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

F Algebra Solve linear equations with one operation

E Algebra Simplify by adding and subtracting terms

E Algebra Use simple formulas

E Algebra Form simple algebraic expressions

D Algebra

Simplify by multiplying and dividing letters and numbers

D Algebra

Solve linear equations with two or more operations

D Algebra Expand single brackets

Reflection

Answers

Algebra GFED

Situation – Warm up

1. Simplify 4x + 2x − 1 + 5 (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 + 25 3 p + 9 2x − 1 -8 9y x + 2

2 x − 3 5 p 7p 2y C + 5 6x 8xy

3y + 1 y − 4 -2x + 7y ( ) ( ) + + − −

× ÷

Algebra GFED

PromptsThinking 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 3Three 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 4Use 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 + 25 3 p + 9 2x − 1 -8 9y x + 2

2 x − 3 5 p 7p 2y C + 5 6x 8xy

3y + 1 y − 4 -2x + 7y ( ) ( ) + + − −

× ÷

Algebra GFEDAlgebra 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 + 25 3 p + 9 2x − 1 -8 9y x + 2

2 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.

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.

What does term mean? What does simplify mean?

A ‘small’ chunk of algebra, e.g. 7y Collect 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 + 4

2. 5C + 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 = 8p C + 5 − 5 = C y − 4 + 2y = 3y − 4 3y + 1 + y − 4 + -2x + 7y − 4x + 6x = 11y − 3

2. and 3. (i) 3y + 1 = 7

3y = 6 1 mark y = 2 1 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 + 1 + 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 + 25 6x – 4x + 3 − 2 = 2x − 1

2 + 3 = 5 6x – 4x + 9y – 2y = -2x + 7y

x + 2 − 5 = x − 3 3y + 1 – (y – 4) = 2y + 5

2. 2 of: 8xy ÷ 4x = 2y8xy ÷ 2y = 4x4x × 2y = 8xy

3. Some false statements include:p + 9 = p subtract p from both sides to get 9 = 03y + 1 − 2y = y − 4 simplify and subtract y from both sides to get

1 = -4x + 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?