1. Fractions – Multiplying – Complete Lesson
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2. Starter
A task at the beginning of the lesson that reviews a skill required for the learning.
Knowledge Check
Questions to assess students’ current understanding and to consequently show progress.
Real-Life Example
A ‘hook’ to raise interest and provide a concrete example.
Demonstration
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AFL Questions
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Plenary
An opportunity for students to prove/evaluate their learning.

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4. 10 x3 ÷2 -5 x2 x5 +5 ÷5 16 ??
÷10 -5 x8

5. Multiplying Fractions
30 July 2019
Multiplying Fractions

6. KNOWLEDGE CHECK
1 3 × =
3 4 × 4 5 =
2 5 ÷ 1 6 =

7. KNOWLEDGE CHECK
1 3 × = 2 15
3 4 × 4 5 = = 6 10 = 3 5
2 5 ÷ 1 6 = =2 2 5

8. 1 3 of 1 4 means 1 3 × 1 4 = 1 12 Georgie took a 1 4 of the cake!
She split the piece into 3 and
gave one piece each to Tom and Rob.
How big was the piece Tom ate?
1 3 of means 1 3 × =

9. Area = 8 × 6 = 48 metres2 How do we find the area of a field? 8 metres

10. We can see it is a quarter of the whole field.
What if we want to find the area of half the length,
and half the width?
4 metres
3 metres
We can see it is a quarter of the whole field.

11. ? 1 4 1 5 1 6 What if we want to find the area of half the length,
and a third of the width?
What fraction of the field is the area?
1 4
1 5
1 6 ? or or

12. This is an easy way to multiply fractions.
1 2
1 3
1 2 × 1 3 = 1 6

13. What is the fraction for…
1 2 × 1 4 =
1 8
1 2 × 1 5 =
1 10
1 2
1 2
1 4
1 5

14. What is the fraction for…
1 3 × 1 4 =
1 12
2 3 × 1 4 =
2 12
1 3
2 3
1 4
1 4

15. Draw diagrams in your books to help calculate the answers. 1) 2)
1 4
1 3 × 1 3 =
1 4 × 1 5 =
1 5 3) 3)
1 3 × 2 3 =
3 4 × 2 3 =

16. Answers Draw diagrams in your books to help calculate the answers. 1)2)
1 3
1 4
1 3 × 1 3 = 1 9
1 4 × 1 5 = 1 20
1 3
1 5 3) 3)
1 3
3 4
1 3 × 2 3 = 2 9
3 4 × 2 3 = 6 12
2 3
2 3
Can we make
this fraction simpler?
Answers

17. Can we write a rule for multiplying fractions,
Draw diagrams in your books to help calculate the answers. 1) 2)
1 3
1 4
1 3 × 1 3 = 1 9
1 4 × 1 5 = 1 20
1 3
1 5
Can we write a rule for multiplying fractions,
just using numbers? 3) 3)
1 3
3 4
1 3 × 2 3 = 2 9
3 4 × 2 3 = 6 12
2 3
2 3
Can we make
this fraction simpler?
Answers

18. Is Anna right? 1 3 × 2 3 = 2 9 To multiply fractions,
1 3 × 2 3 = 2 9
2 3
To multiply fractions,
multiply the numerator,
then multiply the denominator.
ANNA says….
Is Anna right?

19. To quickly multiply fractions we
multiply the numerators
and multiply the denominators
(1 x 1)
(1)
1 2 × =
1 6
(6)
(2 x 3)

20. To quickly multiply fractions we
multiply the numerators
and multiply the denominators
(1 x 2)
(2)
1 3 × =
2 9
(9)
(3 x 3)

21. To quickly multiply fractions we
multiply the numerators
and multiply the denominators
(1 x 2)
Can we simplify
this fraction?
(2)
1 4 × =
2 12
= 1 6
(12)
(4 x 3)

22. To quickly multiply fractions we
multiply the numerators
and multiply the denominators
(2 x 1)
Can we simplify
this fraction?
(2)
2 3 × =
2 15
(15)
(3 x 5)

23. To quickly multiply fractions we
multiply the numerators
and multiply the denominators
(3 x 2)
Can we simplify
this fraction?
(6)
3 4 × =
6 20
= 3 10
(20)
(4 x 5)

24. To quickly multiply fractions we
multiply the numerators
and multiply the denominators
(5 x 3)
Can we simplify
this fraction?
(15)
5 6 × =
15 30
= 1 2
(30)
(6 x 5)

25. What’s wrong? What’s the answer?
2 3 × = 6 15
8 15
Sarah
2 3 × = 6 15
Julie
2 5

26. 3 4 × 1 6 =
4 5 × 1 6 =
5 6 × 2 7 =
1 3 × 1 5 =
5 7 × 5 6 =
2 3 × 1 4 =
× 3 4 =
3 4 × 2 5 =
×1 1 2 =

27. 3 4 × 1 6 = 3 24 = 1 8
4 5 × 1 6 = 4 30 = 2 15
5 6 × 2 7 = = 5 21
Answers
1 3 × 1 5 = 1 15
5 7 × 5 6 = 25 42
2 3 × 1 4 = 2 12 = 1 6
× 3 4 = 9 8 =1 1 8
3 4 × 2 5 = 6 20 = 3 10
×1 1 2 = 33 8 =4 1 8

28. 1 2 𝑜𝑓 1 3 1 2 × 1 3 = 1 6 Ben, Bob and Bill split a pizza equally.
Ben gave half his pizza to
his sister, Anna.
What fraction of the whole Pizza did Anna get?
Ben
Bob
Bill
Anna
1 2 𝑜𝑓 1 3
1 2 × 1 3 =
1 6
Anna got of the whole pizza.

29. Jim, Jane, Jack and John split a pizza equally.
Jim gave half his pizza to
his brother, David.
What fraction of the whole Pizza did David get?
Jim
Jane
Jack
John
David
1 2 𝑜𝑓 1 4
1 2 × 1 4 =
1 8
David got of the whole pizza.

30. Mary split her birthday cake into 8 equal pieces.
Sally split one of the pieces into two.
What fraction of the whole cake is
one of Sally’s pieces?
1 8
1 16
1 2 𝑜𝑓 1 8
1 2 × 1 8 =
1 16

31. Mary split her birthday cake into 7 equal pieces.
Sally split one of the pieces into 3.
What fraction of the whole cake is
one of Sally’s pieces?
1 7
1 21
1 3 𝑜𝑓 1 7
1 3 × 1 7 =
1 21

32. Calculate of
1 3
1 6
1 3 𝑜𝑓 1 2
1 3 × 1 2 =
1 6

33. Calculate of
1 3
1 12
1 4 𝑜𝑓 1 3
1 4 × 1 3 =
1 12

34. Calculate of
2 3
1 12
1 12
1 4 𝑜𝑓 2 3
1 4 × 2 3 =
2 12
= 1 6

35. Calculate of
2 3
1 12
1 12
1 12
1 12
1 12
1 12
3 4 𝑜𝑓 2 3
3 4 × 2 3 =
6 12
= 1 2

36. Draw diagrams in your books to help calculate the answers.
1 2 of =
2 5 of =
2 3 of =
1 5 of =
1 3 of =
4 5 of =

37. Draw diagrams in your books to help calculate the answers.
1 2 of = 1 6
2 5 of = = 2 20
2 3 of = = 1 2
1 5 of =
1 3 of = 2 9
4 5 of = = 3 5

38. × = × = × = × = × = = × = × = = × = Multiplying Fractions : Amber1. a) 4 2 b) 1 5 1. a) 4 2 b) 1 5 × = × = × = × = 5 15 7 14 5 15 7 14
Simplify!
Simplify! c) 2 5 2 8 × = = d) × = c) 2 5 × = = d) 2 8 × = 5 6 3 27 5 6 3 27 3.
Calculate the area of this rectangle. 3.
Calculate the area of this rectangle.
5 7 × 3 4 =
5 7 × 3 4 = 2. a) 2. a)
5 6 m
5 6 m
6 7 × 4 9 =
3 4 m
6 7 × 4 9 = b) b)
3 4 m
Multiplying Fractions : Green
Multiplying Fractions : Green
5 7 × 3 4 =
6 7 × 2 3 =
5 7 × 3 4 =
6 7 × 2 3 = 1. a) b) 1. a) b)
4 9 × 3 8 =
7 10 × 5 7 =
4 9 × 3 8 =
7 10 × 5 7 = c) d) c) d)
× 3 4 =
× 3 4 = 2. a)
How can we calculate this? 2. a)
How can we calculate this?
× 3 5 =
×1 2 7 =
× 3 5 =
×1 2 7 = b) c) b) c) 3. a)
Can we make this calculation easier before multiplying?
(Look again at Question 1 part d) 3. a)
Can we make this calculation easier before multiplying?
(Look again at Question 1 part d)
4 5 × 3 4 =
4 5 × 3 4 =

39. × = × = × = = × = Multiplying Fractions : Amber 1. a) 4 2 1 5 b) 5 157 14
Simplify! c) 2 5 2 8 × = = d) × = 5 6 3 27 3.
Calculate the area of this rectangle.
5 7 × 3 4 = 2. a)
5 6 m
6 7 × 4 9 = b)
3 4 m
Multiplying Fractions : Green
5 7 × 3 4 =
6 7 × 2 3 = 1. a) b)
4 9 × 3 8 =
7 10 × 5 7 = c) d)
× 3 4 = 2. a)
How can we calculate this?
× 3 5 =
×1 2 7 = b) c) 3. a)
Can we make this calculation easier before multiplying?
(Look again at Question 1 part d)
4 5 × 3 4 =

40. Answers × = × = × = = × = Multiplying Fractions : Amber 1. a) 4 2 8 53 15 7 2 14
Simplify! c) 2 5 10 1 d) 4 2 8 × = = × = 5 6 30 3 9 3 27 3.
Calculate the area of this rectangle.
5 7 × 3 4 = 15 28 2. a)
15 24 = 5 8 m2
5 6 m
6 7 × 4 9 = = 8 21 b)
3 4 m
Multiplying Fractions : Green
5 7 × 3 4 = 15 28
6 7 × 2 3 = = 4 7 1. a) b)
4 9 × 3 8 = = 1 6
7 10 × 5 7 = = 1 2 c) d)
× 3 4 = 5 3 × 3 4 = = 5 4 =1 1 4 2. a)
How can we calculate this?
× 3 5 = =1 1 20
×1 2 7 = = b) c) 3. a)
Can we make this calculation easier before multiplying?
(Look again at Question 1 part d)
4 5 × 3 4 = 3 5

41. Answers

42. Answers

43. 1 4 of 1 5 means 1 4 × 1 5 = 1 20 Georgie took a 1 5 of the cake!
She split the piece into 4 and
gave one piece to Tom, Ann and Rob.
How big was the piece Ann got?
1 4 of means 1 4 × =

44. Check your success! I can multiply fractions with 1 as the numerator.
I can multiply fractions with any numerator.
I can multiply mixed numbers.

45. Check your success! I can multiply fractions with 1 as the numerator.
I can multiply fractions with any numerator.
I can multiply mixed numbers.

46. How to multiply fractions.
Write a text message to a friend describing…
How to multiply fractions.

47. tom@goteachmaths.co.uk Questions? Comments? Suggestions?
…or have you found a mistake!?
Any feedback would be appreciated .
Please feel free to