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      Checking understanding of factors, multiples, squares and cubes

      Lesson details

      Learning outcome

      I can state the factors and multiples for different numbers and identify square and cube numbers.

      Key learning points

      1. Multiples of a given number are the product of that number and an integer.
      2. Factors of an integer can be identified by checking for a remainder when dividing.
      3. In the statement factor x factor = product, the product is a multiple of each of the factors.
      4. If a is a factor of b then b is a multiple of a

      Keywords

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

      • Numerical factor - A numerical factor is a factor that is an integer.

      • Square - A square number is the product of two repeated integers.

      • Cube - A cube number is the product of three repeated integers.

      • Product - A product is the result of two or more numbers multiplied together.

      Common misconception

      There is often confusion between factors and multiples.

      Highlight that the number of dots in an array is the multiple and the number of dots in each column & row are the factors.

      Teacher tip

      During the explanation part of the lesson where examples of factors and multiples are given, let the students provide their own example of factors and multiples. Ensuring to state from their calculation, which are factors and which is the multiple.

      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 of the following is the same as $$ 5\times5 $$ ?

      5 + 5
      Correct answer: 5 + 5 + 5 + 5 + 5
      $$ 5^5 $$
      1 + 1 + 1 + 1 + 1

      Q2.
      Which of the following are the first five numbers in the 6 multiplication table?

      6, 7, 8, 9, 10
      2, 4, 6, 8, 10
      Correct answer: 6, 12, 18, 24, 30
      6, 5, 4, 3, 2, 1

      Q3.
      __________ are any positive or negative whole number or zero.

      Decimals
      Fractions
      Correct answer: Integers
      Primes

      Q4.
      What is the row and column dot length of this array?

      An image in a quiz
      Correct answer: 3 dots by 4 dots
      6 dots by 2 dots
      12 dots by 1 dot
      3 dots by 3 dots

      Q5.
      A 3 by 4 array, 6 by 2 array and a 12 by 1 array all have the same number of dots. How many dots does each array have?

      Correct Answer: 12, twelve

      Q6.
      How many dots are in an array with a row and a column length of 10?

      Correct Answer: 100, one hundred, hundred, 1 hundred

      6 Questions

      Q1.
      A __________ is the result of two or more numbers multiplied together.

      cube
      decimal
      factor
      Correct answer: product

      Q2.
      Which of the following is a multiple of 8?

      20
      21
      22
      Correct answer: 24
      25

      Q3.
      How many multiples of 3 are there?

      3
      10
      12
      100
      Correct answer: infinite

      Q4.
      A numerical __________ is an integer which exactly divides another integer.

      cube
      decimal
      Correct answer: factor
      product

      Q5.
      Which of the following is a factor of 12?

      Correct answer: 4
      24
      48
      60

      Q6.
      Work out the unknown number: "I am less than 100. I am a multiple of 2. I am a square number. I am a cube number."

      Correct Answer: 64, sixty four, sixty-four

      To help you plan your 7 maths lesson on: Checking understanding of factors, multiples, squares and cubes, download all teaching resources for free and adapt to suit your pupils' needs...