For some students, the concept of the distributive property is completely abstract and something they cannot begin to understand. To help students make the connection, it is important to show them how the distributive property works, in a concrete way. Once students understand this, they can begin to use the distributive property to help them solve multiplication facts that look intimidating. For third graders, this may be equations that have larger factors, like 6, 7, 8, 9, or 12. For fourth and fifth graders, this may be multiplying two digit numbers or later three digits.
To begin to introduce the distributive property in a concrete way, start with a times-table showing numbers 1-10 (or 1-12), and a blank table. It is important that this table does NOT include zeros, as this will throw off the entire problem.
Then, choose an equation that you want to model to your students. For this example, I have chosen 7×6. For the first step, cut out 7×6 using your blank times table. You may use markers or dashes to mark the size of the shape.
Lay the cut out blank table over your times table so students can see that it represents 7×6.
Discuss how the distributive property allows us to break an equation up into two parts. Explain how 7×6 may be a hard fact to remember, and that you can break it up into facts you do remember. For this example, we’ll break it up into 7×5 and 7×1, since fives facts are usually easy for students to memorize.
Cut apart the blank table to represent two pieces measuring 7×5 and 7×1. Allow the students to see how the new pieces show these two facts. Lay them on the times table one at a time so students can visually see them on the facts. (Do not lay them side by side on the table at this point!)
On the board, or a nearby piece of paper, write down the two facts that are represented. Have students tell you the products of the two facts that are shown.
Now, lay the pieces side by side on the times table. Show students how the original fact, 7×6 is represented.
Pose the question to the class–what operation should we do to the two products in order to find our total product? (Add). Represent this with the equations (7×5)+(7×1)=(7×6) or (35)+(7)=(42)
Repeat this as needed with other facts.
For fourth and fifth graders, this concrete understanding of the distributive property will help them solve other, larger facts.
Questions to pose:
- How can we use the distributive property to solve 7×44?
- How can we use the distributive property to solve 8×415?