Further divisibility patterns for students to investigate

Without doing any calculations what other numbers do you think might divide equally by 5 or 10. Why?

Encourage students to list their ideas and reasoning (e.g. if the last digit of a

number is a 5 or 0 then it will divide equally by 5;

if the last digit of a number is a 0 then it will divide equally by 10).

Pose the following question:

Further divisibility patterns

How would you decide whether a number is divisible (a number that divides equally with no remainder) by 4? Where would you start?

Possible student responses: colour in the fours pattern on a 100 chart; look at the final digit; look at where the pattern repeats.

In pairs, students work out a theory for knowing which numbers are divisible by 4, and why.Have a 100 chart or multiplication facts table available for students to use if they so choose.

Going further

Further divisibility patterns

Teaching tipsNote: As every 100 is divisible by 4 only the numbers formed by the tens and ones digits need to be considered.

Alternatively, present a conjecture for students to prove or disprove, such as: If the number formed by the last two digits of a number is divisible by four, then the whole number is divisible by four.

Further divisibility patterns

Going furtherAs a class, students can share their reasoning and test out their theories using randomly generated numbers from the learning object, L2006 The divider: with or without remainders.

Without doing any calculations, do you think each of these numbers are divisible by 4 and why?

Follow up investigation: What numbers are divisible by 3, by 6, by 9, and why?

Further divisibility patterns