For many students, the multiplication facts are usually much easier to grasp than the division facts when learning about fact families. I believe that the reason for this is that students have a limited understanding of why the facts are called fact families. Students get used to switching the numbers in multiplication facts, such as 3×4=12 and 4×3=12, without understanding why they are doing it. It is a bit more challenging for students to understand the same concept with division.
Therefore, teaching fact families with arrays is a great way for educators to model problems for students, for students to experience hands-on learning, and a way to give students the opportunity to think about and explain their answers aloud.
I always begin an introduction to fact families by modeling an example for students. I begin with four number sentences, such as 3×4=12, 4×3=12, 12÷3=4, and 12÷4=3, and write them on the board. I like to use overhead counters because they are an excellent visual tool which allows students to see what I am doing. I model three rows of four to show 12, then I model four rows of three to show 12. At this point, I explain that the two arrays both have 12 counters, and that is why they are related facts. Then, I model the division facts by taking the same 12 counters I used before and dividing them into four groups of three, and then three groups of four. This shows students that these division facts are in the same family as the multiplication fact since there are always 12 counters.
After modeling the problem, I give students the opportunity to practice what I modeled. I usually have students practice the problem on the board first, so that they have the opportunity to create the arrays on their own. Then I give students hands-on practice with a different problem. They can use counters, unifix cubes, or even graphing paper. After the activity, I discuss why fact families are important. I tell them that it helps in many ways. It helps students divide larger numbers, and it helps when tackling algebra and word problems. What follows are more fact family activities and lessons.
Multiplication and Division Fact Families:
The Commutative Cookie
Student use unifix cubes (cookies) to model multiplication fact families in arrays. This lesson highlights the term commutative property. Students discover why factors can be switched and the product remains the same.
Multiplication and Division with Arrays
In this lesson students work with fact families using a variety of manipulatives, including pegboards/tees, counters, and graphing paper. The tools are used to create arrays and to teach students multiplication and division with arrays.
Fact Families Worksheet
This is a good worksheet to use as a group activity. The problem solving activities on this worksheet would be good for students to practice while working together in groups.
Complete the Fact Family Worksheet
This is a simple worksheet in which students are given one number sentence and need to come up with the other three number sentences in each given fact family. The use of counters or graphing paper would be helpful for creating arrays.
Division and Multiplication Facts Worksheet
This is a worksheet with instructions for students. Students use graphics to come up with fact families.