# Number Families on a Hundred Chart

First, let me clarify. Fact families are not mentioned at all in the common core standards or the newly revised Texas TEKS. What IS mentionedโover and over againโis the relationship between the operations. For example, take a look at these 1st-grade standards:

1.OA.3–Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known.

1.OA.4–Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.

Here’s one implication of thatโnot only should students understand the relationship between 8 + 3 = 11 and 11 – 3 = 8 (fact families), but they also need to understand that if 72 + 24 = 96, then 96 – 24 = 72 (number families).

So, I’m working with a little fella, and he’s having a really hard time with that concept. He’s in 3rd grade, but he just doesn’t grasp the relationship between addition and subtraction. We were working together today, and I happened to have a 100 chart laying around, so I decided to use it to make the learning more concrete. Notice what I didโhe was having trouble with the abstract concept of number families, so I took it back to a more concrete level.

Here’s how it went:

Put your counter on 72. What’s 24 more than 72? (We had to really practice being able to skip count rows by 10 and then switch to ones. Also, I kept my finger on the 72 square as he moved his counter 24 spaces ahead). Great! It’s 96, right? Let’s write a number sentence to show what we did…72 + 24 = 96.

Put your counter on 24. What’s 72 more than 24? (I should note that he did not see the obvious connection at this point. That’s how I knew that he needed lots of practice at this concrete level). (34, 44, 54, 64, 74, 84, 94, 95, 96) ย Excellent! Write a number sentence to show that…24ย + 72 = 96.

Your counter is on 96. What’s 24 less than 96? (86, 76, 75, 74, 73, 72) Right, now can you write a number sentence for that? 96 – 24 = 72.

Put your counter on 96. What 72 less than 96? ย (86, 76, 66, 56, 46, 36, 26, 25, 24) You got it! Now, how about a number sentence. 96 – 72 = 24

We will continue to practice this the next time we get together, and then we’ll take it to an open number line. ย Activities such as this one encompass so many different skillsโpatterns on the hundred chart (he REALLY wanted to count by 1s at first), skip counting, and mental computation. It’s a great little small-group activity!

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1. Mrs. Yazzie's Classroom News says:

I just love your blog, your ideas, and your printables. As I read your posts I feel like I’m in a fabulous PD and I’m inspired to be my best. I love taking your coaching back to my classroom. Thank you!

1. Donna Boucher says:

What an amazingly sweet comment! You just made my night. Thanks so much. ๐

1. Donna Boucher says:

Wouldn’t it be great if all schools had math coaches, Barbara!

2. Tammy says:

The progression you took him through makes so much sense. I needed that!
❀ Tammy
Forever in First

1. Donna Boucher says:

3. TheElementary MathManiac says:

Wow! What a simple but very effective lesson. You moved his conceptual development way ahead in a short amount of time. I agree with Mrs. Yazzie that reading your blog is like doing very effective professional development.

Tara
The Math Maniac

1. Donna Boucher says:

Aw, thanks, Tara! Yes, it was neat to see him really grasp the concept!

4. Sue Wiese says:

I use multiplication charts for students who are just beginning to learn division. They really get it when I show them that a multiplication chart is a backwards division chart!

1. Donna Boucher says:

Exactly, Sue! They think it’s magic. Ha ha.

5. Sara at school says:

A very belated thanks for sharing this!

6. Marjana Helton says:

Hello,
I would like to say Thank you so much for your structured speech with the student. I teach RTI math to 6-8 graders and I really struggle with begging concepts and how to present them Next year I want to collaborate with Elem. Teachers so I can pick their brains and experience like the above should go when it is being taught to someone much older. I can do what you did but might not have realized what was a normal wait time and what was a struggling student. Mahalo and I will look for more of your thoughts on things.