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      General algebraic forms for specific number properties

      I can fluently write general algebraic forms for different number properties.

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      Lesson 7 of 14
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      • Year 11

      General algebraic forms for specific number properties

      I can fluently write general algebraic forms for different number properties.

      Lesson details

      Key learning points

      1. The divisibility tests can be used to help write general algebraic forms of multiples.
      2. By understanding the general algebraic form of multiples, other values can be expressed.

      Keywords

      • Multiple - A multiple is the product of a number and an integer.

      • Integer - An integer is any positive or negative whole number or zero.

      Common misconception

      Pupils may think it is acceptable to use the same letter for all expressions.

      It may be acceptable for the letter to be the same but that depends on what the letter is representing. This is explored in the first learning cycle with chocolates.

      Writing an appropriate general algebraic form can be challenging. Encourage pupils to come up with alternative correct forms and ask them to test their generalisations for different values.
      Teacher tip

      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

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      6 Questions

      Q1.
      Which of these are integers?

      Correct answer: 5
      Correct answer: -1
      $$1\over 2$$
      20.4
      Correct answer: 0

      Q2.
      A multiple is the product of a number and...

      Correct answer: an integer.
      any other number.
      a positive number.
      itself.

      Q3.
      Which of these are multiples of 3?

      Correct answer: 54
      73
      125
      Correct answer: 231
      334

      Q4.
      Which of these is an example of consecutive integers?

      Correct answer: -5, -4, -3, -2
      -0.5, 0.5, 1.5, 2.5
      Correct answer: -1, 0, 1, 2
      0, 2, 4, 6
      23, 24, 25, 27

      Q5.
      Which of these shows consecutive even integers?

      5, 7, 9, 11
      10, 11, 12, 13
      14, 18, 22, 26
      Correct answer: 30, 32, 34, 36

      Q6.
      Which shows consecutive square numbers?

      2, 4, 6, 8
      Correct answer: 4, 9, 16, 25
      1, 5, 10, 20
      Correct answer: 49, 64, 81, 100
      121, 144, 196, 225

      Assessment exit quiz

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      6 Questions

      Q1.
      Which of these expressions could be even if $$n$$ is an integer?

      Correct answer: $$n$$
      Correct answer: $$2n$$
      Correct answer: $$3n$$
      $$2n + 1$$
      $$10n - 1$$

      Q2.
      Which of these expressions must be even for any integer $$n$$?

      $$7n$$
      Correct answer: $$14n$$
      $$3n + 6$$
      Correct answer: $$4n + 2$$
      $$9(2n + 3)$$

      Q3.
      Which of these expressions are always odd for any integer value of $$n$$?

      Correct answer: $$2n -1$$
      $$3n$$
      Correct answer: $$4n + 3$$
      Correct answer: $$5(2n+1)$$
      $$7n + 1$$

      Q4.
      Which of these statements are true for the expression $$6n + 3$$ when $$n$$ is an integer?

      It could be a multiple of 6.
      Correct answer: It could be a multiple of 3.
      It could be a multiple of 2.
      Correct answer: It is always odd.
      Correct answer: It is always 3 less than a multiple of 6.

      Q5.
      Which of these must represent 3 consecutive odd numbers when $$n$$ is an integer?

      $$5n, 7n, 9n$$
      $$n + 1, n + 3, n + 5$$
      Correct answer: $$2n -1, 2n + 1, 2n + 3$$
      $$2n + 1, 2n + 2, 2n + 3$$
      $$2(2n+1), 2(2n+3), 2(2n + 5)$$

      Q6.
      Which of these represent any 2 different even numbers?

      $$2n$$ and $$2n$$ where $$n$$ is an integer.
      $$2n$$ and $$2n + 2$$ where $$n$$ is an integer.
      Correct answer: $$2n$$ and $$2m$$ where $$n$$ and $$m$$ are integers and $$n \ne m$$.
      $$2n$$ and $$12n$$ where $$n$$ is an integer and $$n \ne 0$$.
      $$2n + 1$$ and $$2m + 3$$ where $$n$$ and $$m$$ are integers.

      Lesson appears in

      UnitMaths / Functions and proof

      Maths

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