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?