Math Match-up Game for Addition & Subtraction and Cumulative Property

Math was never my strong suit. I learned early on that I was “not good at math,” that “math was hard,” that “math was not for girls,” etc. I hated math. I remember sitting in algebra class, completely clueless and having my teacher stand over my shoulder waiting for me to do the next step on an equation and I just steadied my pencil there, terrified to write something, because I knew I’d be wrong.

Math was not my favorite class. I struggled. While I did well in all my other classes, Algebra and Chemistry (with even more math) eluded me and I received my lowest grades of Cs and Ds there. Many years after receiving my GED, I attended community college and had to take remedial math classes and thankfully I had a great teacher who, despite being brilliant when it came to math, seemed open to understanding the difficulties her students were having. I learned so much in her classes and ultimately got through college Algebra. Later, while attending university, I took every class I could to avoid Calculus: so I took Statistics, Symbolic Logic, and Trigonometry. Let me tell you, that was a lot of work to avoid one class! In most of these classes I received average scores. I may have gotten an A in Statistics, but I don’t remember.

Despite taking all of that math, I still believed I was not good at it.

Later, when I decided to unschool/homeschool Kathryn, I picked up a book by John Holt entitled Learning All the Time and in one chapter, I learned more about math than in all those years of classes. There, I learned that the problem for most children is that they are presented with say:

1+2=3      2+2=4     2+3=5     2+4=6      2+5=7     2+6=8       2+7=9      2+8=10

and told to memorize these facts.

Okay fine, but as a child, I found myself asking why?

How do we know this? How is this fact?

Nothing I was learning answered these questions. Of course I went through school in the 1980s and things were different, but not that different. I saw the same method of “teaching” when my sons were in school.

What I learned from John Holt was a method of showing children how the above facts are not just individual, abstract “problems,” but rather a representation of something. It’s hard to show this to a child when they are forced to memorize all of the twos, then all of the threes, etc.

However, let them pick a number, say 5 and you can show them the various ways they can represent that number. Let them start with toys, or legos, or whatever. Let them organize them to show five.

example: (note stars represent toys)

**     ***

*      ****

***      **

****      *



All of these groupings are just different ways to show five. Once they grasp that, you can introduce numbers.

2        3

1        4

3        2

4        1

5        0

0        5

As you do this, as if they notice any similarities? They may recognize that {1    4} looks similar to {4    1}, for example. This is good. If they don’t see this yet, that’s okay. Show them and move on. Children learn at different rates. No big deal.

Now, you can introduce the math facts. I use Saxon Math and love it. It includes fact cards and while the curriculum asks that we use the cards the old fashioned way (look at the “problem” on the front, take a guess, check your answer on the back), I took Holt’s ideas into account and my daughter’s inclination to want to play games, and we changed it up a bit.



Math Match-Up:

You’ll need:

Cards with the numbers 0-9 (you can easily make your own with yardstick and a Sharpie)

Cards with various addition and subtraction equations. Our kit from BookShark came with these, but you can make your own. Make sure you have several that equal each of the numbers from 0-9. Write the equation on the front and the answer on the back.

How to play:

Take turns drawing a number and flip it face up to the side. You will be finding the equations that equal this number.

The equations are placed in a “pond,” with the answers face up. (later you can do this the opposite as your child gains the skills and knowledge, but let your child lead the way) You and your child take turns finding the number in the bond, then turn them over and read the equation aloud. Place them with the number. As you play, notice the pairs. Example: 0+1=1 AND 1+0=1. Group these. See if your child begins to notice too. This is a great way to teach the cumulative property from the get-go, rather than presenting it alter as another “problem” to solve in the math world.

Play as long as your child is interested. My daughter played for over an hour and I finally had to ask to stop, because I needed to clean up for lunch! You know what? That’s okay!



I think it’s a good idea to have challenging bits in any lesson, along with review of “easy” things. For one thing, giving a child the opportunity to say, “Hey, that one is easy!” is empowering. The challenging bits are great because if we stick to following a strict curriculum that is “age-level appropriate,” we may actually hold our children back without meaning to.

Here’s an example from just yesterday with my daughter. As I was getting the cards ready for the game, she was completing her math sheet. I considered using 9+9 in the game, but thought perhaps it was too challenging. I noticed that the bottom of her sheet had equations to complete, so as I always do, I gave her the Teddybear Counters, in case she needed help with visualization and counting (they come with the BookShark curriculum). Well, one of the problems happened to be 9+9. She paused in her work, “Mom, what’s 9+9?” I suggested she use her bears if she needed them. “Oh wait,” she said. “18!”


I was kind of amazed. We’d only just talked about this one last week. She moved on to 8+8 and knew it was 16 without using her bears.

You better believe I adjusted my plan for the game to include these equations! Again, the beauty of homeschool is the flexibility and the child-centered instruction.


If you try the game I’ve described here, please let me know how it goes!

My advice is this: let it be fun. Don’t stress it! Adjust according to your child’s needs. Contrary to what public school makes it seem, there’s no race when it comes to learning. We all learn at our own pace and that’s a beautiful thing.

Happy learning!



Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: