Welcome GCSE Maths

Objectives Learners will be able to... Define sets of numbers by describing or by listing. Explain the terms ‘universal’, ‘null or empty’, ‘Intersection’ and ‘Union’. Use correct notation when working with sets.

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.

5a + 15 Expanding Brackets 5(a + 3) Expanding brackets is often called “multiplying out” brackets because we use multiplication to get rid of the brackets. 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) + 2(y - 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)

Could you mark this questions? Question: “Fully 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 solving

Starter – problem solving

1 x = 4 2 x = 4 x = 6 3 3x = 12 2x - 7 = 1 3x + 5 = 23 4 x = 9 5 x = -12 x = 48 6 x = 12 4 7x = 63 x + 7 = -5 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

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.

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

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

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

Solving practice Answer questions by applying skills on solving. Answer questions by applying expanding knowledge to solve

Extenstion work