First, let me clarify. Fact families are not mentioned at all in the common core standards or the newly revised Texas TEKS. What IS mentioned–over and over again–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 that–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 120 chart (from my __new Kindergarten unit__) laying around, so I decided to use it to make the learning more concrete. Notice what I did–he was having trouble with the abstract concept of number families, so I took it back to the 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) * Excellent! Write a number sentence to show that…24 + 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? * (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__. Activities such as this one encompass so many different skills–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!

Download this cute 120 chart free!

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!

What an amazingly sweet comment! You just made my night. Thanks so much. 🙂

That’s a great idea! Thanks. I wish we had a math coach out our school:)

❀Barbara❀

Grade ONEderfulRuby Slippers Blog DesignsWouldn’t it be great if all schools had math coaches, Barbara!

The progression you took him through makes so much sense. I needed that!

❀ Tammy

Forever in FirstSo glad it was helpful, Tammy. 🙂

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

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

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!

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

A very belated thanks for sharing this!

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.