
Number Sequences
1
2
Start at 2 and count down in steps of
2
5
3
4
25
Fractions –
5
1 1 1
2
1
2
2
2
3
1
2 4
1
2
0 1 2 3 4
2 1
3
1
1
5 5
4
5
2
5
0
5
−
2
−
4
5 −1
1
5 −1
3
5
1
4 4
1
3
2
2
3
1
4
4
4
4
3
5
2
4 6
1
4 7
3
4
7
Use the counting stick to count up and down in these
fractions.

Activity
2
Number Sequences
2
1
5 2
2
5
2
2
4
5
Complete the missing values on the number line.
26
Fractions –
5

Activity
2
Number Sequences
Complete the missing values on the number line.
2
1
5 2
2
5
2
5
1
4
27
Fractions –
5
5 2
3 2
4
5
3

Activity
3
Number Sequences
• 3
, 1 1
, ,
2 2
5 5
5
•
3
2, , 2, 2
2
3
7 7
• 5 5
, , 4
4
, 4
• 3 2
, 3 1
,
, 4
8 2
Find the missing fractions in the sequences.
28
Fractions –
5

Activity
3
Number Sequences
• 3
, 1 1
, 1 4
, 2 2
5 5 5
5
• 2
, 1 1
, 2, 2
2
3 3
3
• 3 2
, 3 1
, 3 6
,
4
8 2
8
Find the missing fractions in the sequences.
29
Fractions –
5
• 5 5
, 5 1
, 4 4
,
4
7 7
7

Discus
s
What are the intervals between the fractions?
Are the fractions increasing or decreasing?
By how much are they increasing or decreasing?
Can you convert the mixed numbers to improper
fractions?
Does this make it easier to continue the sequence?
Number Sequences
30
Fractions –
5

5
Fluency Teaching
Slides
Compare & Order
(Less than 1)

Activity
1
Compare & Order (Less than
1)
Compare 1
and 3
.
2
4
>
32
Fractions –
5

Activity
1
1)
3
4
1
2
>
Compare 1
and 3
.
2
4
1
2
3
4
33
Fractions –
5

Activity
1
1)
Use bar model to compare 3
and
5
.
4 8
<
34
Fractions –
5

Activity
1
1)
3
4
5
8
5
8
3
4
<
Use bar model to compare 3
and
5
.
4 8
35
Fractions –
5

Activity
1
•
3 and
5
5 16
•
7 and
4
9 18
• 1
and
6
3
9
1)
Use this method to compare:
36
Fractions –
5

Activity
1
• 3
and 5
5
16
• 7
and
4
9
18
• 1
and
6
3
9
1)
Use this method to compare:
>
7
9
4
18
>
<
5
16
3
5
3
5
5
16 <
7
9
4
18
<
6
9
1
3
1
3
6
9 >
37
Fractions –
5

Activity
2
1)
>
Use common numerators to compare 4
and
2
.
5 7
2
and 4
7 8
1 and
5
3 10
6 and
3
11 5
Use this method to help you
compare:
?
38
Fractions –
5

Activity
2
1)
4
5
2
7
>
2
7
4
5
2
and 4
7 8
1 and
5
3 10
6 and
3
11 5
Use common numerators to compare 4
and
2
.
5 7
compare:
?
39
Fractions –
5

Activity
2
1)
Use common numerators to compare.
and
• 2 4
7
8
• 1
and
5
3
10
•
6 and
3
11 5
4
8
2
7
>
1
3
5
10
<
3
5
<
4
8
2
7 <
1
3
5
10
>
6
11
6
11
3
5 >
40
Fractions –
5

Activity
3
•
•
•
1 7 1
3 13 2
3 5 2
13 6 5
8 4 3
9 7 5
1)
Order the fractions from greatest to smallest:
41
Fractions –
5

Activity
3
1)
Order the fractions from greatest to smallest:
42
Fractions –
5
->
‐ 5
->
‐ 8
->
‐
7 1
1
13 2 3
2 3
6 5 13
3 4
9 5 7
•
•
•
1 7 1
3 13 2
3 5 2
13 6 5
8 4 3
9 7 5

Discus
s
How does a bar model help you to visualise fractions?
Should both of your bars be the same size? Why? What does
this show you?
If the numerators are the same, how do you compare
your fractions?
If the denominators are the same, how do you compare
your fractions?
Do you always have to find a common denominator?
Can you find a common numerator?
1)
43
Fractions –
5

5
Fluency Teaching
Slides
Compare and
Order (More
than 1)

Activity
1
Compare and Order (More than
1)
6
and 8
4 3
10 and
5
7
2
8
and 9
7 4
Use a bar model to compare 6
and
9
.
5 7
compare:
?
>
45
Fractions –
5

Activity
1
1)
and
9
.
5 7
compare:
?
6
5
7
9
>
9
7
6
5
46
Fractions –
5
6
and 8
4 3
10 and
5
7
2
8
and 9
7 4

Activity
1
1)
Use a bar model to compare:
• 6
and 8
4
3
•
10 and
5
7
2
• 8
and
9
7
4
8
3
>
10
7
5
2
<
<
6
4
6
4
8
3
<
10
7
5
2
>
9
4
8
7
8
7
9
4 >
47
Fractions –
5

Activity
2
1)
1 2
and 2 1
1 3
and 2 1
1 1
and 2
1
4 3 7 2 7
4
and
14
.
5 6
compare:
?
<
48
Fractions –
5

Activity
2
1)
1 2
and 2 1
1 3
and 2 1
1 1
and 2
1
4 3 7 2 7
4
and
14
.
5 6
<
1
3
5
compare:
?
1
4
6
1
4
6
1
3
49
Fractions –
5
5

Activity
2
1)
Use a bar model to compare:
1
2
4 2
1
3
>
1
3
7 2
1
2
<
1
1
7 2
1
4
<
1
2
4
2
1
3
<
1
3
7
2
1
2
>
1
1
7
2
1
4 >
50
Fractions –
5
• 1 2
and 2 1
4
3
• 1
3
7
and 2
1
2
• 1 1
and
2 1
7
4

7 10 7 10 1 6
3 9 6 11 1 2 1 22
18 18 18 22 22
22
Therefore the
order:
Therefore the
order:
Activity
3
1)
Order the fractions from greatest to smallest
using common denominators.
51
Fractions –
5

Activity
3
1)
11
7 10 7 10 1 6
3 9 6 1 2 1 22
42 20 21 20 33
28
18 18 18 22 22
22
Therefore the
order:
Therefore the
order:
7 7 10
3 6 9
1
1 1
6 10 52
Fractions –
5
Order the fractions from greatest to smallest
using common denominators.

Discus
s
How do you represent the fractions?
How does a bar model help you see which fraction is the
greatest?
Can you use your knowledge of multiples to help you?
Can you predict which fractions will be greatest? Explain
your answer.
Is it more efficient to compare using numerators or
denominators?
1)
53
Fractions –
5

5
Fluency Teaching
Slides
Add and Subtract
Fractions

Activity
1
Add and Subtract Fractions
5 +
4 2 +
4 2 +
7
7 7 3 3 6
6
+ =1
2 4 1
5 5 5
5 5
Here is a bar model to calculate 2
+
4
.
Use a bar model to solve the
calculations:
?
55
Fractions –
5

Activity
1
Use a bar model to solve the calculations:
• 5 +
4
7 7
• 2 +
4
3 3
• 2 +
7
6 6
=1
2
7
=2
=1
3
6
56
Fractions –
5

Activity
2
5 +
2 1 +
7 8 +
8
7 7 3 3 6
6
3 1 4
4 4 4
+ = =1
4 4
Here is a bar model to calculate 3
+
1
.
Use a bar model to solve the
calculations:
?
57
Fractions –
5

Activity
2
Use a bar model to solve the calculations:
58
Fractions –
5
• 5 +
2
7 7
• 1 +
7
3 3
• 8 +
8
6 6
7
= 7
= 1
= 8
= 2 2
3
3
=
16 = 2
4
6
6

Activity
3
1 −
3
4
7
−
7
3 3
7 7
Here are two bar models to calculate 6
−
4
.
What is the difference between the two
methods?
Use your preferred method to calculate:
4
−
1 9
−
6
?
59
Fractions –
5

Activity
3
• 1 − 3
4
• 4 −
1
5 5
• 9 −
6
8 8
• 7 −
7
3 3
Use your preferred method to calculate:
=
1
60
Fractions –
5
4
=
3
5
=
3
8
= 0

• 3
+ 1
= 2
+
5 5 5
• 8
− 6
=
− 3
9 9
9
•
+
3 =
12 −
5
7 7
7
Activity
4
Calculate:
61
Fractions –
5

• 3 +
1 =
2 +
2
5 5 5
5
• 8 −
6 =
5 −
3
9 9 9
9
• 4 +
3 =
12 −
5
7 7 7
Activity
4
Calculate:
62
Fractions –
5

Discus
s
How many equal parts do you need to split your bar into?
Can you convert the improper fraction into a mixed number?
How does the bar model help you balance both sides of the equals
sign?
Fractions- 5 63

5
Fluency Teaching
Slides
Add Fractions
within 1

Activity
1
Add Fractions within 1
1 1
+ = + = =
2 1 3 1
3 6 6 6 6 2
1 +
3
5 10
1 +
3
3 9
2 +
2
4 10
Malachi is calculating 1
+
1
.
3
6
He uses a
diagram to
represent
the sum.
Use Malachiʻs method to
solve:
?
65
Fractions –
5

Activity
1
Use Malachi’s method to solve:
66
Fractions –
5
=
5
10
=
6
9
=
7
10
• 1 +
3
5 10
• 1 +
3
3 9
• 2 +
2
4 10

Activity
2
2
3
2
3
^
1
6
+ = + =
1 2 1 4 5
6 3 6 6 6
2 +
1
4 8
2 +
2
3 9
1 +
1
3 6
6 3
Rosie is using a bar model to solve 1
+
2
.
Use the bar model to
solve:
?
67
Fractions –
5

Activity
2
• 2 +
2
3 9
• 1 +
1
3 6
Use the bar model to solve:
2
4
^ ^
1
8
• 2 +
1 =
5
4 8
8
^
2
3
^
2
9
=
8
9
^ ^
1 1
3 6
=
3
68
Fractions –
5
6

Discus
s
Can you find a common denominator? Do you need to
convert both fractions or just one?
Can you explain Malachi and Rosie’s method to a partner?
Which method do you prefer?
How do Malachi and Sophie’s methods support finding a
common denominator?
69
Fractions –
5

5
Fluency Teaching
Slides
Add 3 or
More
Fractions

Activity
1
^
Add 3 or More
Fractions
^
4
8
1
2
^
^
2 1
4 4
+ +
1 2 1
3 6 9
+ +
1 1 1
2 4 12
2 4 8
Tia uses a bar model to calculate 1
+ 1
+
2
.
^ ^
2 2
8 8
Use the bar model to
solve:
?
71
Fractions –
5
=1

Activity
1
^
Add 3 or More Fractions
^
3
9
1
3
Use the bar model to solve.
=
7
9
+ +
1 2 1
3 6 9
+ +
1 1
1
2 4 12
^ ^
3 1
9 9
^
2
6
^
2
6
^ ^
6
12
1
2
^ ^
3 1
12 12
^ ^
2 1
4 4
=
10
12
72
Fractions –
5

Activity
2
Can you draw what Leanna’s cake could look
like? What fractions could you divide your cake
into?
?
73
Fractions –
5
Leanna baked a cake for Tia’s birthday.
She decorated 1
of the cake with green, 2
with blue
and
3
9 5
with orange.
18
What fraction of the cake is
decorated altogether?

Activity
2
Leanna baked a cake for Tia’s birthday.
74
Fractions –
5
1 +
2 +
5
3 9
18
=
6 +
4 +
5
18 18
18
=
15
18
1
3
2
9
5
18

Activity
3
Complete the fractions.
1
+
5
6 18 54
+
30
=1
1 2 4
3 6 12
+ + =1
75
Fractions –
5

1
+
5
+
30
=1
6 18 54
Activity
3
1 2 4
3 6 12
+ + =1
Complete the fractions.
76
Fractions –
5

Discus
s
Can you find a common denominator?
Do you need to convert both fractions or just one?
Can you explain Tia’s method to a partner?
How does Tia’s method support finding a common
denominator?
Can you draw what Leanna’s cake would look like?
What fractions would you divide your cake into?
Why would a bar model not be efficient for this question?
77
Fractions –
5

5
Fluency Teaching
Slides
Add
Fractions

Activity
1
Add Fractions
Step 1
1
+
4
+
4
=
36
4 16 64 64
Step 2 Step 3
1
4
1
1
16
1
16
4 1
16
1
16
1
4
1 1
16 16
1 1
16 16
1
64
1
64
1
64
1
64
79
Fractions –
5

Activity
1
Add Fractions
4
+
2
+
9
7 14 21
3
+
8
+
11
12 24 36
1
+
4
+
6
5 10 15
Explain each step of the calculation in the previous
slide. Use this method to help you add the following
fractions.
Give your answer as a mixed
number
.
?
80
Fractions –
5

Activity
1
Add Fractions
•
4 2 9
7 +
14 +
21 =
•
12 24 36
3 +
8 +
11
=
•
1 4 6
5 + 10 + 15
=
Explain each step of the calculation in the previous
slide. Use this method to help you add the following
fractions. Step 1 Step 2 Step 3
=
24
21
=
32
36
15
= 15
1 1 1 1
7 7 7 7
1 1 1 1
1
14
7 7 7 7 1
14
1
21
1
21
1
21
1
21
1
21
1
21
1
21
1
21
1
21
7 7 7
1 1 1 1
7
1
14
1
14
1
12
1
12
1
12
1 1 1
1
24
1
24
1
24
12 12 12 1
24
1
24
1
24
1
24
1
24
1 1 1
1 1 1 24
1
24
1
24
1
12 12 12 24 24 24
1 1
36
1
36
1
36
1
36
1
36
24
1
1
36
1
36
1
36
24
1
36
1
36
1
36
1
5
1
1
10
1
10
5 1
10
1
10
1 1
1
15
1
15
1
5
10
1
10
1
1
15
1
15
10 10
1
15
1
15
81
Fractions –
5

Activity
2
Add Fractions
+ +
1 3 5
2 4 8
2 +
3 +
7 1 +
3 +
5
3 6 12 2 4 8
4 +
3 +
2
5 10 20
Use the bar model to add the
fractions. Record your answer as a
mixed number.
Draw your own models to
solve:
?
7
= 1 8
82
Fractions –
5

Activity
2
Add Fractions
•
2 +
3 +
7
3 6 12
• 1 +
3 +
5
2 4 8
•
4 +
3 +
2
5 10 20
Use the bar model to add the
fractions. Record your answer as a
mixed number.
= 1
9
12
= 1 7
8
= 1
4
83
Fractions –
5
20

Discus
s
How does the pictorial method support you in adding
the fractions?
Which common denominator will you use?
How do your times tables support you in adding
fractions?
Which representation do you prefer and why?
Add Fractions
84
Fractions –
5

5
Fluency Teaching
Slides
Add
Mixed
Numbers

Activity
1
Add Mixed Numbers
2
2
+3
6
=5
10
=6
5 10 10
2+3=5
2 6 4 6 10
5 + 10 = 10 + 10 = 10
5+
10
=5
10
=6
10 10
Add the fractions by adding the whole first and then the
fractions.
Step 1
Step 2
Step 3
86
Fractions –
5

Activity
1
Add Mixed Numbers
• 4 5
+1 2
=
8
16
•
7
7 +3
9
=
10 20
• 6 8
+2 4
=
15
5
Add the fractions by adding the whole first and then the
fractions.
87
Fractions –
5

Activity
1
Add Mixed Numbers
Give your answer in its simplest form.
Step 1
Step 2
Step 3
4+1 = 5
5 +
2 =
10 +
2
8 16 16 16
=
12
16
5+ 12
=5 12
=5 3
16 16
4
4
5
+1
2
8
16
7
7
+3
9
10
20
6
8
+2
4
15
5
7+3 = 10
7 +
9 =
14 +
9
=
23
20
10+
23
= 11
3
20
20
6+2 = 8
8 +
4 =
8 +
12
10 20 20 20 15 5 15 15
=
20
15
8+ 20
=9 5
= 9 1
15 15
3
88
Fractions –
5

Activity
2
Add Mixed Numbers
2
7 +1
9 =
25 +
27 =
50 +
27 =
77 or 4
5
9 18 9 18 18 18 18
18
2
6
+3
4
10
5
4
1
+1
9
8
24
2
1
+2
7
6
12
Add the fractions by converting
them to improper fractions.
Add these fractions by converting them to improper
fractions:
?
89
Fractions –
5

Activity
2
Add Mixed Numbers
Add the fractions by
converting them to improper
fractions.
2
6 +3
4 =
26 +
19 =
26 +
38 =
64 or 6
4
10 5 10 5 10 10 10
10
4
1 +1
9 =
33 +
33 =
99 +
33 =
132 or 5
12
8 24 8 24 24 24 24
24
2
1 +2
7 =
13 +
31 =
26 +
31 =
57 or 4
9
6 12 6 12 12 12 12
12 90
Fractions –
5

Activity
3
Add Mixed Numbers
Add these fractions.
5
6
+3
4
7
5
33
+2
7
8
40
31
+2
7 91
Fractions –
5

Activity
3
Add Mixed Numbers
5
6 +3
4 =
41 +
19 =
205 +
133 =
338 or 9
23
7 5 7 5 35 35 35
35
33 +2
7 =
33 +
87 =
165 +
87 =
252 or 6
12
8 40 8 40 40 40 40
40
31 +2
7 =
31 +
31 =
62 +
31 =
93 or 7
9
6 12 6 12 12 12 12 92
Fractions –
5
Add these fractions.

Discus
s
How can you partition these mixed numbers into whole
number and fractions?
What will be the total of the whole numbers? Can you add
the fractions straight away?
What will these mixed numbers be as improper fractions?
If you have an improper fraction in the question, should
you change it to a mixed number first? Why?
Add Mixed Numbers
93
Fractions –
5

5
Fluency Teaching
Slides
Subtract Fractions

Activity
1
Subtract Fractions
1
4
4
16
4
−
1
=
3
16 16 16
Step 1 Step 2 Step 3
1
4
1
4
1
4
95
Fractions –
5

Activity
1
Subtract Fractions
Explain each step of the calculation in the previous slide.
Use this method to help you subtract the following fractions.
3
−
1
4 8
6
−
4
7
14
96
Fractions –
5

Activity
1
Subtract Fractions
Explain each step of the calculation in the previous slide.
Use this method to help you subtract the following fractions.
• 3 −
1
4 8
•
6 4
7 −
14
1
4
1
4
1
4
1
4
1
4
1
4
1
4
1
4
1
4
1 1 1 1 1 1
7 7 7 7 7 7
1 1 1 1 1 1
7 7 7 7 7 7
1 1 1 1 1 1
7 7 7 7 7 7
3
4
6
8
6
7
12
14
− =
6 1 5
8 8 8
12
−
4
=
8
14 14 14
97
Fractions –
5

Activity
2
Subtract Fractions
Zach has 5
left, Esin has 12
.
8
16
Zach and Esin both have a pizza of the same size.
How much more does Esin
have?
?
98
Fractions –
5

Activity
2
Subtract Fractions
Zach and Esin both have a pizza of the same size.
99
Fractions –
5
Zach has 5
left, Esin has 12
.
8
16
Zach
Esin
12 −
5 =
12 −
10 =
2 =
1
16 8 16 16

Activity
3
Subtract Fractions
1
8
10
2
10
2
10
6
=
12
5 10
Tia uses a number line to find the difference
between
2
and 6
.
10 5
8 +
2 =
10 =1
10 10 10
Use this method to help you solve
these:
?
100
Fractions –
5
2 and
9
5 15
11 and
9
4
4
14 and
3
6
12

Activity
3
Subtract Fractions
•
2 and
9
5 15
•
11 and
9
4
4
•
14 and
3
6
12
101
Fractions –
5
Use the method in the previous slide to find the
difference between:
1
5
2
5
3 9
5= 15
1
4
9
4
10
4
11
4
1
4
1 +
1 =
2 =
1
4 4 4 2
9
12
3
12
1
masterthecurriculum.
co.uk
14
6
8
6
9 +
8 =
25 = 2
1
12 6 12 12
1
5

Discus
s
What could the common denominator be?
Can you draw a model to help you solve the problem?
What will these mixed numbers be as improper fractions?
Is it easier to use a take away bar model (single bar model) or
a bar model to find the difference (comparison model)?
Subtract Fractions
102
Fractions –
5

5
Fluency Teaching
Slides
Subtract Mixed
Numbers (1)

Activity
1
Subtract Mixed Numbers (1)
1
3
5
1
3
−
3
= 1 3
5 10
10
1
6
10
1
−
3
3
5
10
these:
?
104
Fractions –
5
2
5 −
5 1
3 −
4 1
6 −
2
7 14 8 16 9
18

Activity
1
• 2
5 −
5
7 14
• 1
3 −
4
8 16
• 1
6 −
2
9 18
Use the method in the previous slide to solve:
2
5
14
1
2
16
1
10
18
105
Fractions –
5

Activity
2
+ 1
1
3
=1
6
5
10
4
10
4
1
10
6
1
10
+
2
10
Use a number line to find the difference
between
5
1
3
and
10
4
:
1
2
10
2 6
and 3
7
14
5 3
and 4
8
16
1 8
and 15
9
18
these:
?
106
Fractions –
5

Activity
2
• 2 6
and 3
7
14
• 5 3
and 4
8
16
• 1 8
and 15
9
18
2
9
14
2
5
16
1
1
18
+ 2
3
14
3
2
14
12
2
14
+
9
14
+ 5
4
16 5
4
16 5
6
16
+
2
16
+ 1
15
18 1
15
18 1
16
18
+
1
18
107
Fractions –
5

Activity
3
• 1
3−
6
4
12
•
2
4 −
3
5
10
•
1
3 −
5
7
21
Solve:
108
Fractions –
5

Activity
3
• 1
3−
6 =1
9 −
6 = 1
3
4 12 12 12
12
•
2
4 −
3 = 2
8 −
3 = 2
5
5 10 10 10
10
•
1
3 −
5 = 1
9 −
5 = 1
4
7 21 21 21
21
Solve:
109
Fractions –
5

Discus
s
Which fraction is the greatest? How do you know?
If the denominators are different, what do we do?
Can you simplify your answer?
Which method do you prefer when subtracting fractions:
taking away or finding the difference?
110
Fractions –
5

5
Fluency Teaching
Slides
Subtract Mixed
Numbers (2)

Activity
1
We can work out 2 3
− 3
using this
method.
5
10
2
3
5 2
6
– 3
= 2 3
10 10 10
2
6
10
2
2 -
8 3
6 -
8 4
2 -
16
3 9 7 21 4
20
these:
?
112
Fractions –
5

Activity
1
• 2
2 -
8
3 9
• 3
6 -
8
7 21
• 4
2 -
16
4 20
1
7
9
3
10
21
14
3
20
113
Fractions –
5

Activity
2
5 1
− 4
= 4 + 1 1
- 4
= 4 + 1 5
- 12
= 4 8
3 5 3 5 15 15
15
Use flexible partitioning to solve 5 1
−
4
.
3 5
2
2 -
12 3
2 -
6 1
1 -
5
5 15 7 21 9
18
these:
?
114
Fractions –
5

Activity
2
2 2
− 12
= 1 + 1 2
− 12
= 1 + 1 6
− 12
= 1 9
5 15 5 15 15 15
15
3 2
− 6
= 2 + 1 2
− 6
= 2 + 1 6
− 6
= 3
7 21 7 21 21 21
1
1 −
5 = 1
2 −
5 =
15
9 18 18 18
18
115
Fractions –
5

Activity
3
7
Rosie has 4 2
bags of
sweets.
7
She shared 6
of a bag with her
friends.
How much does she have
left?
?
116
Fractions –
5
Solve:

Activity
3
7
Rosie has 4 2
bags of
sweets.
7
She shared 6
of a bag with her
friends.
Solve:
117
Fractions –
5
4 2
− 6
= 3 + 1 2
− 6
= 3
3
7 7 7 7
7

Discus
s
Is flexible partitioning easier than converting the mixed number
to an improper fraction?
Do you always have to partition the mixed number?
When can you subtract a fraction without partitioning the
mixed number in a different way?
118
Fractions –
5

5
Fluency Teaching
Slides
Subtract 2 Mixed
Numbers

Activity
1
Subtract 2 Mixed Numbers
2 – 1 = 1
2
2
−1
3
=1
1
3 6
6
120
Fractions –
5
Here is a bar model to calculate 2 2
−1
3
.
3 6
2
6 - 1
4
7
14
3
6 -
8 4
3 - 2
7
7 21 4
20
2 −
3 =
4 −
3 =
1
3 6 6 6 6
Use this method to
calculate:
?
Why does this method not work effectively for 2 1
- 1
1
?
6 3

Activity
1
1
8
14
3
10
21
8
2
20
•
2
6 - 1
4
7
14
• 3
6 -
8
7 21
•
4
3 - 2
7
4
20
121
Fractions –
5

Activity
2
4
1
− 2
1
= 4
1
−2
2
= 3
5
−2
2
=1
3
4 2 4 4 4 4
4
Here is a bar model to calculate 4 1
− 2
1
.
4 2
2
1 - 1
4
5
10
5
5 - 2
11
8
16
3 2
- 18
3
9
Use this method to
calculate:
?
122
Fractions –
5

Activity
2
=2
10
−1 =
2 4 8
10 10
2
1 - 1
4 5
5 - 2
11 3
2
5 10 8 16
3 - 18
9
=5
10
−2
11
= 2
15
16 16
16
=3
6
−1
8
= 1
7
9 9
9
123
Fractions –
5

Discus
s
Why is subtracting the wholes and parts separately easier
with some fractions than others?
Can you show the subtraction as a difference on a number
line?
How are these different to taking away?
Does making the whole numbers larger make the subtraction
any more difficult? Explain why.
124
Fractions –
5

5
Fluency Teaching
Slides
Multiply by an
Integer (1)

Activity
1
Multiply by an Integer (1)
4
Work out 1
× 3 by counting in
quarters.
4
1
×3 = + + =
1 1 1 3
4 4 4 4
5×
1
10 7
1
×4 2× 1
2
Use this method to
calculate:
?
126
Fractions –
5

Activity
1
= 1
+
1
+
1
+
1
+
1
=
5
10 10 10 10 10 10
• 5×
1
10
•
1
7
×4
• 2× 1
2
= + + + =
1 1 1 1 4
7 7 7 7 7
2 2 2
127
Fractions –
5
=
1 +
1 =
2
=1

Activity
2
4
7
Tia uses a single bar model to work out 1
×4 =
4
.
7 7
1 1 1 1
7 7 7 7
4× 1
5 9
1
×2 3× 1
7
Use this method to
calculate:
?
128
Fractions –
5

Activity
2
129
Fractions –
5
4
5
• 4× 1
5
9
• 1
×2
1
• 3× 7
1 1 1 1
5 5 5 5
1 1
9 9
2
9
3
7
1 1 1
7 7 7

Activity
3
0
130
Fractions –
5
Leanna uses a number line and repeated addition to work out:
5× 1
7 4
1
×2 8× 1
3
Use this method to
calculate:
?
3
1
×
5
2
5 =
3
=1
3
1 2
1 1 1 1 1
3 3 3 3 3

Activity
3
131
Fractions –
5
• 5× 1
7
4
• 1
×2
• 8× 1
3
5
7
1
2
2
2
3
0 1 2
1 1 1 1 1
7 7 7 7 7
0 1 2
1
4
1
4
0 1 2
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
3
Leanna uses a number line and repeated addition to work out:

Discus
s
How is multiplying fractions similar to adding
fractions?
What is similar/different between
Which bar model do you find the most useful?
Which bar model helps you to convert from an improper
fraction to a mixed number most effectively?
What has happened to the numerator/denominator?
3
4
x 2
3
4
3
x
132
Fractions –
5

5
Fluency Teaching
Slides
Multiply by an
Integer (2)

Activity
1
134
Fractions –
5
9
Count the number of ninths to work 2×
1
.
1
9
1
9
4× 3
5 9
6
×2 3× 7
8
Use this method to
calculate:
?

Activity
1
135
Fractions –
5
• 4×
3
5
9
• 6
×2
• 3×
7
8
12 2
5 =
25
1
5
1
5
1
5
1
5
1
5
1
5
1 1 1
5 5 5
1 1 1
5 5 5
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1 1 1 1 1 1 1
8 8 8 8 8 8 8
1 1 1 1 1 1 1
8 8 8 8 8 8 8
1 1 1 1 1 1 1
8 8 8 8 8 8 8
12 = 1
1
9
3
21 = 2
5
8
8

Activity
2
1 1 1 1
5 5 5 5
2
5
2
5
5
Use the model to solve 2×
2
.
Use this method to
calculate:
?
136
Fractions –
5
4× 2
3 9
7
×3 5×
7
15

Activity
2
8 = 2
2
3 3
21 = 2
1
9
3
35 = 2
1
15 3
• 4× 2
3
7
• 9 ×3
7
• 5× 15
1
15
1 1 1 1 1 1 1 1 1 1 1 1 1 1
15 15 15 15 15 15 15 15 15 15 15 15 15 15
1
15
1 1 1 1 1 1 1 1 1 1 1 1 1 1
15 15 15 15 15 15 15 15 15 15 15 15 15 15
1
15
1
15
1
15
1
15
1
15
1 1 1 1 1 1 1 1 1
9 9 9 9 9 9 9 9 9
1 1 1 1 1 1 1 1 1
9 9 9 9 9 9 9 9 9
1
9
1
9
1
9
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
137
Fractions –
5

Activity
3
5
Use the number line to help you solve 2×
2
.
0 1
1
5
1
5
1
5
1
5
2
5
2
5
Use this method to
calculate:
?
138
Fractions –
5
5×
3
10 4
3
×8 8×
6
12

Activity
3
139
Fractions –
5
• 5×
3
10
4
• 3
×8
6
• 8× 12
15 = 1
1
10 2
4
24
= 6
12
48
= 4
0 1
0 1 2
0 1 2
masterthecurriculum.co
.uk
3
2
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
3 4 5 6
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
4
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12

Discus
s
Can you show 3 lots of on a bar
model?
How does repeated addition help you with this
multiplication?
How does a number line help you see the multiplication?
3
10
How many tenths do you have
altogether?
140
Fractions –
5

5
Fluency Teaching
Slides
Multiply by an
Integer (3)

4
Use repeated addition to work out 2 3
×2.
4×2 3
10 4
1 3
×7 8×5 6
9
Use this method to
calculate:
?
2 3
×2 = 2 3
+2 3
= 4 6
= 5 2
or 5
1
4 4 4 4 4
2
142
Fractions –
5
Activity
1

= 2 3
+2 3
+2 3
+2 3
= 8 12
= 9 2
or 9
1
10 10 10 10 10 10
5
Activity
1
• 4×2 3
10
4
• 1 3
×7
• 8×5 6
9
= 1 3
+1 3
+1 3
+1 3
+1 3
+1 3
+1 3
= 7 21
= 12
1
4 4 4 4 4 4 4 4
4
= 5 6
+5 6
+5 6
+5 6
+5 6
+5 6
+5 6
+5 6
= 40 48
= 45
1
9 9 9 9 9 9 9 9 9
3
143
Fractions –
5

Activity
2
3
Partition your fraction to help you solve 2 2
×4.
2×4=8
3
2
×
8
2
4=
3
=2
3
8+ 2 2
=10 2
3
3
Step 1
Step 2
Step 3
5
1 4
×6 10
2 3
×4 9
7 8
×3
Use this method to
calculate:
?
144
Fractions –
5

Activity
2
1×6 = 6
4
×6 =
24
= 4
4
5 5 5
6 + 4 4
= 10 4
5
5
Step 1
Step 2
Step 3
5
1 4
×6 10
2 3
×4 9
7 8
×3
2×4 = 8
3
×4 =
12
= 1
1
10 10 5
8 + 1 1
= 9 1
5
5
7×3 = 21
8
×3 =
24
= 2
2
9 9 3
21 + 2 2
= 23 2
3
3
145
Fractions –
5

Activity
3
Convert to an improper fraction to calculate:
1 7
×3 = 15
×3= 45
= 5
5
8 8 8
8
7
2 5
×7 12
4 1
×6 20
7 8
×3
Use this method to
calculate:
?
146
Fractions –
5

= 19
×7 = 133
= 19
7 7
Activity
3
7
• 2 5
×7
12
• 4 1
×6
20
• 7 8
×3
= 49
×6 = 294
= 24 1
12 12
2
=
148 ×3 =
444 = 22
1
20 20
5
147
Fractions –
5

Discus
s
How would you represent this mixed number?
What is the denominator? How do you know?
How many whole numbers are there? How many parts are
there?
What is multiplying fractions similar to? (repeated addition)
What representation would you use to convert a mixed number
to an improper fraction?
148
Fractions –
5

5
Fluency Teaching
Slides
Fraction of an
Amount

Activity
1
Fraction of an Amount
?
30
5
Find 1
of
30.
30÷5 = 6
5
1
of 30 is 6.
7
1
of 49 4
1
of 24 9
1
of 72 m
Use this method to
solve:
?
150
Fractions –
5

Activity
1
?
49
7
• 1
of 49
4
• 1
of 24
9
• 1
of 72 m
24
?
?
72 m
49÷7 = 7
7
1
of 49 is 7
24÷4 = 6
4
1
of 24 is 6
9
151
Fractions –
5
72÷9 = 8
1
of 72 is 8 m

Activity
2
5
Find 2
of
30.
?
30
5
30÷5 = 6
6×2 = 12
2
of 30 is 12.
Use this method to
solve:
?
152
Fractions –
5
7
4
of 49 4
3
of 24 9
2
of 72 m

Activity
2
?
49
7
49÷7 = 7
7×4 = 28
4
of 49 is 28
7
• 4
of 49
4
• 3
of 24
9
• 2
of 72 m
?
24
?
72
m
4
24÷4 = 6
6×3 = 18
3
of 24 is 18
72÷9 = 8
8×2 = 16
153
Fractions –
5
9
2
of 72 is 16 m

Activity
3
Draw a bar model to help calculate:
154
Fractions –
5
8
• 3
of 2 cm
9
• 5
of 180 litres
6
• 4
of 30 kg

Activity
3
Draw a bar model to help calculate:
8
• 3
of 2 cm
•
5
9
of 180
litres
4
• 6 of 30 kg
?
2
cm
180 litres
?
?
30 kg
1
2÷8 =
4
1
×3 =
3
4 4
3
of 2 cm is 3
cm
8 4
180÷9 = 20
20×5 = 100
9
5
of 180 litres is
100 litres
6
30÷6 = 5
5×4 = 20
4
of 30 kg is 20 kg
155
Fractions –
5

Discus
s
How many equal groups can you share 49 into? Why?
What does each equal part represent as a fraction and
an amount?
What could you do to 1 metre to make the calculation
easier?
1 litre =
156
Fractions –
5

5
Fluency Teaching
Slides
Fractions
as
Operators

Activity
1
Fractions as Operators
?
5
158
Fractions –
5
Esin has calculated and drawn
a bar model for two
calculations.
5× 2
= 10
= 2
5 5
5
2
of 5 = 2
What’s the same and what’s different about the
calculations?
?

Activity
1
?
5
159
Fractions –
5
5× 2
= 10
= 2
5 5
5
2
of 5 = 2
Both calculations give the same
results.
The first calculation is using the fractions as
multiplication by an integer
, the second calculation
is using fraction of an amount.
Esin has calculated and drawn
a bar model for two
calculations.

9
1
of 5
=
5
9
Activity
2
Complete:
5
3 lots of 1
=
3
5
3
5
5 lots of = 3
8
4 lots of 6
=
3
7
1
of 14 =
2
1
4
of 8 = 2
Which calculation on each row is easier?
Why?
?
160
Fractions –
5

Activity
2
Complete:
3 lots of 1
= 3
5
5
5
5 lots of 3
= 3
8
4 lots of 6
= 3
7
1
of 14 = 2
4
1
of 8 = 2
1
of 5 = 5
9 9
161
Fractions –
5

7
10× 3
=
3
7
of 10 = 4
2
7
Activity
3
Use this to complete:
12 12
5
2
5
× 3
= 3
of
= 4
9 9
1 × 2
= of 15 =
6
5
162
Fractions –
5

Activity
3
Use this to complete:
10× 3
= 3
of 10 = 42
7 7
7
12× 3
= 3
of 12 = 4
9 9
15× 2
= 2
of 15 = 6
5 5
163
Fractions –
5

Discus
s
What is the same and different about these bar models?
Is it easier to multiply a fraction or find a fraction of an
amount?
Does it depend on the whole number you are multiplying by?
Can you see the link between the numbers?
164
Fractions –
5

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