What are the possibilities? Content covered Algebra GFED Situation Some more to try Reflection Thinking harder Warm up Test yourself cards A short activity to get students thinking about the information in a question – ideal for the beginning of the lesson Choose the activity(ies) that best suit your students’ learning needs. Four questions to encourage students to think about alternative questions using the same information Four questions to encourage students to use higher order thinking skills to consider question alternatives Three more questions to practise the same approach in different contexts An opportunity for students to assess and reflect on their progress, including the grade they are working at Key points which can be printed and used at home or in pairs in the classroom

Algebra GFED Situation – Content covered FAlgebraSolve linear equations with one operation EAlgebraSimplify by adding and subtracting terms EAlgebraUse simple formulas EAlgebraForm simple algebraic expressions DAlgebraSimplify by multiplying and dividing letters and numbers DAlgebraSolve linear equations with two or more operations DAlgebraExpand single brackets Reflection

Answers Algebra GFED Situation – Warm up 1.Simplify 4x + 2x − (The answer is not in the box.) 2.Which of the expressions above are divisible by 5? 3.Which two expressions have a difference of 5? 4.Write and answer a simple question using some of the expressions above. 4x 5C p + 9 2x − y x x − 3 5 p 7p 2y C + 5 6x 8xy 3y + 1 y − 4 -2x + 7y ( ) ( ) + + − − × ÷

Algebra GFED Prompts Thinking prompts Thinking prompts Answers Algebra GFED Situation – What are the possibilities? 1.Write an equality by combining some of the above to form the left-hand side. 2.(i) Solve 3y + 1 = 7 (ii) Simplify 7p + p + 3 − 5[4 marks] 3.Make up a mark scheme for this question. 4.Write a contextualised exam question that uses some of the expressions above. Question 3 Three kinds of marks can be given: B for something being correct, irrespective of method M for carrying out a correct step A for a correct answer Question 4 Use the Prompts button to help students who are unfamiliar with this style of question. Use the Thinking prompts button to help students be more creative with their questions. 4x 5C p + 9 2x − y x x − 3 5 p 7p 2y C + 5 6x 8xy 3y + 1 y − 4 -2x + 7y ( ) ( ) + + − − × ÷

Algebra GFED Situation – Thinking harder Answers 1.Write two equalities using the items above. 2.Write two equalities that involve 8xy. 3.Write two false statements using the items above. 4.Write three statements that might be true using the items above. Give reasons for your choices. 4x 5C p + 9 2x − y x x − 3 5 p 7p 2y C + 5 6x 8xy 3y + 1 y − 4 -2x + 7y ( ) ( ) + + − − × ÷

Algebra GFED Answers Algebra GFED Situation – Some more to try 1.Jack hires a cordless hammer drill for £20, plus £15 per day. Write an expression for the cost of hiring it for N days. How much will it cost to hire for 3 days? 3.2x + 3= 1 3x − 7= 9 4 − x = 2 2.(x + 3) (x − 4) (x + 7) (2x − 1) (x − 3) (x + 1) Pair up the three equations with the three answers so that x has the same value for each equation. What is this value of x? Which pair, when added together and simplified, gives 2x − 3?

I can  Simplify by adding and subtracting terms Simplify by multiplying and dividing letters and numbers Solve linear equations with one operation Solve linear equations with two or more operations Use simple formulae Algebra GFED Situation – Reflection Self assess Find or write some evidence to support your assessment. Write down your next steps. You may wish to use the Test yourself cards. Self assess Find or write some evidence to support your assessment. Write down your next steps. You may wish to use the Test yourself cards. E E E D D Click below the button to reveal the grades.

These cards contain some of the key terms and skills you will need to answer algebra questions. Copy down the ones you need or ask your teacher for a printout. These cards contain some of the key terms and skills you will need to answer algebra questions. Copy down the ones you need or ask your teacher for a printout. What does term mean?What does simplify mean? A ‘small’ chunk of algebra, e.g. 7yCollect like terms or cancel What does solve mean?What is an equation? In the case of an equation, find the value (or values) of the unknown Two expressions with an = sign between them How do you solve equations?What does expression mean? By getting the unknown on its own on one side of the equation by using inverses or doing the same to both sides a ‘larger’ chunk of algebra with multiple terms joined by operations, e.g. 3p − 7y How do you simplify expressions? How do you substitute? By doing the sums that you can do i.e. collecting like terms Replace the letters in an expression or formula by numbers Algebra GFED Situation – Test yourself cards

Algebra GFED Situation – Answers for Warm up 1.6x C + 25 and 5 3.x + 2 and x − 3 4. Possible simple questions are: –Simplify 7p × 2y [answer 14py] –Simplify x − 3 − 8 [answer x − 11] –Solve y − 4 = 3 [answer y = 7] –Multiply out 3(x + 2) [answer 3x + 6]

Algebra GFED Situation – Answers for What are the possibilities? 1.Some true statements you could write down are: 7p + p = 8pC + 5 − 5 = Cy − 4 + 2y = 3y − 4 3y y − x + 7y − 4x + 6x = 11y − 3 2. and 3. (i) 3y + 1 = 7 3y = 61 mark y = 21 mark (ii) 7p + p + 3 − 5 8p − 2 2 marks Examiner note: ‘ 8p’ scores 1 mark and ‘ − 2’ scores the second mark. 4.The exam questions would normally be a selection to test techniques and do not need to have any connection with each other. Possible exam questions, in addition to those in Warm up question 4, are: –Solve 2x − 1 = 5[2 marks, grade E] –Solve p + 9 = -8[1 mark, grade E] –Simplify 3y y − 4 − 2y[2 marks, grade E] –Simplify 9y × 7p[1 mark, grade D ]

Algebra GFED Situation – Answers for Thinking harder 1.e.g. 5(C + 5) = 5C + 256x – 4x + 3 − 2 = 2x − = 56x – 4x + 9y – 2y = -2x + 7y x + 2 − 5 = x − 3 3y + 1 – (y – 4) = 2y of:8xy ÷ 4x = 2y 8xy ÷ 2y = 4x 4x × 2y = 8xy 3.Some false statements include: p + 9 = p subtract p from both sides to get 9 = 0 3y + 1 − 2y = y − 4simplify and subtract y from both sides to get 1 = -4 x + 2 = x − 3 subtract x from both sides to get 2 = -3 4.e.g. p + 9 = 5 (true when p = -4) y − 4 = 2y (true when y = -4) 2x − 1 = x + 2(true when x = 3)

1.Jack hires a cordless hammer drill for £20, plus £15 per day. Write an expression for the cost of hiring it for N days. How much will it cost to hire for 3 days? 3.2x + 3= 1 3x − 7= 9 4 − x = 2 2.(x + 3) (x − 4) (x + 7) (2x − 1) (x − 3) (x + 1) Pair up the three equations with the three answers so that x has the same value for each equation. What is this value of x? Which pair, when added together and simplified, gives 2x − 3? 15N + 20 £65 (x − 4) (x + 1) x = 3 Algebra GFED Situation – Answers for Some more to try

Algebra GFED Situation – Prompts Think of a really boring question… Think of a really obvious question… Think of a really hard question… Think of a really strange question… Think of a really short question… Think of a really easy question…

Algebra GFED Situation – Thinking prompts Is there a question that would involve multiplication? Is there a question that would involve the number 90? Is there a question that would mean dividing? Could I make a question worth 2 marks? Could I make a question with fractions in it? Could I make a question with an answer less than 1? Could I make a question worth 5 marks? Is there a question that would mean adding some of the numbers?