Why Fact Families are Important for Understanding Subtraction

It’s not uncommon for teachers to spend a lot of time focusing on teaching the addition facts and then brush over subtraction.

Subtraction has been the ‘poor relation’ that receives less attention. In fact, sometimes students are not helped to see that there is any relationship at all between addition and subtraction.

(NZMaths n.d.)

One of the top strategies for learning the subtraction facts is to ‘think addition’. This is when children use the known addition fact to solve the subtraction problem. For example, 11 – 6, think … what do I add to 6 to make 11?

But we can’t assume that because we have taught 6 + 5 = 11 students will automatically make that connection. They need to be shown it.

Introducing Number Fact Families

A number fact family is a group of math facts that use the same three numbers. They’re a great way to show children the link between addition and subtraction. For example, using the numbers 2, 4 and 6, we can make the following equations:

• 2 + 4 = 6
• 4 + 2 = 6
• 6 – 2 = 4
• 6 – 4 = 2

We can’t expect children to understand this link. We need to show them the connection through the use of concrete materials. This concrete stage of learning or the ‘doing’ stage allows students to manipulate objects and leads to a greater understanding of how fact families work.

Moving from Concrete to Representational to Abstract (CRA) Instruction

The first stage in CRA instruction is to model fact families using concrete materials. Provide students with six counters (unifix cubes, beans, buttons, etc) and ask them to separate them into two groups. They may give you a group of 2 and a group of 4. Write down the number fact 2 + 4 = 6. Ask them to turn it around by moving one group to the left of the other and now they have 4 + 2 = 6. Ask them to cover or take away 4 counters and write 6 – 4 = 2. Then take away 2 counters and write 6 – 2 = 4

You can also place the counters in a tens frame if you have one on hand.

Continue to use counters with other numbers and write the matching equations. We should give students as much time as they need to understand the connection between addition and subtraction before we move onto the representational level.

Representational Level of Instruction

The representational level of learning involves drawing pictures that represent the concrete materials previously used.

To demonstrate number fact families, provide students with a ten strip, cut to the number you are focusing on. In this case, it’s 8. Instead of using counters, students draw 2 groups of circles that add together to make 8. You can also have them stamp them. The representational level is semi-concrete. Students are drawing their answers rather than making them.

Have students show subtraction by folding the amount they will be taking away under the strip. The can see that 5 circles are left.

Abstract Level of Instruction

When your students have demonstrated mastery at the representational level they’re ready for the abstract level. This level uses only numbers and mathematical symbols. In this level, you might use worksheets but I have a preference for hands-on activities.

Number fact family cards are perfect for reinforcing the concepts you’ve taught at the concrete and representational levels. Students are not just searching for three numbers that form a number bond but they are understanding why they belong together.

You can grab a fact family freebie below.

If fact family cards are what you’re looking for as you move into the abstract level of instruction, you can find a pack in our store. Just click on the link or on the picture below. They’re perfect for using in centers as a game or individual activity. If you would prefer to purchase from our store on Teachers Pay Teachers, please click this link.

Once you’ve taught your students about number fact families, then teaching them mental math strategies that really consolidate the subtraction facts will be the next step. You can find out more on this blog post – 8 Strategies that will make Subtraction Easy

NZmaths n.d. Number families and relationships, https://nzmaths.co.nz/resource/number-families-and-relationships