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      Brackets in equations

      Lesson details

      Learning outcome

      I can appreciate the significance of the bracket in an equation.

      Key learning points

      1. Multiplying both sides of an equation by the same term can be shown using brackets.
      2. An expression involving brackets can be expanded.
      3. Equations involving brackets can be expressed in words.
      4. Equations involving brackets can be represented using bar models.

      Keywords

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

      Common misconception

      That "$$x$$ times five, plus three" is the same as "$$x$$ plus three, times five".

      Use visual representations to demonstrate why and how they are different. Use algebra tiles if you have them, or get pupils to draw them.

      Teacher tip

      In addition to using visual representations to show the difference between $${5x+3}=10$$ and $$5(x+3)=10$$ you can also work backwards. Give them visual representations and ask them to write the equation.

      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.
      Turning the expression $$5(y-2)$$ into $$5y-10$$ is known as the brackets.

      Correct answer: multiplying out
      erasing
      factorising
      Correct answer: expanding

      Q2.
      $$2(x+4)$$ and $$2x+4$$ are the equivalent expressions. True or false?

      True. There is a $$2$$, an $$x$$, and a $$+4$$. That means they are the same.
      Correct answer: False. $$2$$ lots of $$(x+4)$$ is $$(x+4)+(x+4)$$ which is $$2x+8$$ not $$2x+4$$
      You cannot know until you know the value of $$x$$.

      Q3.
      Which of these are expressions for the perimeter of this square?

      An image in a quiz
      $$5y+3$$
      $$4\times5y+3$$
      Correct answer: $$4(5y+3)$$
      $$20y+3$$
      Correct answer: $$20y+12$$

      Q4.
      What equation does this bar model represent?

      An image in a quiz
      $$4y=12$$
      $$4y=20$$
      Correct answer: $$4y+12=20$$
      $$4y+20=12$$
      $$4(y+12)=20$$

      Q5.
      Expand $$7(y+8)$$.

      $$7y+8$$
      $$7y+15$$
      Correct answer: $$7y+56$$
      $$y+56$$

      Q6.
      Expand $$-7(y+8)$$.

      $$7y-56$$
      Correct answer: $$-7y-56$$
      $$-7y+56$$
      $$7y+56$$

      6 Questions

      Q1.
      If you multiply both sides of an equation by $$2$$, you will maintain .

      the value
      Correct answer: equality
      equation
      the expressions

      Q2.
      True or false? Multiplying by $$5$$ and then adding $$10$$ is the same as adding $$10$$ then multiplying by $$5$$.

      True. Both have $$\times 5$$ and $$+10$$ so they are the same function.
      Correct answer: False. Order matters.

      Q3.
      What equation does this bar model represent?

      An image in a quiz
      Correct answer: $$3\times x + 5 = 17$$
      $$x + 5 \times 3 = 17$$
      $$(x + 5) \times 3 = 17$$
      $$x + 5 = 17$$
      Correct answer: $$3x + 5 = 17$$

      Q4.
      What does this bar model represent?

      An image in a quiz
      $$3\times x + 5 = 17$$
      Correct answer: $$(x + 5) \times 3 = 17$$
      Correct answer: $$3(x + 5) = 17$$
      $$x + 5 \times 3 = 17$$
      Correct answer: $$3x + 15 = 17$$

      Q5.
      Multiply both sides of this equation $${1\over3}x-5 = 2x+7$$ by $$3$$.

      $$x-5=6x+7$$
      Correct answer: $$x-15=6x+21$$
      $$3x-15=6x+21$$
      Correct answer: $$3({1\over3}x-5) = 3(2x+7)$$

      Q6.
      Which of the below is the most efficient first step to solve the equation $${3\over{x}}= 10$$ ?

      $$3({3\over{x}})= 3(10)$$
      Correct answer: $$x({3\over{x}})= x(10)$$
      $$10({3\over{x}})= 10(10)$$
      $$10x({3\over{x}})= 10x(10)$$

      To help you plan your 8 maths lesson on: Brackets in equations, download all teaching resources for free and adapt to suit your pupils' needs...