Top Drawer Teachers The Australian Association of Mathematics Teachers (AAMT) Inc. http://topdrawer.aamt.edu.au

1. Further divisibility patterns
for students to investigate

2. 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

3. 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

4. Teaching tips
Note: 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

5. Going further
As 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

6. Going further
As 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