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      Representing an unknown or variable

      Lesson details

      Learning outcome

      I can recognise that a letter can be used to represent a specific unknown or a variable and know the difference.

      Key learning points

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

      Keywords

      • 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.

      Common misconception

      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.

      Teacher tip

      You may wish to print the expression cards in learning cycle 2 so pupils can arrange them in order on desks. Give plenty of discussion time to see what ideas they have explored.

      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.
      The value halfway between 13 and 27 is

      Correct Answer: 20, twenty

      Q2.
      Complete the calculation: $$20+40\times 4$$ =

      Correct Answer: 180

      Q3.
      Select any values which are integers.

      0.1
      $$3\over 16$$
      Correct answer: -3
      -0.5
      Correct answer: 0

      Q4.
      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
      Correct answer: False - an equation must have an equals sign
      Impossible to tell

      Q5.
      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?

      Correct answer: $$4\times (a+6)=40$$
      $$a+6\times 4=40$$
      $$(a+6)\times 4$$
      $$6a\times 4$$
      $$4a+6$$

      Q6.
      Which of the expressions below represent the algebra tiles in this diagram?

      An image in a quiz
      $$3x$$
      $$4x$$
      $$x+3y$$
      $$4$$
      Correct answer: $$x+3$$

      6 Questions

      Q1.
      A letter can be used to represent , (quantities with set values) or variables (quantities that can take on a range of values).

      Correct Answer: unknowns, unknown

      Q2.
      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?

      Correct answer: $$n$$ is a variable
      $$n$$ is an unknown
      $$n$$ represents the number of hours Andeep sleeps
      Correct answer: $$n$$ represents the number of nights

      Q3.
      True or false: $$3n$$ is always bigger than $$n$$

      True - multiplying any number by 3 makes the value bigger
      Correct answer: False - Multiplying a negative number by 3 makes the value smaller
      They are always the same

      Q4.
      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
      Correct answer: mass of the lamb
      time to cook the lamb
      70 minutes

      Q5.
      For the statement $$x+y=44$$. What value can $$x$$ have if it is 10 times bigger than $$y$$?

      Correct Answer: 40, forty

      Q6.
      Match the expression with its relationship to the size of $$x$$

      Correct Answer:$$x^2$$,is smaller than $$x$$ when $$x$$ is between 0 and 1
      Correct Answer:$$x-3$$,is always smaller than $$x$$
      Correct Answer:$$x+1$$,is never smaller than $$x$$
      Correct Answer:$$4x$$ ,is smaller than $$x$$ when $$x$$ is negative
      Correct Answer:$$2x-10$$,is smaller than $$x$$ when $$x$$ is less than 10

      To help you plan your 7 maths lesson on: Representing an unknown or variable, download all teaching resources for free and adapt to suit your pupils' needs...