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      Securing understanding of expressions and equations

      Lesson details

      Learning outcome

      I can manipulate a simple equation using a bar model.

      Key learning points

      1. Calculations can be evaluated by following the standard order of operations for 4 operations.
      2. Calculations including exponents and brackets can be evaluated following the standard order of operations.
      3. A bar model can be used to represent an equation.
      4. A bar model can be used to find unknowns in a simple equation.

      Keywords

      • Equation - An equation is used to show that one number or calculation is equal to another.

      • Exponent - An exponent is a number positioned above and to the right of a base value. It indicates repeated multiplication.

      • Commutative - An operation is commutative if the values it is operating on can be written in either order without changing the calculation.

      Common misconception

      Pupils think division has to be calculated before multiplication and addition before subtraction.

      Show pupils different ways of working out the same calculation that gives the same answer.

      Teacher tip

      Be careful with language around priority of operations. Avoid saying 'do the brackets first' as this leads to misconception around expanding brackets. Give pupils time to explore methods that lead to the same answer.

      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.
      Given that $$12+6=18$$, which equations are also true?

      $$18+6=12$$
      Correct answer: $$18-6=12$$
      Correct answer: $$18-12=6$$
      $$12-6=18$$

      Q2.
      Calculate: $$2+4\times 5$$ =

      Correct Answer: 22, twenty two, twenty-two

      Q3.
      Calculate: $$10\times(6+3)$$ =

      Correct Answer: 90, ninety

      Q4.
      Select another way of writing $$4\times 4\times 4$$

      $$3^4$$
      $$4^2$$
      $$3\times 4$$
      Correct answer: $$4^3$$
      12

      Q5.
      The calculation $$38\times 14$$ is the same as $$14\times 38$$ because multiplication is __________.

      associative
      Correct answer: commutative
      distributive
      divisible
      exponential

      Q6.
      Andeep is 1.4 metres tall, when he stands on a stool he is 1.7 metres tall. Which bar model represents this scenario?

      Correct Answer: An image in a quiz
      An image in a quiz
      An image in a quiz
      An image in a quiz
      An image in a quiz

      6 Questions

      Q1.
      Find the value represented by the square in the bar model shown. The square represents

      An image in a quiz
      Correct Answer: 7, seven

      Q2.
      Here is $$7^4$$. What does the number 4 represent in this example?

      the base
      Correct answer: the exponent
      the cube
      the square
      the multiple

      Q3.
      Which equations match the bar model 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
      An image in a quiz

      Q4.
      Calculate: $$5\times(4+8)\div2^2$$ =

      Correct Answer: 15, Fifteen

      Q5.
      Select any calculation that matches the description: 'I am thinking of a number. I add 5, then multiply by 10, then subtract 2"

      Correct Answer: 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
      An image in a quiz
      An image in a quiz

      Q6.
      Starting with the smallest, sort these calculations into order of size when evaluated.

      1 - $$2\times 5+4\times3$$
      2 - $$2\times (5+4\times3)$$
      3 - $$(2\times 5+4)\times3$$
      4 - $$2\times (5+4)\times3$$

      To help you plan your 7 maths lesson on: Securing understanding of expressions and equations, download all teaching resources for free and adapt to suit your pupils' needs...