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      Use a complete list of factors to explain when a number is a square number

      Lesson details

      Learning outcome

      I can use a complete list of factors to explain when a number is a square number.

      Key learning points

      1. A square number has an odd number of factors.
      2. A square number is the product of multiplying a number by itself.

      Keywords

      • Factor - Factors are whole numbers which exactly divide another whole number.

      • Square number - A square number is the result of multiplying an integer (not a fraction) by itself.

      Common misconception

      Pupils record the number of factors for a square number as even as they record the same number twice when writing down the factors of the square arrangement.

      Highlight the need to only record each number as a factor once. You may like to record this on the tail of the factor bug to help emphasise this.

      Teacher tip

      In this lesson, time should be given over to allow pupils to explore and investigate the factors in square and composite numbers. Encourage additional exploration into larger integers and promote further pattern seeking opportunities.

      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.
      Which factor is missing from the factor bug?

      An image in a quiz
      Correct Answer: 3, three

      Q2.
      What number has only the following factors: 1, 2, 11, 22

      Correct Answer: 22, twenty two

      Q3.
      Which factor is missing from the factor bug?

      An image in a quiz
      Correct Answer: 5, five

      Q4.
      Which of these is the correct full list of factors of 26?

      1, 2, 6, 10, 13, 26
      2, 13
      Correct answer: 1, 2, 13, 26
      1, 2, 4, 13, 6.5, 26

      Q5.
      What is the missing factor of 54 from this list? 1, 2, 3, 6, 18, 27, 54

      Correct Answer: 9, nine

      Q6.
      What is the missing factor of 69 from this list? 1, 23, 69

      Correct Answer: 3, three

      6 Questions

      Q1.
      Which multiplication is shown by this array?

      An image in a quiz
      4 × 4 =
      4 × 1 =
      2 × 4 =
      Correct answer: 2 × 2 =

      Q2.
      What square number is represented by this incomplete factor bug?

      An image in a quiz
      Correct Answer: 36, thirty six

      Q3.
      Tick the square numbers.

      Correct answer: 16
      48
      Correct answer: 81
      110
      200

      Q4.
      Tick the lists which show factors of a square number.

      Correct answer: 1, 3, 9
      1, 2, 3, 4, 6, 8, 12, 24
      Correct answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
      1, 2, 5, 10, 25, 50

      Q5.
      Match the expression to the correct square number.

      Correct Answer:3$$^2$$,9

      9

      Correct Answer:7$$^2$$,49

      49

      Correct Answer:1$$^2$$,1

      1

      Correct Answer:4$$^2$$,16

      16

      Q6.
      Complete the missing square number from this list: 1, 4, 9, , 25

      Correct Answer: 16, sixteen

      To help you plan your 5 maths lesson on: Use a complete list of factors to explain when a number is a square number, download all teaching resources for free and adapt to suit your pupils' needs...