Be My Multiple, I'll be Your Factor
Class 5 · Mathematics
5 ideas in Class 5 Mathematics, explained in plain words, with games and quizzes to practise.
Multiples of a Number
Part of: Multiples
Multiples of a number are what you get when you count in jumps of that number: 4, 8, 12, 16 and so on are the multiples of 4. A number is a multiple of 4 if it can be shared into groups of 4 with nothing left over.
Why it matters. Multiples are the base of the times tables, division and fractions. Children who see them as skip counting find later topics much easier.
Try it in two minutes
- Sit in a circle and count from 1. Everyone clap instead of saying a multiple of 3.
- Ask: which numbers did we clap for? What do you notice about them?
- Change the rule to multiples of 5 and play again.
Try at home. Ask your child to write the first ten multiples of 6 and check each one by counting in sixes.
Common Multiples
Part of: Multiples
A common multiple is a number that appears in the lists of multiples of two different numbers. 12 is a common multiple of 3 and 4 because it is in both the 3 times table and the 4 times table. The smallest one is the first meeting point of the two lists.
Why it matters. Common multiples help us match two repeating things, such as two buses leaving at different gaps or two kinds of packs. They also prepare children for adding fractions.
Try it in two minutes
- Write the multiples of 2 on one strip of paper and the multiples of 5 on another, up to 30.
- Ask your child to circle the numbers that appear on both strips.
- Ask: what is the smallest number on both strips?
Try at home. Repeat with the multiples of 3 and 4 and find the smallest number they share.
Factors of a Number
Part of: Factors
Factors of a number are the numbers that divide it exactly with nothing left over. For 20, we can write 20 as 4 times 5 or 2 times 10 or 1 times 20, so 1, 2, 4, 5, 10 and 20 are its factors. If 4 is a factor of 20, then 20 is a multiple of 4.
Why it matters. Factors are used in sharing things equally, in simplifying fractions and in division. Children who know them can check quickly whether a share will be fair.
Try it in two minutes
- Give your child 12 small objects such as buttons or pebbles.
- Ask them to make equal rows in as many ways as they can and say how many rows and how many in each row.
- Write down the numbers used. These are the factors of 12.
Try at home. Repeat with 18 objects and list all the factors found.
Common Factors and Factor Trees
Part of: Factors
A common factor of two numbers divides both of them exactly. 1, 2, 3 and 6 are common factors of 12 and 18, and 6 is the biggest. A factor tree splits a number into two factors, then splits those again, until only small numbers are left at the ends of the branches.
Why it matters. Common factors help in sharing two different amounts into the same equal groups. Factor trees show children how a number is built from smaller numbers.
Try it in two minutes
- Write the factors of 8 on one card and the factors of 12 on another.
- Ask your child which numbers appear on both cards. Name the biggest one.
- Draw a tree for 12: write 12, draw two branches to 3 and 4, then split the 4 into 2 and 2.
Try at home. Ask your child to draw two different factor trees for 36.
Multiples and Factors in Everyday Problems
Part of: Using multiples and factors
Factors tell us which equal groups or tile sizes fit exactly, and multiples tell us when repeating jumps meet. For example, a 12 foot path can be covered with 3 foot tiles because 3 is a factor of 12.
Why it matters. Many real jobs such as tiling, packing and planning need numbers that fit exactly. Children who can choose between factors and multiples solve these jobs without trial and error.
Try it in two minutes
- Lay out 24 matchsticks or spoons in a row on the floor.
- Ask: can we split them into equal groups of 5? Of 6? Of 8? How do you know?
- Ask which group sizes are factors of 24 and which are not.
Try at home. Ask your child to find all the ways to arrange 18 coins in equal rows.
What your child will practise
- Common Factors and Factor Trees: Candy Quick Fire (Quick Fire)
- Common Multiples: Space Puzzle (Clue Puzzle)
- Factors of a Number: Mission Control Quest (Match It Up)
- Multiples and Factors in Everyday Problems: Number Quest (Collect the Answer)
- Multiples of a Number: Jungle Quest (Flip and Match)
- Quiz: Common Factors and Factor Trees (8 questions)
- Quiz: Common Multiples (8 questions)
- Quiz: Factors of a Number (8 questions)
- Quiz: Multiples and Factors in Everyday Problems (8 questions)