Divisibility patterns

Knowledge of place value and number properties such as divisibility can equip students to carry out a range of computations mentally.

Students use knowledge of multiplication and division facts to determine which numbers are divisible by various factors.

Pose the scenario:

Someone said that if you know what a number is divisible by, you can solve a lot of division problems in your head.


I have 20 biscuits to pack with 5 biscuits in each box. How many boxes will I need?

  • Will this divide equally?
  • How did you decide?
    Note whether students used their knowledge of multiplication facts (i.e. 4 \(\times\) 5 = 20, so 20 ÷ 5 = 4).
  • What other numbers will divide into 20 equally?
  • How did you decide?


List student responses and the reasons given (e.g. "2 will work because 2 tens is 20 and 20 is an even number so it will divide equally by 2")


You will need a 1–100 chart and the multiplication fact grid.

Your students can get extra practice using the learning object L2006 The divider: with and without remainder.

Curriculum links

Year 4: Recall multiplication facts up to 10 x 10 and related division facts