Algebraic Thinking through Fact Families

Fact families are students first introduction to algebraic thinking. Let’s take a look at some fun effective strategies for fact families.

My first few years teaching was in first grade. I remember looking at the state standards and smiling when I saw algebra. Algebra? In first grade? Really?

When I thought algebra, I thought of my freshman algebra class. I certainly didn’t connect it to first grade. I didn’t realize how simple algebraic thinking would actually be for them.

An Algebraic Thinking Lesson in First Grade

I love a challenge. I started teaching 40 first graders at a private school while getting my credential. This meant my ‘student teaching’ observations were in my own class. Since I love challenges, I choose an algebra standard for my first observation.

I had some adorable first graders come up to the front of the room. First, I handed them each a card with part of an addition fact. Then, I had them switch places to make the turn around fact. Then, the person with the sum moved to the front and the one with plus flipped the card over to a minus. By the time we were done, they had done what I called the turn around dance. Here is a little 15 second video to demonstrate. (You’ll have to imagine the kiddos.)

At first I was the dance director, eventually students could direct each other. This simple activity helped spark conversation about where the biggest number went for addition and subtraction.

The Turn Around Dance

This year, I had an intervention group of third graders that struggled with basic addition and subtraction. Some of them would tell me that addition was fine but they hated subtraction. When I told them that knowing how to add meant that they knew how to subtract, they didn’t believe me. After teaching them the turn around dance, they asked if they could do it again the next day.

Flashcards in Color or B&W

Eventually, I wanted to move them from whole group instruction to partner and independent work, and that is how my Addition and Subtraction to 18 Fact Families packet was born.

Each day, the students had 6 triangle flashcards to practice.

At first I gave them a scaffolded worksheet so the spot where the largest number went had a circle. I wanted them to focus at first on the concept that addition made things bigger and subtraction made things smaller.

Numbers as Manipulatives

In the beginning, I had them demonstrate at least one fact family with manipulatives when they wrote the numbers.

Eventually they moved on to the worksheet that wasn’t scaffolded. Then, they moved to white boards.

The students eventually told me how easy it was. The numbers became manipulatives they could move around and the commutative property began to become second nature to them.

I loved how these girls decided to categorize addition problems and subtraction problems.
Patterns are so helpful in math.

Later in the year, I had a group of first graders with the same objective. While the objective was on grade level for them, they took FOREVER cutting. So, I didn’t have them cut them out before working.

Once the concept was solidified, we moved from worksheets to whiteboards.

The first graders loved drawing the triangles.

What is more fun than having your teacher take a picture of something you are proud of?

Even though I used this resource a few times this year, I just uploaded it for you this week. I like to make sure it is really ready for sharing.

I made a video showing what it contains:

Fact Family: Addition & Subtraction to 18 {Triangle Flashcards, Worksheets, Art Extension Activities, Number Cards for a Turn Around Dance, Quizzes and Certificate

While I was finalizing this to share, I realized I wanted one for multiplication and division. The multiplication and division version is very similar. I’m so excited to use it this year with some third graders.

Take a look at these posts about fact fluency!

An Algebraic Thinking Lesson in First Grade

The Turn Around Dance

Numbers as Manipulatives

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