GCSE Maths Solving Jo Wright

Quick Wits Week 14

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.

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

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

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

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

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

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)

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)

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)

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

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?

Tarsia puzzle

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

Lesson 2 Expanding Factorising

Starter – problem solving

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

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.

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

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

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.

Solving equations 3x + 7 = x + 12

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

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 + 6 + p - 2 (c) 8a + b + 5b - a (d) 4y + 3w + y – 7w (e) g – 4h + 8g + 6h (*f) 3ab + 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) 12d (c) 3c (d) 5a + 2 (e) 3b - 11 (f) 3c + 1 (g) 2c - 6 (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

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 6b – 10 Factorise a² + 3a Factorise 20a – 15ab