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      Substituting particular values

      Lesson details

      Learning outcome

      I can substitute particular values into a generalised algebraic statement to find a sense of how the value of the expression changes.

      Key learning points

      1. Expressions and formulae in context can be evaluated for particular values.
      2. Changing the value of the letter changes the expression.
      3. Exploring what values give a particular solution can help understand the expression.
      4. Expressions may have multiple variables and we can substitute some or all of them for numbers.

      Keywords

      • Substitution - Substitute means to put in place of another. In Algebra, substitution can be used to replace variables with values.

      Common misconception

      Pupils may struggle with exponents especially which value to square when variables have coefficients

      Reminder of priority of operations and the exponent acts on the value it is directly preceded by.

      Teacher tip

      You may which to explore calculator use including squaring a negative on a calculator and the use of brackets. Get students familiar with using arrow keys to change the values they are substituting. An emulator or visualiser might be useful.

      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.
      Calculate $$(-5)^2$$

      Correct Answer: 25, twenty five

      Q2.
      Select the correct first step to evaluate $$ 2+3\times 5^2$$

      $$2+3=5$$
      $$3\times 5= 15$$
      Correct answer: $$5^2=25$$

      Q3.
      Evaluate $${12\times 2\over 4}-2$$

      Correct Answer: 4, four

      Q4.
      Starting with the first step, put these lines of working in order to show how to evaluate $${25+2\times (2+1)^2\over 10}-4$$

      1 - $${25+2\times 3^2\over 10}-4$$
      2 - $$ {25+2\times 9\over 10}-4$$
      3 - $$ {25+18\over 10}-4$$
      4 - $$ {43\over 10}-4$$
      5 - $$ 4.3-4$$

      Q5.
      In the equation $$2a+1=5-3a$$, $$5-3a$$ is called an .

      Correct Answer: expression

      Q6.
      Match up the directed number calculation with the correct value.

      Correct Answer:$$(-10)^2$$,100
      Correct Answer:$$-10\times 2$$,-20
      Correct Answer:$$-10\times -2$$,20
      Correct Answer:$$2-10$$,-8
      Correct Answer:$$2--10$$,12
      Correct Answer:$$-2--10$$,8

      6 Questions

      Q1.
      To evaluate an expression for a given value of its variable we can the value in place of the variable

      Correct Answer: substitute

      Q2.
      Match up the expressions with their value when $$r=7$$

      Correct Answer:$$r+50$$,57
      Correct Answer:$$r^2$$,49
      Correct Answer:$$6r$$,42
      Correct Answer:$$r-1$$,6
      Correct Answer:$$2r-10$$,4
      Correct Answer:$$ r+1\over 4$$,2

      Q3.
      For what value of $$y$$ does $$3y$$ have the same value as $$y+6$$? $$y=$$

      Correct Answer: 3, three

      Q4.
      For which values of $$y$$ is $$y^2-3$$ smaller than $$y$$?

      Correct answer: 0
      Correct answer: 2
      4
      -3
      Correct answer: -1

      Q5.
      For the values of $$a, b$$ and $$c$$ shown evaluate the expression $$2ab-c$$

      An image in a quiz
      Correct Answer: 26, twenty six, twenty-six

      Q6.
      For the values of $$a, b$$ and $$c$$ shown evaluate the expression $$(2a)^2-bc$$

      An image in a quiz
      Correct Answer: 112

      To help you plan your 7 maths lesson on: Substituting particular values, download all teaching resources for free and adapt to suit your pupils' needs...