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.