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.

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.

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.

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.

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.

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.