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      Additive relationships

      Lesson details

      Learning outcome

      I can appreciate that an additive relationship between variables can be written in a number of different ways.

      Key learning points

      1. When adding or subtracting, terms may only be combined if the order of each variable in each term is the same.
      2. The sum of the terms can be thought of as a term, despite being comprised of multiple terms.
      3. a + b = c also means that a = c − b
      4. a = c − b can also be written as a = c + (−b)

      Keywords

      • Equation - An equation is used to show two expressions that are equal to each other.

      Common misconception

      Rearranging equations means you can just swap where terms are.

      Remind pupils that subtraction and division are not commutative so swapping the order will matter.

      Teacher tip

      Being able to draw bar models to represent an additive relationship can really support pupils.

      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.
      63 + 37 = 100 being rearranged to 37 + 63 = 100 is an example of __________.

      categorisation
      Correct answer: commutativity
      congruency
      coordination
      cumulation

      Q2.
      When rearranging equations, you must perform the same operation to both sides in order to maintain __________.

      equation
      Correct answer: equality
      equalness
      equilateral

      Q3.
      In the equation 172 + 398 = 570, the term 570 can be described as the __________ of 172 and 398.

      factor
      multiple
      product
      Correct answer: sum

      Q4.
      Given that 1734 + 2117 = 3851, which of these calculations are correct?

      Correct answer: 2117 + 1734 = 3851
      1734 + 3851 = 2117
      3851 + 2117 = 1734
      Correct answer: 3851 − 2117 = 1734
      2117 = 1734 − 3851

      Q5.
      Match each operation to its inverse operation.

      Correct Answer:Addition,Subtraction

      Subtraction

      Correct Answer:Subtraction,Addition

      Addition

      Correct Answer:Multiplication,Division

      Division

      Correct Answer:Squaring,Square rooting

      Square rooting

      Q6.
      Which of these equations can be represented by this bar model?

      An image in a quiz
      Correct answer: $$x+3=15$$
      $$x=3+15$$
      Correct answer: $$15-x=3$$
      $$3x=15$$
      $$x-15=3$$

      6 Questions

      Q1.
      $$3x^2+4x=13$$ being rearranged to $$4x+3x^2=13$$ is an example of __________.

      constants
      communication
      Correct answer: commutativity
      cumulativity

      Q2.
      Which of these equations are valid rearrangements of the generalisation $$a+b=c$$ ?

      $$b+c=a$$
      Correct answer: $$b+a=c$$
      $$b-c=a$$
      Correct answer: $$c-b=a$$
      Correct answer: $$c-a=b$$

      Q3.
      Which of these equations are valid rearrangements of the equation $$100-2x=5y$$ ?

      Correct answer: $$100-5y=2x$$
      $$100+5y=2x$$
      Correct answer: $$2x+5y=100$$
      $$2x+100=5y$$
      $$2x-100=5y$$

      Q4.
      Which of these equations are represented in this bar model?

      An image in a quiz
      Correct answer: $$23+2c=9d$$
      $$2c-9d=23$$
      Correct answer: $$9d-2c=23$$
      Correct answer: $$9d-23=2c$$
      $$23-9d=2c$$

      Q5.
      Which of the below are correct rearrangements of the equation 71 + 13 + 15 = 99 ?

      Correct answer: 71 = 99 − 15 − 13
      71 = 99 − (15 − 13)
      Correct answer: 71 = 99 − (15 + 13)
      71 = 99 − 15 + 13
      71 = 99 + 15 − 13

      Q6.
      Which of the below are correct rearrangements of the equation $$9x^3+2y-7=3z$$ ?

      $$9x^3=3z+2y-7$$
      $$9x^3=3z+(2y-7)$$
      Correct answer: $$9x^3=3z-(2y-7)$$
      $$9x^3=3z-2y-7$$
      Correct answer: $$9x^3=3z-2y+7$$

      To help you plan your 9 maths lesson on: Additive relationships, download all teaching resources for free and adapt to suit your pupils' needs...