I have started tutoring a recent 3rd grade graduate (A) who is struggling in math. Today was our first session, so I tried a few problems out on her to see where the struggle really lies.

Her mom told me she’s had problems with multiplication, which upon investigation was clear – she struggles with multiplication. But I had a feeling that wasn’t where the *real* problem was, so I talked to her about addition and had her practice some (relatively) simple math facts – like 10 + 20 = 30, and 10 + 2 = 12. Unfortunately, she couldn’t easily and quickly give me the answer – she struggled with these concepts, which are usually understood before a child even begins to learn multiplication.

**Addition War**

So I decided to play a little game with her I called “addition war.” For those unfamiliar with the card game “war”, it goes like this – each player starts out with a stack of playing cards. At the same time, the two flip over the card, and whoever flips over the higher card wins the “battle” and keeps the two cards. The person who ends up with all the cards is the winner of the war. For “addition war” we took out all the face cards and then we would each flip over a card. Whoever could add the two numbers together first would win the cards. I knew that I would be fast at this game than a third grader (although it’s great practice for me, too!) so I gave her a few seconds head start. I figured that should be all she needed, but it soon was evident that her problem isn’t just with multiplication – she lacks some fundamental concepts for adding in her head, which will cause problems when she tries to do multiplication, and when she tries to memorize times tables (which will have no concrete meaning to her).

**Fact Families of 10**

With this in mind, we went back to the basics – addition fact families for the number 10. After A masters addition fact families for 10, we’ll move on to what I call “adding to ten” – when you have 7+5, instead of counting up from 7, you add 7 + 3 + 2 = 10 + 2 = 12. This is a much faster way to add numbers, but you have to be really solid on your fact families (especially for 10 – most of the others are relatively easy to remember, and A seems to know most of the smaller fact families, but we will probably need to work on those, too).

To review – the addition fact families for 10 are

10

1,9

2,8

3,7

4,6

5,5

This means that each pair of numbers add up to 10. In order to really drill these “families” in, we used those same face cards (from addition war) as flash cards. I would flip over a card, and A would tell me the other member of the fact family. We wrote all the fact families on a piece of paper for a “cheat sheet” at first. We set a timer for 2 minutes so she would have a reason to be fast, and then I bribed her with chocolate. She gets a fun size candy bar if she can reach our goal of 75 cards in 2 minutes. Today her best score was 52 in 2 minutes, but that was pretty good, since she is still taking a few minutes to name the missing fact family member. We played four or five times today, and it seemed to really help.

**Math Manipulatives – Cuisenaire Rods**

After we had used the flash cards for a while, we used the Cuisenaire rods to show the fact families. The thing I love about Cuisenaire rods (and really any math manipulative) is that when the student gets a chance to *touch* math, they are a lot better able to understand it. Math concepts can be abstract, and making them concrete helps students (especially children who developmentally aren’t abstract thinkers) understand. A was able to see the fact families, and get to know them a little better. We talked about how as one of the fact family members get bigger, the other gets smaller (see the stair step pattern?) and that is because we always want to have ten – so we are moving one “unit” at a time from one side of the fact family to the other. This will take a lot of looking at and playing with until A really understands it, but I can tell that she already understands it better than when we started today.

Another game we started to play was “speed” with the fact families. We laid out a bunch of cards and then matched them with their fact families and as she matched them, she turned them over and I would put more cards down for her to match with the fact family. This worked okay, but I think the flash cards was more what she needed today.

**Goals and Progress**

My goal with A is to get her to the point where she can add pairs of one digit numbers without thinking about it for too long. I think we made great progress. She and I will probably be meeting every weekday this summer. Hopefully by the end of the summer we will have multiplication mastered as well. But math concepts have to be built on a strong foundation, so the foundation is what we’re working on right now.

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