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Lesson 3 of 17
New
New
- Year 7
Representing a generalised number
I can use a letter to represent a generalised number.
Lesson details
Key learning points
- A letter can be used to represent an unknown number in context.
- A letter can be used to represent a variable number in context.
- A letter can be used in an expression to represent a number in an expression.
- A bar model can be used to represent an expression.
Keywords
Unknown - An unknown is a quantity that has a set value but it is represented by a symbol or letter.
Variable - A variable is a quantity that can take on a range of values.
Common misconception
Pupils often think a=1 b=2 ... or that a letter represents an object
Letters represent a numerical value either unknown or variable. Avoid always using the first letter of the words used in a scenario.
You may wish to allow students to explore the two paddleboard companies without structure first. Ideas can be written on big sheets of paper or on sticky notes and collected together. Students may draw tables or graphs or think of examples.
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
6 Questions
Q1.An __________ is used to show one number or calculation is equal to another.
An __________ is used to show one number or calculation is equal to another.
addition
Correct answer: equation
equation
exponent
expression
Q2.It costs £5 to enter a fairground and then £2 for each ride. How much would it cost to enter the fair and ride 3 rides?
It costs £5 to enter a fairground and then £2 for each ride. How much would it cost to enter the fair and ride 3 rides?
Correct Answer: £11, 11, eleven pounds, 11 pounds
£11, 11, eleven pounds, 11 pounds
Q3.Select any calculation which represents the statement "I am thinking of a number. I multiply it by 10, then add 5, then subtract 2"
Select any calculation which represents the statement "I am thinking of a number. I multiply it by 10, then add 5, then subtract 2"
Correct Answer: An image in a quiz
Correct Answer: An image in a quiz
Q4.Which of these bar models represent the equation shown?
Which of these bar models represent the equation shown?
Correct Answer: An image in a quiz
Correct Answer: An image in a quiz
Q5.In a game, these shapes are worth different amounts of points. If a square is worth $$6$$ and a circle is worth $$4$$, what is the total number of points in the diagram shown?
In a game, these shapes are worth different amounts of points. If a square is worth $$6$$ and a circle is worth $$4$$, what is the total number of points in the diagram shown?
Correct Answer: 32, thirty two
32, thirty two
Q6.In a game, these shapes are worth different amounts of points. If a square is worth $$2$$ and a circle is worth $$-5$$, what is the total number of points in the diagram shown?
In a game, these shapes are worth different amounts of points. If a square is worth $$2$$ and a circle is worth $$-5$$, what is the total number of points in the diagram shown?
Correct Answer: -2, negative two
-2, negative two
Assessment exit quiz
6 Questions
Q1.Match the keyword to the definition
Match the keyword to the definition
Correct Answer:equation,a mathematical statement showing one thing equal to another
equation - a mathematical statement showing one thing equal to another
Correct Answer:generalised rule,a statement that applies to all relevant cases in a scenario
generalised rule - a statement that applies to all relevant cases in a scenario
Correct Answer:unknown,a quantity that has a set value, represented by a letter
unknown - a quantity that has a set value, represented by a letter
Correct Answer:variable,a quantity that has a range of values.
variable - a quantity that has a range of values.
Q2.True or false: It is always possible to work out the value of a variable.
True or false: It is always possible to work out the value of a variable.
True - with enough information you can use a bar model to find the value.
Correct answer: False - variables do not have set values, they vary depending on the situation
False - variables do not have set values, they vary depending on the situation
Q3.Which equation is represented by the bar model below?
Which equation is represented by the bar model below?
$$ y+2=x-5$$
Correct answer: $$x+5-2=y$$
$$x+5-2=y$$
$$y-2-5=x$$
$$y=x-2$$
Q4.Select the statement that can be represented by the equation $$a-4+2=19$$
Select the statement that can be represented by the equation $$a-4+2=19$$
I am thinking of a number, I add 4 and 2 then subtract from my number to get 19
I am thinking of a number, I subtract it from 19 and the answer is $$4+2$$
Correct answer: I am thinking of a number, I subtract 4 then add 2 and my answer is 19
I am thinking of a number, I subtract 4 then add 2 and my answer is 19
I am thinking of a number, I subtract 4 and 2 to get 19
Q5.A taxi journey costs £3 plus £2 per mile travelled. Which equation represents this?
A taxi journey costs £3 plus £2 per mile travelled. Which equation represents this?
Correct answer: $$c=2a+3$$
$$c=2a+3$$
$$3+2=c$$
$$3a+2b=c$$
$$3a+2=c$$
Q6.A taxi journey costs £3 plus £2 per mile. What is the maximum number of miles you could travel if you had £15 to spend?
A taxi journey costs £3 plus £2 per mile. What is the maximum number of miles you could travel if you had £15 to spend?
Correct Answer: 6, six
6, six
