Year 8 Mathsw/c 22nd June 2020

I hope you all have all been enjoying spending time with your families. Maybe you have been reading in the sun or

meeting friends at a safe distance!

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

Pupil and parent learning sheet

Week beginning: 22nd June 2020

This week's work for Year 8 maths is concentrating on consolidating and extending your use of algebra.By the end of this week, you should be able to: 1. Collect like terms in order to simplify algebraic expressions.2. Simplify algebraic expressions using multiplication.3. Solving equations

Your work this week will include the following activities:

A choice of bronze silver and gold questions on each topic. Maybe even diamond!

A challenging and creative extension task. If you are particularly proud of your creation then e-mail it to learningfromhome@ipsleyacademy.co.uk. Also keep it as Mrs Shirley wants to make a display of your fabulous ‘lock-down work’.

For extra help with maths learning, you may also want to look at the following: Mymaths.co.uk Username: ipsleyPassword: divisionType ‘simplifying 1’ and ‘simplifying 2’ in the search bar for extra help. Also try ‘equations’.

3

2x - x is the same as : x5x - 2x is the same as : 3x

5 +7x - 3 - 2x is the same as : 5x +29f - f - 11f is the same as : -3f

8x + 2w - 3w + x is the same as : 9x-w8g - g + 5 - 4g is the same as : 3g +5

Simplifying Expressions- Collecting Like Terms

4

1) 5x - x - x 2) 7h - 2h - 3h 3) 8e - 7e 4) 7y + y - 2y5) 9w - w 6) 8g - 2g + 5g7) 7a + a - 4a - 2a + 5a

1) 4x + 6x + 3y + 2y 2) 4f + 3w + 2w3) 7h + 3c + 2h + 8c 4) 5g + g + 3t5) 8a + 4k + 2k + a 6) a + b + a + b7) 3x + 2 + 2x + 1 8) x + 1 + x + 2x9) 5h + 3g + 7 + 2g 10) 7 + x + x + y + 2

Bronze Challenge – Simplify these expressions

Silver Challenge – Simplify these expressions

5

1) 5x – x - x 2) 7h - 2h - 3h 3) 8e - 7e 4) 7y + y - 2y5) 9w - w 6) 8g - 2g + 5g7) 7a + a - 4a - 2a + 5a

3x 2h

e 6y

8w 11g

7a

1) 4x + 6x + 3y + 2y 2) 4f + 3w + 2w3) 7h + 3c + 2h + 8c 4) 5g + g + 3t5) 8a + 4k + 2k + a 6) a + b + a + b7) 3x + 2 + 2x + 1 8) x + 1 + x + 2x9) 5h + 3g + 7 + 2g 10) 7 + x + x + y + 2

10x + 5y 4f + 5w

9h + 11c 6g + 3t

9a + 6k 2a + 2b

5x + 3 4x + 1

5h + 5g + 7 9 + 2x + y

Bronze Challenge

Silver Challenge

ANSWERS!

- 4 - 3 - 2 - 1 0 1 2 3 4

Subtract Add

3x + 2y – 2x – 5y is the same as : x - 3y

2x + 4y – 5x – 8y is the same as : - 3x - 4y

4a – 2b – a – 2b is the same as : 3a - 4b

3h – 4r + h – 2r – 1 + r + 3 is the same as : 4h - 5r + 2

3x + 5xy – x + xy + 4 is the same as :

8a + 4ab – 3a – b + 1 is the same as :

6x2 – 5xy + x2 – yx + y is the same as :

2x + 6xy + 4

5a + 4ab – b + 1

7x2 – 6xy + y

Help for Gold/Diamond challenge

7

1) 4x - 5x + 3y - 2y 2) 2a – 3b – b + a3) 6g – g + 8 – 3y 4) 3g + g – 3w – w 5) 4x + 3 – x – 7 6) 4t + 1 – 4t + 2a7) 6c + 2 + 2c – 2 – 7c 8) 6 – 2x – 5y – x + y9) 4h + 3 – h + 3f – 9h – 5 + h – 110) 1 – x + y – 2x – 2y – 1 + 3x + y

1) 4xy + 3x + xy 2) 4fg – f – 3fg3) 5 + x + 5x – 2x2 4) 9a3 + 2a2 + a3 – a5) 6km – 7 – 9km + mk – 1 + m2

6) abc + cba + bca7) 5wxy + 8w2xy – 5wxy – 8w2x8) 7ax + 5 – 12xa + 3a – 4x + a – x9) 4πr2 + 8πr2 + 4ad – 12ad + 510) 6πr + 9r – πr + πd – πr3

Go

ld C

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Diam

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Simplify the following expressions:

8

1) 4x - 5x + 3y - 2y 2) 2a – 3b – b + a3) 6g – g + 8 – 3y 4) 3g + g – 3w – w 5) 4x + 3 – x – 7 6) 4t + 1 – 4t + 2a7) 6c + 2 + 2c – 2 – 7c 8) 6 – 2x – 5y – x + y9) 4h + 3 – h + 3f – 9h – 5 + h – 110) 1 – x + y – 2x – 2y – 1 + 3x + y

- x + y 3a – 4b

5g – 3y + 8 4g – 4w

3x – 4 2a + 1

c 6 – 3x – 4y

- 5h – 3 + 3f

0

1) 4xy + 3x + xy 2) 4fg – f – 3fg3) 5 + x + 5x – 2x2 4) 9a3 + 2a2 + a3 – a5) 6km – 7 – 9km + mk – 1 + m2

6) abc + cba + bca7) 5wxy + 8w2xy – 5wxy – 8w2x8) 7ax + 5 – 12xa + 3a – 4x + a – x9) 4πr2 + 8πr2 + 4ad – 12ad + 510) 6πr + 9r – πr + πd – πr3

5xy + 3x fg – f

5 + 6x – 2x2 10a3 + 2a2 – a

- 2km – 8 + m2

3abc

8w2xy – 8w2x

- 5ax + 4a – 5x + 5

12πr2 – 8ad + 5

5πr + 9r + πd – πr3

Go

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Diam

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6 x 3x

Terms can be multiplied together as in the following examples. Note:

• Multiply the coefficients (the numbers in front of the letters)

• List the letters- we write a x b x c as abc

• Think carefully about the powers. E.g. a2 x a = a3

Multiplying Terms- Model Examples

= 18x 2a x 3b = 6ab

3x x 2x = 6x2

x x x2 = x3

5p x 2p x p = 10p3

-2 x 3x2 = -6x2

Task- Choose either the bronze or silver questions here

Simplify the following expressions

=

=

=

=

=

(a) 6 x 8p

(b) 5m x 3

(e) 4p x 3q

(c) 2x x 7x

(d) x2 x 2x

(f) 3xy x 2x =

=

=

=

=

=

(g) m x 3m2

(h) 3a x 2b2 x c

(k) -3a2 x 3a

(i) y2 x 7y

(j) 4 x -3x2

(l) -2p2 x pq2 =

ANSWERS!

= 48p

= 15m

= 12pq

= 14x2

= 2x3

(a) 6 x 8p

(b) 5m x 3

(e) 4p x 3q

(c) 2x x 7x

(d) x2 x 2x

(f) 3xy x 2x = 6x2y

= 3m3

= 6ab2c

= -9a3

= 7y3

= -12x2

(g) m x 3m2

(h) 3a x 2b2 x c

(k) -3a2 x 3a

(i) y2 x 7y

(j) 4 x -3x2

(l) -2p2 x pq2 = - 2p3q2

Gold Challenge Diamond Challenge

When dividing, you divide the

coefficients and then subtract the

powers

The best thing to do here is write out the multiplication

e.g.(4m3)2=4m3 x 4m3

= 16m6

This will make you less likely to forget

to square the coefficient too!

Solving Equations

8x - 5 = 11

Example Question 3: solve

8x = 16

x = 2

Add 5 to both sides.

Divide both sides by 8

Example Question 2 : solve

5p = 15

p = 3Divide both sides by 5

x - 5 = 11

Example Question 1: solve

x = 16

Add 5 to both sides.

Whatever we do to one side of the equation we must do to the other.

4p + 10 = - 2

Example Question 4: solve

4p = -12

p = -3

Subtract 10 from both sides.

Divide both sides by 4

1) x + 3 = - 4

2) x - 7 = - 4

3) x + 4 = - 3

4) 3 + x = 5

5) - 5 + x = 8

6) 7 = x - 3

7) 10 = x + 4

8) - 3 = x - 4

9) 1 = x + 2

10) - 6 = x - 1

1) 2x = 12

2) 3x = 15

3) 5x = 30

4) 4x = 20

5) 7x = 28

6) 9x = 18

7) 6x = 24

8) 10x = 40

9) 3x = 9

10) 4x = 28

1) x + 3 = - 4

2) x - 7 = - 4

3) x + 4 = - 3

4) 3 + x = 5

5) - 5 + x = 8

6) 7 = x - 3

7) 10 = x + 4

8) - 3 = x - 4

9) 1 = x + 2

10) - 6 = x - 1

1) 2x = 12

2) 3x = 15

3) 5x = 30

4) 4x = 20

5) 7x = 28

6) 9x = 18

7) 6x = 24

8) 10x = 40

9) 3x = 9

10) 4x = 28

x = - 7

x = 3

x = - 7x = 2

x = 13x = 10

x = 6x = 1

x = - 1x = - 5

x = 6

x = 5

x = 6

x = 5

x = 4

x = 2

x = 4

x = 4

x = 3

x = 7

17

1 ) 3x + 4 = 16

2) 4x – 15 = 13

3) 2x + 9 = 15

4) 5x – 10 = 15

5) 6x + 3 = 51

6) 7x + 3 = 10

7) 4x – 3 = 33

8) 18 = 3x + 6

9) 26 = 5x – 4

10) 4 = 4x - 8

1) 2x + 3 + 4 = 17

2) 2x + 3x + 6 = 26

3) x + 4 + 2x + 6 = 31

4) 4x + 7 – 2 – x = 11

5) x + 3 + 4x – 5 = 18

6) 3x – 4 + 2x + 1 = 47

7) 6x + x – 3 – 7 = - 24

8) x + 2x + 3x + 5 = - 13

9) 3x – 5x + 4 = - 2

10) 4x – 7x – 3 – 4 = - 16

Silver Challenge Gold ChallengeHere you should

simplify first then solve

18

1 ) 3x + 4 = 16

2) 4x – 15 = 13

3) 2x + 9 = 15

4) 5x – 10 = 15

5) 6x + 3 = 51

6) 7x + 3 = 10

7) 4x – 3 = 33

8) 18 = 3x + 6

9) 26 = 5x – 4

10) 4 = 4x - 8

x = 4x = 7

x = 3

x = 5

x = 8

x = 1

x = 9

x = 4

x = 6

x = 3

1) 2x + 3 + 4 = 17

2) 2x + 3x + 6 = 26

3) x + 4 + 2x + 6 = 31

4) 4x + 7 – 2 – x = 11

5) x + 3 + 4x – 5 = 18

6) 3x – 4 + 2x + 1 = 47

7) 6x + x – 3 – 7 = - 24

8) x + 2x + 3x + 5 = - 13

9) 3x – 5x + 4 = - 2

10) 4x – 7x – 3 – 4 = - 16

x = 7

x = 4

x = 5

x = 2

x = 4

x = 10

x = - 2

x = - 3

x = 3

x =3

19

1) 6x + 2 = 3x + 17 2) 5x – 5 = 4x + 1

3) 2x + 4 = 3x + 1 4) x – 2 = 2x – 9

5) 7x + 6 = 3x + 14 6) 3x + 2 = 2x – 2

7) 3x – 5 = x – 15 8) 4x + 8 = 2x – 6

9) 5 + 2x = x + 2 10) 20 + 3x = 9x - 4

Diamond Challenge 7q + 6 = 3q + 14

4q + 6 = 144q = 8

q = 2

Subtract 3q from both sides.

Subtract 6 from both sides Divide both

sides by 4

20

1) 6x + 2 = 3x + 17 2) 5x – 5 = 4x + 1

3) 2x + 4 = 3x + 1 4) x – 2 = 2x – 9

5) 7x + 6 = 3x + 14 6) 3x + 2 = 2x – 2

7) 3x – 5 = x – 15 8) 4x + 8 = 2x – 6

9) 5 + 2x = x + 2 10) 20 + 3x = 9x - 4

x = 5 x = 6

x = 3 x = 7

x = 2 x = - 4

x = - 5 x = - 7

x = - 3 x = 4

Diamond Challenge 7q + 6 = 3q + 14

4q + 6 = 144q = 8

q = 2

Subtract 3q from both sides.

Subtract 6 from both sides Divide both

sides by 4

ExtensionOn the next two slides you will see examples of how patterns can make linear sequences (this means that they go up or down by the same amount each time). You could think of your own pattern and make a poster about it. Alternatively you could use one of the examples given and continue it further. Make sure it looks beautiful and save it to bring it back to school for Mrs Shirley to make a display.

Don’t forget to take a photo and send it to

learningfromhome@ipsleyacademy.co.uk

Number sequences can be used to solve problems involving patterns in diagrams.

How many squares of chocolate (S) will

the 10th diagram (D) contain?

D= 1

D= 2

D=3

S=4

S=1 S=3 S=5 S= 7

S = 2D - 1 S10 = 2 x 10 - 1 = 19

How many wooden braces (B) will there be, in the 20th panel (P)?

1 2 3P

B = 3P + 1 B20 = 3 x 20 +1= 61

4 7 10B

How many stone slabs (S) will the 15th diagram (D)

contain?1

2

3

D

1 5 9S

S = 4D - 3 S15 = 4 x 15 – 3 = 57

How many steel braces (B) will there be, in the 28th panel (P)?

1 2 3P

6 11 16B

B = 5P + 1 B28 = 5 x 28 + 1 = 141