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Lesson 6 of 17
  • Year 7

Representing an unknown or variable

I can recognise that a letter can be used to represent a specific unknown or a variable and know the difference.

View unit
Lesson 6 of 17
New
New
  • Year 7

Representing an unknown or variable

I can recognise that a letter can be used to represent a specific unknown or a variable and know the difference.

Lesson details

Key learning points

  1. A letter can be used to represent a specific unknown in a variety of ways.
  2. A letter can be used to represent a variable in a number of ways.
  3. It is possible to tell the difference between letters representing unknowns or variables

Keywords

  • Unknown - An unknown is a quantity that has a set value but is represented by a symbol or letter.

  • Variable - A variable is quantity that can take on a range of values.

  • Formula - A formula is a rule linking sets of physical variables in context. The plural of formula is formulae.

Common misconception

Pupils may think that letters always represent a set value that can be 'found'.

Highlight the distinction between unknowns and variables. Allow pupils to explore expressions intrinsically before substituting in values.


To help you plan your year 7 maths lesson on: Representing an unknown or variable, download all teaching resources for free and adapt to suit your pupils' needs...

You may wish to print the expression cards in learning cycle 2 so pupils can arrange them in order on desks. Give plenty of discussion time to see what ideas they have explored.
Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
The value halfway between 13 and 27 is

Correct Answer: 20, twenty

Q2.
Complete the calculation: $$20+40\times 4$$ =

Correct Answer: 180

Q3.
Select any values which are integers.

0.1
$$3\over 16$$
Correct answer: -3
-0.5
Correct answer: 0

Q4.
True or false: $$52y$$ is an equation for the number of weeks in a given number of years.

True - there are 52 weeks in a year
Correct answer: False - an equation must have an equals sign
Impossible to tell

Q5.
Sofia is thinking of a number. When she adds 6 then multiplies her number by 4 she gets 40. Which is an equation representing Sofia's number?

Correct answer: $$4\times (a+6)=40$$
$$a+6\times 4=40$$
$$(a+6)\times 4$$
$$6a\times 4$$
$$4a+6$$

Q6.
Which of the expressions below represent the algebra tiles in this diagram?

An image in a quiz
$$3x$$
$$4x$$
$$x+3y$$
$$4$$
Correct answer: $$x+3$$

Assessment exit quiz

Download quiz pdf

6 Questions

Q1.
A letter can be used to represent , (quantities with set values) or variables (quantities that can take on a range of values).

Correct Answer: unknowns, unknown

Q2.
Andeep says: I sleep 8 hours a night, I can write the number of hours I sleep for any number of nights as $$8n$$. which of the following are true?

Correct answer: $$n$$ is a variable
$$n$$ is an unknown
$$n$$ represents the number of hours Andeep sleeps
Correct answer: $$n$$ represents the number of nights

Q3.
True or false: $$3n$$ is always bigger than $$n$$

True - multiplying any number by 3 makes the value bigger
Correct answer: False - Multiplying a negative number by 3 makes the value smaller
They are always the same

Q4.
To cook a lamb ‘well done’ the recipe says the length of time (mins) is 50 × mass (kg) + 20. What is the variable in this scenario?

how hot the oven is
volume of the lamb
Correct answer: mass of the lamb
time to cook the lamb
70 minutes

Q5.
For the statement $$x+y=44$$. What value can $$x$$ have if it is 10 times bigger than $$y$$?

Correct Answer: 40, forty

Q6.
Match the expression with its relationship to the size of $$x$$

Correct Answer:$$x^2$$,is smaller than $$x$$ when $$x$$ is between 0 and 1

is smaller than $$x$$ when $$x$$ is between 0 and 1

Correct Answer:$$x-3$$,is always smaller than $$x$$

is always smaller than $$x$$

Correct Answer:$$x+1$$,is never smaller than $$x$$

is never smaller than $$x$$

Correct Answer:$$4x$$ ,is smaller than $$x$$ when $$x$$ is negative

is smaller than $$x$$ when $$x$$ is negative

Correct Answer:$$2x-10$$,is smaller than $$x$$ when $$x$$ is less than 10

is smaller than $$x$$ when $$x$$ is less than 10