Divisibility Book
Divisibility Rules
The students will make a booklet containing the divisibility rules.
State Standards:
Numbers and Operations – Use divisibility rules to determine if a number is a
factor of another number.
Materials: paper and markers to make the books. Each student will use 2 sheets of
standard 8x11 paper, cut lengthwise in half, stapled together.
Key Questions: Ask whether big numbers are divisible by 2, 3, 5, 6, 9 or 10.
Procedure: A table of numbers 1 – 100 is used. When discussing a number, such as two,
all numbers that are divisible by two are displayed, while the numbers that are not
divisible by two are covered up. The students are asked if they see a pattern in the
numbers. The students will soon realize that all numbers that are divisible by 2 are even
numbers, which is the divisibility rule for two. The divisibility rule for thee is not as easy,
so more leading is required. Once students find out that the divisibility rule for thee is
adding up the single digits and if it adds up to a number that are divisible by three, the
number is divisible from thee. The same thing is done for 5, 6, 9, and 10. In order for the
students to come up with the divisibility rule for 6, the tables for 2 and 3 can be printed
on transparencies, and then placed onto of each other to reveal the numbers divisible by 6.
As you go though the rules, have the students construct their rule books. Give examples
for each rule as you go along.
Transparencies can be used for the tables. I put the tables in a PowerPoint presentation
(Divisibility book) to make it more colorful and fun.
Follow-up activity: the students will be using their divisibility rule books for an in class
assignment the next day, as well as on their homework.
Reflection: The students seemed to really enjoy making the books and it gave them a
chance to pull out the color pencils and get creative. There was a kid or two in each class
that remembered ‘something’ from 4th grade about the rules and with a little push usually
figured out the rules. The hardest one to figure out was probably 3 since you can see a
pattern, but can’t really figure out the rule from it. The numbers after 3 is much easier
since they can see the pattern and derive it from what they see. Once they get to 9 they
know the trick for 3 so they figure the one for nine out with no problem.