When teaching multiplication and division, it is important to help students understand the relationship between the two operations. One way to do this is by using fact family triangles. A fact family triangle is a visual representation of the relationships between multiplication and division facts within a family. In this blog post, we will discuss how to use fact family triangles to help students learn and understand multiplication and division. We will also provide several examples of how to use these triangles in the classroom!

Read more information about fact family triangles in our post about the connection between Addition and Subtraction.

Download a FREE Multiplication and Division Fact Family Worksheet here.

**What are Fact Families?**

A fact family is a set of related multiplication and division facts that share a common factor. If students understand the connection between multiplication and division and their fact families, they can memorise their timestables facts in half the time. Multiplication facts can be thought of as division facts and vice versa. For examples 3 x 4 = 12, can also be thought of as 4 x 3 = 12 and 12 ÷ 3 = 4 and 12 ÷ 4 = 3.

**What are Multiplication and Division Fact Family Triangles?**

Fact family triangles are a great way to help students understand and memorise multiplication and division facts. When using these triangles, it is important to emphasise the relationship between the operations of multiplication and division. Multiplication can be thought of as repeated addition, while division can be thought of as finding how many times one number goes into another. For example, in the triangle below, the multiplication sentence “three times four equals twelve” can also be read as “four groups of three equals twelve” or “twelve divided by four equals three” and “twelve divided by three equals four”. This emphasises the relationship between multiplication and division and how they are related operations.

Using fact family triangles are one of my favourite ways to teach the connection between number facts with students because they are just so easy. With the visual representation of 3 numbers, fact family triangles are a great way to help students learn and practise their multiplication and division facts.

Multiple exposures – check.

Easy to prep – check.

Easy to differentiate – check.

So many times, students have said, “I finally get it!” after using Fact Family Triangles.

**How to Use Fact Family Triangles**

Begin by introducing students to the idea of 3 for Free. If you know a multiplication sum, then you automatically know another. And you also know 2 division facts. Demonstrate to students how you are using the same numbers each time, just they are in a different order. Really break down what this means by using visual representations of the terms “groups of” and “shared between”.

This poster is available in my Fact Family Triangles Pack

Then give the students three numbers that are a fact family. See if the students can figure out a multiplication or division sum that uses those three numbers. Once you have 4 sums written on the board, introduce students to the idea of fact families.

Then put 3 new numbers in a triangle format. With the largest number being at the top and the two smaller numbers down the bottom, one on each side. Introduce this to students as a fact family triangle.

Modelling is key when using this strategy with students. So after you have demonstrated how to use the fact family triangle on the whiteboard, it is now the turn of the students.

Have students work in pairs or small groups to create their own fact family triangles. Give them a set of three numbers and see if they can come up with the 4 fact family sums.

Do you want to see our Addition and Subtraction in action? See the resource here.

**Differentiation:**

– For lower primary students, you may want to give them a list of numbers to choose from to create their own fact family triangle. This will ensure that the three numbers they choose will make a multiple set of sums.

– For upper primary students, you could challenge them further by asking them to come up with the 3 numbers themselves.

**Using Fact Family Triangles as an Independent Activity**

Using my resource, using Fact Family Triangles can easily be turned into an independent activity. Simply laminate the triangles and place in a container at the front of the room.

Using their workbook, students select a fact family triangle, then go back to their seat and write the 4 sums within that fact family. Then put the triangle back into the box and repeat with a new triangle.

I have included a recording sheet with this resource, so if you would prefer students to use that instead, they easily can.

This activity is great for fast finishers or as an extension activity.

I think you will agree with me that Fact Family Triangles are such a versatile and easy way to help your students understand the relationship between multiplication and division.

Are you interested in grabbing our free fact family worksheet? Use this open-ended worksheet to highlight the connection between number facts.

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