1. GCSE Maths
Solving
Jo Wright

2. Quick Wits Week 14

3. What will you learn today
What will you learn today? By the end of this session I will be able to…
Solve simple equations.
Solve linear equations, with integer digits, in which the unknown appears on either side or on both sides of the equation. substitute positive and negative integers into simple algebraic expressions and formulae
substitute positive integers into algebraic expressions and formulae that include squares and cubes
substitute positive and negative integers into algebraic expressions and formulae that include squares and cubes
Confident use of own calculator and the functions available.
Build confidence in the group and explore maths topics.

4. Expanding Brackets
Expanding brackets is often called “multiplying out” brackets because we use multiplication to get rid of the brackets.

5. 5(a + 3) Expanding Brackets x x 5a + 15
To expand a bracket, multiply the term outside the bracket by everything inside the bracket x
5(a + 3) x 5a
+ 15

7. Expanding brackets and collecting like terms
Multiply out and simplify 3(5y – 3) – 2(4y + 5) 2(3x + 3y + 3) + 2(y – x - 5)

8. Expand these brackets: (Moon method)
Answers:
𝒙 𝟐 +𝟏𝟏𝒙+𝟐𝟖
𝒙 𝟐 −𝟓𝒙+𝟔
𝒙 𝟐 −𝟑𝒙−𝟏𝟎
𝑥+4 𝑥+7
𝑥−3 𝑥−2
𝑥−5 𝑥+2

9. Recap- What is a factor
Factors of 12
Factors of 21

10. Factorise 𝟏𝟎𝒙+𝟐𝟓
Factorising is taking out factors of each part of the expression.
Can I rewrite 10𝑥+25?
10𝑥=5×2𝑥
25=5×5
What appears in both parts?
Factorised: 𝟓(𝟐𝒙+𝟓)

11. Factorise 𝟑 𝒙 𝟐 +𝟓𝒙
Factorising is taking out factors of each part of the expression.
Can I rewrite 3 𝑥 2 +5𝑥?
3 𝑥 2 =3×𝑥×𝑥
5𝑥=5×𝑥
What appears in both parts?
Factorised: 𝒙(𝟑𝒙+𝟓)

12. Factorise 𝟒 𝒙 𝟐 +𝟐𝒙
Factorising is taking out factors of each part of the expression.
Can I rewrite 4 𝑥 2 +2𝑥?
4 𝑥 2 =2×2×𝑥×𝑥
2𝑥=2×𝑥
What appears in both parts?
Factorised: 𝟐𝒙(𝟐𝒙+𝟏)

13. Factorising expressions – on your own
Factorise these expressions by removing a common factor.
4a + 6
7g2 – 2g
12x + 3x2

14. Could you mark this questions?
Question: “Factorise 12xy – 9xyz” Andy says the answer is 3(4xy – 3xyz) Boris says the answer is 6(2xy – 3xyz) Cara says the answer is xy(12 – 9z) Donna says the answer is 3xy(4y – 3z) Are any of these correct?

15. Tarsia puzzle

16. Reflection of the lesson
What did you learn new today?
Why did you learn it?
How are you going to remember it?

17. Lesson 2
Expanding
Factorising

18. Starter – problem solving

19. 1
x = 4 2
x = 4 3
x = 6
3x = 12
2x - 7 = 1
3x + 5 = 23 4
x = 9 5
x = -12 6
x = 48
7x = 63
x + 7 = -5
x = 12 4
To operate:
Click the squares to reveal the question
The answers are revealed by clicking the question
If you want to give them a 30 second countdown, click the sound icon. 7
x = -10 8
x = 8
x = -5 9
x + 8 = -2
2x - 11= 5
x – 8 = -13

20. There is not a set rule for which side they need to be on.
Cancel out amounts so you get unknowns to one side of the equation and known amounts on the other.
There is not a set rule for which side they need to be on.
Make it as easy as possible for yourself.
Cancel out amounts so you get unknowns to one side of the equation and known amounts on the other.
There is not a set rule for which side they need to be on.

21. Expand brackets and solve
4(2x - 1) = 3(x + 4)

22. Something different here…
Solving equations
3(3x + 1) ≥ 21
Something different here…

23. Equations -both sides
Cancel out amounts so you get unknowns to one side of the equation and known amounts on the other.
There is not a set rule for which side they need to be on.
Make it as easy as possible for yourself.
Cancel out amounts so you get unknowns to one side of the equation and known amounts on the other.

24. Solving equations
3x + 7 = x + 12

25. Solving equations – same method
2x - 4 < 5x - 16
Something different here…

26. 5 9 x2 + 4 6 -2 x3 - 2 13 37 x2 + 7 ALGEBRA REVIEW X a 5m n 2p 4 20m b
3) Multiplying expressions
Complete the table below
5) Function machines
Find the output for each function machine
Find the inputs for the function machine
1) Collecting like terms
Simplify these expressions
(a) 3m + 5n + 2n + 12m
(b) 4p p - 2
(c) 8a + b + 5b - a
(d) 4y + 3w + y – 7w
(e) g – 4h + 8g + 6h
(*f) ab + 2a + 5ab – 5b X a 5m n 2p 4
20m b 3h
6hp 3p 5 9 x2
+ 4 6 -2 x3
- 2 13 37 x2
+ 7
4) Expand brackets
Expand 3(2y + 1)
Expand 5(3m - 4)
(*c) Expand 4(2w + 3) + 2(3w + 9)
2) Substitution
a = 3, b = 5, c = -2, d = 10
(a) 4b (b) d
(c) 3c (d) 5a + 2
(e) 3b (f) 3c + 1
(g) 2c (h) ab
(i) 5² (*j) 4b – 6 2
Objective
Mastered
I can collect like terms
  
I can substitute positive values into expressions
I can substitute negative values into expressions
I can multiply an expression by an integer
I can multiply two algebraic expressions
I can expand brackets
I can use a function machine to find an output when given an input
I can use a function machine to find an input when given an output

27. ALGEBRA REVIEW 4) Formulae Substitution The formula t = v – u a
a = 3, b = 5, c = -2, d = 10
(a) 3b – d (b) ac + b
(c) b(4a – 3) (d) a(2b + c) 4
4) Formulae
The formula t = v – u a
is used to calculate time (t).
If v = 21, u = 6 and a = 3, calculate what t will be?
If v = 14, u = 2 and t = 3, calculate what a is?
Expand brackets
Expand 3(4y – 5)
Expand m(3m + 5)
Expand 4(2w – 3) + 2(3w + 9)
Expand 5(2y + 1) – 3(3y – 2)
Expand (p + 3)(p + 5)
Shape algebra
Calculate the perimeter and area of this rectangle 3
4n - 1
Objective
Mastered
I can expand single brackets
  
I can expand separate brackets
I can expand double brackets
I can factorise expressions into single brackets
I can substitute into expressions
I can substitute into formulae
I can solve algebra problems in shapes
2) Factorise
Factorise b – 10
Factorise a² + 3a
Factorise a – 15ab