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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.

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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.

Download all resources
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Share activities with pupils
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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.

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 (2024), 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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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: $$x+3$$

Exit quiz

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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