top of page
Image by Chris Liverani

MathBait™ Multiplication

Remember This?

Share this resource!

In Factor It! students found all the factors of a given value in a tedious but systematic way. Now, we spiral back to the commutative property to allow students to determine an easier and more condensed method to find the factors of a value.


Resource Type


Primary Topic

Primes & Factoring







The purpose of this activity is to recall the commutative property helping students to realize they can cut their work, and their factor trees, in half with this property.

Display the image of the 24 blocks for students.

All possible rectangles made up of 24 blocks

Announce that each rectangle has a twin and ask students to pair the twins. When complete, allow students to explain their choices.

Remind students of the commutative property (discussed earlier in MathBait™ Multiplication). In our rectangles, we can think of the commutative property as counting the total number of squares horizontally, or vertically. Demonstrate with the 4 by 6 rectangle.

A 4 by 6 rectangle with each column circled

We can find the total number of squares by using the columns. Since each column has 4, and there are 6 total, we can count by fours, 6 times, to find 24.

A 4 by 6 rectangle with each row circled

Or, we can use the rows. Since each row has 6 squares and there are a total of 4 rows, we can count by sixes, 4 times, to find 24.

After highlighting 4×6=6×4, ask students how this might lower the amount of work needed to build a factor tree. Work together to rebuild the factor tree for 24, allow students to determine when we have collected all the factors.

A factor tree for 24 showing (1,24), (2, 12), (3, 8), and (4, 6)

Students should recognize, the tree above is sufficient as it contains all the factors (or blocks we can use to build 24) of our target number. Ask students how we can determine when to stop for any value.

Factor tree for 24 with arrow showing 6 on the left matches 6 on the right.

Solidify the idea that once we reach a value which is already on the right, we know we have found all the factors! If we continued after 6, we would find no pairs for 7, then a pair for 8 which is already on our tree, then again no pairs until 12 and 24. If needed, display the previous factor tree in which we attempted all values. This is great news! We can do much less work to find all the factors.

Allow students a few minutes to build their smaller factor trees independently. We recommend assigning values such as 6, 8, 9, 12, 14, 16, and 18.

The material on this page is copyrighted by MathBait™. Please use and enjoy it! MathBait™ provides a temporary license for Non-Commercial purposes. You are not permitted to copy, distribute, sell, or make derivative work without written permission from MathBait™. 

Tell us what you think!

Click to rate this activity

© MathBait®
bottom of page