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Year 7

Representing a generalised number

I can use a letter to represent a generalised number.

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New
New
Year 7

Representing a generalised number

I can use a letter to represent a generalised number.

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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 an unknown number in context.
  2. A letter can be used to represent a variable number in context.
  3. A letter can be used in an expression to represent a number in an expression.
  4. 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 (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.
An __________ is used to show one number or calculation is equal to another.
addition
Correct answer: 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?
Correct Answer: £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"
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Q4.
Which of these bar models represent the equation shown?
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
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?
An image in a quiz
Correct Answer: 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?
An image in a quiz
Correct Answer: -2, negative two

Exit quiz

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6 Questions

Q1.
Match the keyword to the definition
Correct Answer:equation,a mathematical statement showing one thing equal to another

a mathematical statement showing one thing equal to another

Correct Answer:generalised rule,a statement that applies to all relevant cases in a scenario

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

a quantity that has a set value, represented by a letter

Correct Answer:variable,a quantity that has a range of values.

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 - 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
Q3.
Which equation is represented by the bar model below?
An image in a quiz
$$ y+2=x-5$$
Correct answer: $$x+5-2=y$$
$$y-2-5=x$$
$$y=x-2$$
Q4.
Select the statement that can be represented by the equation $$a-4+2=19$$
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 and 2 to get 19
Q5.
A taxi journey costs £3 plus £2 per mile travelled. Which equation represents this?
Correct answer: $$c=2a+3$$
$$3+2=c$$
$$3a+2b=c$$
$$3a+2=c$$
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?
Correct Answer: 6, six