Year 8 Mathsw/c 11th May 2020

I hope you all have had a good week and have been getting some fresh air while social distancing. How many of you

managed to attempt the all the questions in last weeks home learning?

Work your way through these slides but remember to take breaks in between.

Pupil and parent learning sheetWeek beginning: 11th May 2020This week's work for Year 8 maths is concentrating on consolidating and extending your use of fractions.By the end of this week, you should be able to: 1. Convert between improper fractions and mixed numbers2. Calculate sums using the four operations with fractions3. Find fractional increases and decreases

Your work this week will include the following activities: An activity to convert between improper fractions and mixed numbers

Using the four operations (add, subtract, multiply, divide) with fractions

Answer questions on fractional increase/decrease

If you complete all your work to a high standard, you may also want to…Have a go at creating your own fractions codebreaker similar to the ones at the end of this presentation. If you do, make sure you send it to us at learningfromhome@ipsleyacademy.co.uk

For extra help with maths learning, you may also want to look at the following: https://corbettmaths.com/2013/02/15/mixed-numbers-to-improper-fractions/https://corbettmaths.com/2013/02/15/improper-fractions-to-mixed-numbers/https://corbettmaths.com/2012/08/21/fractions-addition-and-subtraction/https://corbettmaths.com/2012/08/21/multiplying-fractions-2/https://corbettmaths.com/2012/08/21/division-with-fractions/https://corbettmaths.com/2012/08/21/increasing-or-decreasing-by-a-fraction-of-a-quantity/

You DO NOT need to print any of this work off to complete.

This week we are going to be looking at fractionsand some basic skills we must know about them.

• You are going to have some fractions where you need to convert between the improper fractions and mixed numbers

• You will have some fractions where you will need to complete the sum using one of the four operations

• You will have some amounts you will need to increase or decrease by a fraction

• Your extension is to create your own code breaker similar to the ones at the end of this lesson.

Recap!

• To change a mixed number into an improper fraction you need to• See how many times the denominator goes into the numerator (this is the whole

number)• What is left over? (this becomes the numerator)• The denominator stays the same

• An example: 29

6

• 29 ÷ 6 = 4 𝑟𝑒𝑚𝑎𝑖𝑛𝑑𝑒𝑟 5

•29

6= 4

5

6

Recap!

• To change an improper fraction into a mixed number you need to• Multiply the whole number by the denominator of the fraction

• Add on the numerator to your previous answer (this is the new numerator)

• The denominator doesn’t change

• An example: 13

4

• 1 × 4 = 4

• 4 + 3 = 7

• 13

4=

7

4

Q a) 3 fits into 7 twice with a remainder of 1.

= 2𝟏

𝟑

= 𝟏𝟏

𝟓

Q a) 2x5=10Then 10+ 1=11

Silver Task 1

Gold Task 1

Diamond Task 1

Silver Task 1 - Answers

Gold Task 1 - Answers

THEY WANTED TO TRACE SOMEONE

Diamond Task 1 -

Answers

Recap!

• To add and subtract fractions you need to:• Use your equivalent fractions skills to make the denominators the same on both

fractions• Add/subtract the numerators• The denominator stays the same

• An example 1

4+

5

12:

•1

4=

3

12

•3

12+

5

12=

8

12

Don’t forget to simplify your answer!8

12=

2

3

Don’t forget to simplify!

The denominators are different!

What is the lowest common multiple of 4 and 12?

4 8 12 16 20 24 28 …….12 24 36 48 ……

312

512+

=8

12 =23

x3

Recap! (the same example a different way)

Recap!

• To multiply fractions you need to:• Multiply the numerators (this gives you the numerator in the answer)

• Multiply the denominators (this gives you the denominator in the answer)

• An example 1

4×

5

12:

•1×5

4×12=

5

48

Don’t forget to simplify your answer when you

can!

When multiplying mixed numbers, you must change them into improper

fractions first.

Recap!

• To multiply fractions you need to:• Multiply the numerators (this gives you the numerator in the answer)

• Multiply the denominators (this gives you the denominator in the answer)

• Sometimes you can simplify before carrying out the multiplication. This is done by dividing the diagonally opposite numbers by the same number.

• An example 9

32×

56

33:

• 9 ÷ 3 = 3, 33 ÷ 3 = 11

• 32 ÷ 8 = 4, 56 ÷ 8 = 7

• So the new sum is:3

4×

7

11=

21

44

Recap!

• To divide fractions you need to:• Keep the first fraction the same

• Flip the second fraction over

• Change the divide sign to a multiply sign

• Treat as a multiplication

• An example 2

3÷

8

9:

•2

3×

9

8=

18

24

When dividing mixed numbers, you must change them into improper fractions

first.

KEEPFLIP

CHANGE

Don’t forget to simplify your answer!18

24=

3

4

1. 1 +

7 =

+

7 = 6. 1 –

3 =

7 –

=

2 14 14 14 2 14 14 14

2. 1 + 1 = + 1 =

7. 2 – 1 = – 1 =

3 6 6 6 3 6 6 6

3. 3 + 1 =

+ =

8. 7 – 1 =

– =

8 4 8 4

4. 2 + 3 =

+ =

9. 9 – 3 =

– =

7 14 10 5

5. 1 + 2 =

+ =

10. 1 – 1 =

– =

5 10 4 12

For questions 1 to 10 you first need to change one of the fractions so the denominators are equal.

x2

x2

2 9

14

1

2×

1

2

22

12or

11

6

1

3×

1

2

7

325

6

2

3×

1

2

6

8𝑜𝑟

3

4

2

5×

1

3

7

5×

5

3

1

6

1

7×

1

9

3

98

3

14

12

7

1

4

4

7÷

1

3

1

4÷

1

3

2

15

4

5÷

3

10

40

7

1

63

11

12÷

1

2

3

4

5

6÷

1

5

4

7÷

1

10

2

6𝑜𝑟

1

3

1

2×

3

7

3

14×

1

7

2

12𝑜𝑟

1

6

3

8÷

1

2

40

15𝑜𝑟

8

3

1

4×

2

3

Match the questions up

with the correct answers

You could copy them out onto cut out bits of

paper, and create a matching

game!

11. 1 +

1 =

+

= 16. 5 –

1 =

–

=

3 5 15 15 15 6 5 30 30 30

12. 2 +

1 =

+

= 17. 3 –

2 =

–

=

3 4 12 12 4 3 12 12

13. 1 + 1 =

+ =

18. 7 – 1 =

– =

5 4 20 20 8 2

14. 1 + 2 =

+ =

19. 9 – 3 =

– =

2 9 10 7

15. 1 + 3 =

+ =

20. 9 – 2 =

– =

4 7 11 5

For questions 11-20 you must change both fractions so their denominators are equal

Silver Task 2

A 1

2

N 11

20

B 1

9

O 3

4

C 6

11

P 1

11

D 2

7

Q 10

21

E 1

3

R 1

4

F 5

13

S 4

5

G 8

15

T 6

7

H 9

10

U 5

12

I 1

5

V 3

11

J 6

19

W 7

45

K 1

20

X 8

19

L 2

13

Y 8

11

M 3

5

Z 1

10

Brechin High School Mathematics Department

Can you crack the code?

A 1

2

N 11

20

B 1

9

O 3

4

C 6

11

P 1

11

D 2

7

Q 10

21

E 1

3

R 1

4

F 5

13

S 4

5

G 8

15

T 6

7

H 9

10

U 5

12

I 1

5

V 6

11

J 6

19

W 7

45

K 1

20

X 8

19

L 2

13

Y 8

11

M 3

5

Z 1

10

5

5÷

5

3

2

3×

3

4

3

11÷

1

2

4

7÷

2

3 1

1

2×

3

5

8

25÷

2

5

5

7× 1

1

5

2

25÷

2

5

3

7×

7

9

7

8÷ 1

3

4

45

2×

2

50

1

5× 1

2

3

2

5×

10

5

4

5÷

16

5

Extension:

You now need to finish the phrase.

Create questions that will give the correct letter answer for

someone else to solve.

2

11×

8

2

11

2×

2

5

Answer the questions and simplify your answers. Rearrange the letters to find and finish the phrase!

Silver Task 2

Gold Task 2

Add the fractions

together in two bricks

next to each other to find the value of

the brick above.

11

2𝑚

1) David’s bedroom floor measures

𝟑𝟏

𝟒metres by 3

1

2metres. What is the

area of the floor?

2) Find three different pairs of fractions

which multiply to 25

32

3) Find the volume of this cube:

Gold Task 2

V = b x h x l

1) Work out the areas and perimeters of the following shapes

8) Using the fact that 7

22π , find as a fraction the circumference and area of

a circle with diameter cm5

4.

9) Given that

5

3=a

7

4=b

3

25=c

12

23=d

a a + 2b b 3c + 4d c c2 – (a2 + b2)

d a – b e b – a f 4c – 3d

g ac h 2abd i 2d2 + 3c

j

b

a

k

a

b

l

a

dc +

mm9

23

mm5

31

m11

5

m4

3

a 𝑎 + 2𝑏 b 3𝑐 + 4𝑑 c 𝑐2 − (𝑎2 + 𝑏2)

d 𝑎 − 𝑏 e 𝑏 − 𝑎 f 4𝑐 − 3𝑑

g 𝑎𝑐 h 2𝑎𝑏𝑑 i 2𝑑2 + 3𝑐

j𝑎

𝑏k

𝑏

𝑎l

𝑐 + 𝑑

𝑎

Diamond Task 2

1.14

14= 1

2.3

6=

1

2

3.20

32=

5

8

4.7

14=

1

2

5.4

10=

2

5

6.4

14=

2

7

7.3

6=

1

2

8.20

32=

5

8

9.3

10

10.2

12=

1

6

1

2 ×

1

2

22

12 or

11

6

1

3×

1

2

2

6 𝑜𝑟

1

3

25

6

2

3×

1

2

6

8 𝑜𝑟

3

4

2

5×

1

3

2

3×

1

2

1

6

1

7×

1

9

3

98

3

14

12

7

1

4

4

7÷

1

3

1

4÷

1

3

2

15

4

5÷

3

10

40

7

1

63

11

12÷

1

2

3

4

5

6÷

1

5

4

7÷

1

10

2

6 𝑜𝑟

1

3

1

2×

3

7

3

14×

1

7

2

12 𝑜𝑟

1

6

3

8÷

1

2

40

15 𝑜𝑟

8

3

1

4×

2

3

11.8

15

12.11

12

13.9

20

14.13

18

15.19

28

16.19

30

17.1

12

18.6

16=

3

8

19.33

70

20.23

55

Silver Task 2 - Answers

A 1

2

N 11

20

B 1

9

O 3

4

C 6

11

P 1

11

D 2

7

Q 10

21

E 1

3

R 1

4

F 5

13

S 4

5

G 8

15

T 6

7

H 9

10

U 5

12

I 1

5

V 3

11

J 6

19

W 7

45

K 1

20

X 8

19

L 2

13

Y 8

11

M 3

5

Z 1

10

Brechin High School Mathematics Department

Can you crack the code?

A 1

2

N 11

20

B 1

9

O 3

4

C 6

11

P 1

11

D 2

7

Q 10

21

E 1

3

R 1

4

F 5

13

S 4

5

G 8

15

T 6

7

H 9

10

U 5

12

I 1

5

V 6

11

J 6

19

W 7

45

K 1

20

X 8

19

L 2

13

Y 8

11

M 3

5

Z 1

10

5

5÷

5

3

2

3×

3

4

3

11÷

1

2

4

7÷

2

3 1

1

2×

3

5

8

25÷

2

5

5

7× 1

1

5

2

25÷

2

5

3

7×

7

9

7

8÷ 1

3

4

45

2×

2

50

1

5× 1

2

3

2

5×

10

5

4

5÷

16

5

Extension:

You now need to finish the phrase.

Create questions that will give the correct letter answer for

someone else to solve.

2

11×

8

2

11

2×

2

5

Silver Task 2 - Answers

15

25=

3

5

16

22=

8

11

6

10=

3

5

6

12=

1

2

12

14=

6

7

9

10

40

50=

4

5

30

35=

6

7

21

63=

1

3

28

56=

1

2

6

11

90

100=

9

10

5

15=

1

3

20

80=

1

4

10

50=

1

5

20

25=

4

5

M Y M A

E R I S

E A C H

T H S T

MY MATHS TEACHER IS…

Gold Task 2 - Answers

Add the fractions

together in two bricks

next to each other to find the value of

the brick above.

3

4

3

2

9

4

19

20

1

2

29

20

11

12

7

12

3

2

23

18

7

6

22

9

1. 113

8metres

2. One example: 1

2×

5

2×

5

8

3. 8. 33

8

Gold Task 2 - Answers

1) Work out the areas and perimeters of the following shapes

8) Using the fact that 7

22π , find as a fraction the circumference and area of

a circle with diameter cm5

4.

9) Given that

5

3=a

7

4=b

3

25=c

12

23=d

a a + 2b b 3c + 4d c c2 – (a2 + b2)

d a – b e b – a f 4c – 3d

g ac h 2abd i 2d2 + 3c

j

b

a

k

a

b

l

a

dc +

mm9

23

mm5

31

m11

5

m4

3

a 126

35b 24

2

3c 31

4681

11025

d1

35e −

1

20f 16

11

12

g 52

3h 1

11

35i 24

25

72

j 11

20k

20

21l 12

23

36

Diamond Task 2 - Answers

Recap!• To increase/decrease a quantity by a fraction you need to:

• Find the fraction of the original quantity• Divide the quantity by the denominator

• Then multiply your answer by the numerator

• If you are increasing, add this amount on to the original quantity

• If you are decreasing, subtract this amount from the original quantity

• An example: Increase 30 by2

5

• 30 ÷ 5 = 6

• 6 × 2 = 12 Increase means we must add on

• 30 + 12 = 42

6 6 6 6 6

30

6 6

6 6 6 6 6

There are extra parts

to these questions to guide

you if you’re

struggling

There are extra parts

to these questions to guide

you if you’re

struggling

Silver Task 3

Make sure you show all your working out for these questions

Could you try drawing bar models to show your working instead of writing sums?

Gold Task 3

Make sure you show all your working out for these questions

Could you try drawing bar models to show your working instead of writing sums?

Diamond Task 3

Diamond Task 3

£40

40

2 40

+

£9 3 9

-

£36 3 36

-

£320

£18

£144

£56

£64 3 64

+

4 56

+

£463 3 463

-

£320

£280

£1852

Silver Task 3 -Answers

Gold Task 3 - Answers

Diamond Task 3 - Answers

Extension Task

•Can you have a go at creating your own fractions codebreaker?

•There are some examples on the following slides to guide you

•Don’t forget to send your completed codebreaker to learningfromhome@ipsleyacademy.co.uk

Codebreaker Example 1

Codebreaker Example 2

Codebreaker Example 1 – Answers(in case you decided to have a go)

Codebreaker Example 2 – Answers(in case you decided to have a go)