Maths - Class Mrs Potter Class 7/8 Theme: Algebra Summer 2 Week 4

Activity 1: What is algebra – recap if neededFollow the link below for an explanation of what algebra is and watch the video to see how it is used in the work place.

https://www.bbc.co.uk/bitesize/topics/z9yb4wx/articles/zkf7xfrActivity 2: Using algebraic notation – recap if neededFollow the link below and watch the video to look at how to write algebraic expressions and what the rules are.

https://www.bbc.co.uk/bitesize/topics/z9yb4wx/articles/zj8sv9qThen read the slide below in activity 2 and use to complete the tables - reading and forming algebraic expressions.Activity 3: Forming Algebraic expressions - revision

Form expressions for the perimeters of the rectangles under activity 3Activity 4: Forming Algebraic expressions – revision

Read the slides under activity 4 and complete the worksheet on forming expressionsActivity 5: Linking formulas in words and algebra

Try to match the word formulas with correct algebraic formulas – under activity 5Activity 6: Simplifying expressionsFollow the link below to remind you how we collect like terms together

https://www.bbc.co.uk/bitesize/topics/z9yb4wx/articles/zkvxh39Then do the questions under activity 6

Activity 7: More simplifyingFollow the link below to revise more simplifying https://www.bbc.co.uk/bitesize/guides/zx7xsbk/revision/3

Then do the questions under activity 7Activity 8: Multiplying out bracketsFollow the link below on how to multiply out brackets – watch the video, read the explanation and examples, and try the quiz https://www.bbc.co.uk/bitesize/topics/z9yb4wx/articles/zbkyb82

Then try the questions under activity 8Activity 9 – Simplifying extension activityTry the question under activity 9Activity 10 – simplifying – multiplication – extension activityFollow the link below to learn how to simplify when multiplying terms together and try the questions at the endhttps://www.bbc.co.uk/bitesize/guides/zx7xsbk/revision/4

Then try the questions under activity 10

Activity 2

 

Use the rules above to say what each of these expressions mean

Expression Number sentence (what it means)2 + n

6nn - 9

3n + 3n5

n – 52(n+4)

5n2

n + 62n+45 – n

Write expressions for the following number sentences

Number sentence ExpressionAdd 7 to gSubtract 5 from yMultiply 8 by pMultiply f by 6Divide t by 10Divide 15 by vMultiply d by 6 and add 7Multiply 4 by e and subtract 9Add 6 to h and then multiply by 7Multiply k by 5 and then divide by 4Multiply a by aSubtract 6 from n and then divide by 3

Activity 3

Activity 4

24cm²

Now try this worksheet:-Writing Expressions

1. If Miss Green starts with n cubes, give expressions for how many cubes she has if:-

a)4 more are added _______b)6 are taken away _______c) She triples (x3) her number of cubes _______d)She halves her number of cubes ________e)She doubles the number of cubes and adds 5 ______

2. If the number of biscuits in a packet is b, give expressions for the number of biscuits in:-

a)A packet and 8 more biscuits ________b)A packet and 10 more biscuits ________c) A packet with 6 biscuits taken out _________d)A packet with 3 biscuits taken out _________e)2 packets of biscuits ________f) 10 packets of biscuits ________g)2 packets and 8 more biscuits _________h)10 packets and 10 more biscuits ________i) 2 packets with 6 biscuits taken out of 1 of the packets

_________j) 10 packets with 3 biscuits taken out of 1 of the packets

_________k) ½ a packet of biscuits _________l) 6 packets with 3 biscuits taken out of each packet

(challenge – need brackets!!) __________

3. If John has g sweet, give expressions for the number of sweets his friends have if:-

a) Donna has 6 more sweet than John ______b) Amil has 7 fewer sweet than John ______c) Hannah has a quarter of the sweet that John has ______d) Denal has 3 times plus 5 more sweets than John _______

4. If Sumair is f years old, give expressions for the ages of:-a)Sam who is 5 years older than Sumair ________b)Adele who is 12 years older than Sumair ________c) Izadin who is 4 years younger than Sumair _______d)Layla who is twice as old as Sumair _______e)Peter who is half as old as Sumair _______f) Javeer who is three times as old as Sumair plus 2 years

_______g)Sam’s and Adele’s ages together __________________h)Adele’s and Izadin’s ages together _________________i) The total ages of Sumair and her 6 friends (challenge)

_______________________________________(you will need to simplify for parts g, h, and i)

j) If Sumair is 10 work out the ages of her 6 friends and the total age of them altogether.

Sam ____Adele _____Izadin _____Layla _____Javeer _____Total ______

Activity 5

Algebraic Formula Word FormulaA A=πr² 1 The Area of a triangle is the base

times the height then divided by two

B A = ½ ( b h ) 2 Temperature in Fahrenheit is equal to the temperature in Centigrade take away thirty-two then multiply this by five ninths.

C F = 5/9 (C – 32) 3 Cooking time in minutes is equal to the weight in kilograms multiplied by forty five then add thirty.

D V = IR 4 The cost of hiring a car is equal to fifteen times the days you travel then add 0.2 times the number of miles you travel.

E E = ½ mv² 5 The number of energy tablets allowed in a year is equal to the volume of your lungs squared multiplied by twice your mass.

F C = 15d + 0.2 m 6 Density equals the mass of an object divided by its volume

G S = d/t 7 Voltage of electricity is equal to the current multiplied the resistance

H D = m/v 8 Energy equals the velocity squared multiplied by the mass then halved

I T = 45W + 30 9 The area of a circle is the radius squared multiplied by pie.

J T = 2mv2 10 Speed equals the total distance traveled divided by the total time taken.

Activity 6Simplify the following expressions:-

1. a + a + a + a =2. b + b + 2b = 3. 3c + 4c =4. 2d + 3d + d =5. 6e + 5e + 2e + e =6. 5f – f =7. 7g – 3g =8. 9h – 3h – 2h =9. 5i – 5i =10. 4j –2j – 2j =

11. 4k + k – k =12. 6l + 5l – 4l =13. 7m – 5m + m =14. 5n – 3n + 4n – n + 5n =15. 2o – o + o + o + o – 2o =16. 3p – 3p + 3p =17. 6q – 9q + 4q =18. 4r + 5r – 9r =19. 2s + 3s – 5s =20. 4t + t – 6t=21. 5u + u – 6u – 3u =22. v – 3v – 4v =

Activity 7

1. 3t + 3 + 2t + 5t – 6 = 2. 4g + 2b + 3g + 3b =3. w + 3w + 4+ 5 =4. r + 4r + 5 +6 + r =5. t + 5t - 3t + 3 -2 + t =6. a + 3 + 3a + a - 5 - 2a =7. f - 4 + 3f + 6 =8. 5d + 3 + 2d - 6 =9. 5 + y + 5y - 7 =10. 6k – 4k – 3 + 5=11. 5v + 4b – 3v + 4b - 8 =12. 5n +4 – 7p + n + 4 =

13. 7f + 3v + 3f + 2v + 4 =14. 9n + 5 + 3d + 4 - 3n - 2 = 15. 3p + 2 – p + 4 + 5g =16. 5k + 3 + 4h + 3 + - k – h =17. 4d – 5 – 3d + 6 + 6d =18. 5 – 3v + 5 + 4v =19. 4k + 3 – 5f + 6k + 7 + 8f =

Activity 8

Multiply out these brackets.a 5(2t + 3) = b 3(6t – 4) =c 4(9 – 4t) = d 3(7t + 3s) =e 6(2t – 3s) = f 5(t – 8) =g t(t + 3) = h 7(4t – 5s) =i 2t(2t + 3) = j s(3t – 2s) =

2 Match equivalent expressions from each box.The first one is done for you.6(3x –2y) = 18x –12y

6(3x – 2y)8x + 6y

4(6x – 5y)9x – 12y

2(7x + 3y)8(3x – y)

5(6x + 9y)

2(12x – 10y)18x – 12y4(6x – 2y)14x + 6y

2(4x + 3y)3(10x + 15y)

3(3x – 4y)

3 Challenge In this question you need to match the number that you multiply the bracket by to give the expression. One has been done for you.

18t + 27

20t + 28

18t + 24

6

9

5

(2t + 3)=9(2t + 3)

(5t + 7)

(3t + 4)

10t + 15

9t + 12

8t + 12

30t + 42

30t + 40

35t + 49

4

6

3

7

4

10

(2t + 3)

(3t + 4)

(2t + 3)

(5t + 7)

(3t + 4)

(5t + 7)

Activity 9

Expand and simplify        

1)

a)2( x+1)+3( x+2)= b) 4 ( x+3)+2( x+7 )= c) 5( x+3 )+2 (x+7 )=

d) 8( x+10 )+2( x+4 )= e)2(2 x+1 )+3(4 x+2 )= f)

3(5 x+7)+2(6 x+1 )=

2)

a) 5(x + 7) + 3(x – 2) = b) 6(x+4) + 4(x – 3) = c) (3(x+5) + 6(x – 4)

=

d) 2(3x + 4) + 5(2x – 3) = e) 3(2x – 3) + (4x – 5) = f) 5(3x – 4) +

4(2x – 1) =

3)

a)4 ( x+4 )−3( x+2)= b) 5( x+2)−2( x+1 )= c) 7( x+3 )−4 ( x+2)=

d)

2(5 x+10)−2 (3 x+1)=

e)4 (5 x+5)−4 (2x+2)

=

f) 7(2 x+4 )−4 (3x+6 )

=

Activity 10Simplify    

1) r × s × 4 =

2) d x d x t x t x t =

3) 3 x g x j x g x j x 5 x g x g =

4) 4e × 5f =

5) 6h x 8h =

6) s2 x s2 =

7) p3 x p =

8)   x7 × x5 =

9) 4c4 x 5c6 =

10) q x q x q =

11) y6 x y4 x y =

12) 2p2 x 3p4 x 5p3 =