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      Representing a generalised number

      Lesson details

      Learning outcome

      I can use a letter to represent a generalised number.

      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.

      Teacher tip

      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.

      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.

      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

      6 Questions

      Q1.
      Match the keyword to the definition

      Correct Answer: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
      Correct Answer:unknown,a quantity that has a set value, represented by a letter
      Correct Answer: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 - 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

      To help you plan your 7 maths lesson on: Representing a generalised number, download all teaching resources for free and adapt to suit your pupils' needs...