Representing an unknown or variable | Maths | Quizalize & Oak National Academy

Starter quiz

The value halfway between 13 and 27 is ______
- '20' ✓
Complete the calculation: $20+40\times 4$ = ______
- '180' ✓
Select any values which are integers.
- 0.1
- $3\over 16$
- -3 ✓
- -0.5
- 0 ✓
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
- False - an equation must have an equals sign ✓
- Impossible to tell
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?
- $4\times (a+6)=40$ ✓
- $a+6\times 4=40$
- $(a+6)\times 4$
- $6a\times 4$
- $4a+6$
Which of the expressions below represent the algebra tiles in this diagram?
- $3x$
- $4x$
- $x+3y$
- $4$
- $x+3$ ✓

A letter can be used to represent ______, (quantities with set values) or variables (quantities that can take on a range of values).
- 'unknowns' ✓
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?
- $n$ is a variable ✓
- $n$ is an unknown
- $n$ represents the number of hours Andeep sleeps
- $n$ represents the number of nights ✓
True or false: $3n$ is always bigger than $n$
- True - multiplying any number by 3 makes the value bigger
- False - Multiplying a negative number by 3 makes the value smaller ✓
- They are always the same
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
- mass of the lamb ✓
- time to cook the lamb
- 70 minutes
For the statement $x+y=44$ . What value can $x$ have if it is 10 times bigger than $y$ ?
- '40' ✓
Match the expression with its relationship to the size of $x$
- $x^2$
  
  ⇔
  
  is smaller than $x$ when $x$ is between 0 and 1 ✓
- $x-3$
  
  ⇔
  
  is always smaller than $x$ ✓
- $x+1$
  
  ⇔
  
  is never smaller than $x$ ✓
- $4x$
  
  ⇔
  
  is smaller than $x$ when $x$ is negative ✓
- $2x-10$
  
  ⇔
  
  is smaller than $x$ when $x$ is less than 10 ✓

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

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.

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.