# fact families

First graders are expected to add and subtract numbers using a variety of strategies. Many of these strategies require students to relate addition and subtraction facts to one another. Studying addition and subtraction fact families is an incredibly useful strategy towards highlighting these relationships.

The 5 examples listed are certainly not an exhaustive list of tools and lessons that could be used to teach this skill.

They are rather a sample progression from hands-on to abstract thinking!

Which step represents your students’ current level of understanding?

Reframe your thinking- you aren’t teaching fact families but rather the relationship between addition and subtraction!

Use linking cubes to act out a variety of math stories where a group is taken apart and put back together.

As you explore these scenarios and model with linking cubes, record addition and subtraction equations that match the action.

Support your students in generalizing their skill and seeing patterns beyond linking cubes by introducing a new material.

Try a material like red and yellow 2-sided disks.

Show your students a set of disks such as 6 yellow and 4 red disks. Ask your students what they see and notice about these disks.

How might the disks be put together?

What would it look like to break the group apart?

Can you write an equation to match each of these scenarios?

Support your students as they move from hands-on to abstract by adding in a “middle” step representing these relationships in drawings and pictures.

For example, 3 apples and 2 bananas. We can put them together to create 5 fruits! We can also take the 5 fruits apart to show 3 apples and 2 bananas.

Support your students even further by putting these numbers in a number bond as you talk about the parts and the whole.

After your students show confidence with pictures and picture contexts alongside a number bond, take the pictures away!

Given a number bond with numbers in all 3 places, could your students write 4 related equations that show how the parts could be put together and how the whole could be taken apart?

If your students aren’t successful with the number bond alone, move backwards! Reintroduce drawings, pictures or hands-on materials.

You are laying the foundation for the realtionship between addition and subtraction- there is no need to rush!

In the final step, you want to see if your students can related addition and subtraction without the benefit of a representational model or hands-on tool.

But that doesn’t mean you need to give your students “naken numbers”!

Profice a context for your students such as “6 girls and 3 boys are playing together on the playground. That’s 9 kids altogether!” Ask your students if they can record equations to show all of the ways the girls and boys can be put together and the full group of children can be broken in to the boy and girl groups.