the lesson by dividing the students into pairs. For this lesson it
would work best to pair up students based on ability. Those students of
similar abilities should be paired together. Give each pair of students
12 plastic color tiles. Instruct those students to arrange these 12
tiles into an array. Students will create one of the following:
Ask the students to identify how they would express these arrays in numbers. [6X2, 3X4, 12X1.]
This example will lead to a discovery of the commutative property.
Some students will have 6X2 and others will have 2X6. This is a great
opportunity to discuss the commutative property. Bring attention to the
fact that the arrays still look the same they are just positioned
differently. Both problems still only provide the factors 6 and 2.
Then write just the numbers on the board: 1,2,3,4,6,12.
Explain that these are the factors of 12 because they are the only
numbers that can divide evenly with no remainders into that number.
This is easily seen when you refer back to the arrays that they
created. Demonstrate that they can check to see if they have all of
their factors by creating a factor rainbow as seen below.
factor rainbow is a way of showing factor pairs in a list of all of the
factors of a number. Factor rainbows are used to check whether a list
of factors is correct. To create a factor rainbow, the student must
list the factors in order from least to greatest. They can then draw an
arch that links the factor pairs. For square numbers, there will be no
connecting arch in the middle; therefore the student can put a square
around that number.
Provide the students with another example of finding factors of a
number using the color tiles and then creating a factor rainbow.
Possible numbers to use would be 16 or 9. Lead the students through the
process for this example. Then have the pair of students decide on a
number that they would like to find factors of. You may limit this
number to 50, depending on the amount of tiles you have available. When
they have decided on their number they can get that many tiles from a
bucket of tiles located somewhere in the classroom and use them to find
the factors of that number. Instruct the students to create the factor
rainbow in their notebooks. Check their factor rainbows to validate the
students’ understanding before you introduce the main activity.
For the main activity, instruct the students that they are each
going to get a number and it is up to them to find all of the factors
for that number and create a poster that the entire class can use
throughout the year. Give each pair of students a bag of a different
amount of color tiles. (ex. 18, 20, 24, 36, 40, 56, 60) Give the bags
with the lower amounts to the pairs of students who may be struggling.
Instruct the students what to do with tiles using the following
- Challenge the pairs of students to find as many different arrays as
they can, using the plastic color tiles they have been given. They must
use all of the tiles each time.
- Each time they find an array they can then represent it on graph paper.
- The students color one square on the graph paper for every one
plastic color tile in their array. This will form an array on their
- They will cut it out and glue it to their poster and label it with the corresponding factors.
- They continue this process until they believe that they have found all of the factors.
- The students then check their factors by creating a factor rainbow at the bottom of their poster.
- The students must also include a title on their poster. Their poster should look similar to the following:
To conclude the lesson the students will display their posters on
the wall and the class will have a gallery walk. During a gallery walk
each student will walk around the room and look at everyone’s work as
if they were in a gallery. They will each be given some post-it notes
they can use to anonymously comment on any piece of work and place on
the poster. They will also write down two facts they discover after
reviewing all of the posters. [Just because a number is larger doesn’t
mean that it has more factors than a smaller number; all even numbers
have a factor of two; the number 16 is a perfect square; etc.]