Wednesday, May 8, 2013

A Quick but Effective game and lesson for combinations of 10

So today was one of those long hot days where kids would rather be anywhere but in school.  I knew I needed something fun and engaging to do with my K and 1 kids at the end of the day.  These are all kids who I have pulled for some small group work because they need more practice with their combinations of 10.  I have played variations of this game over the years but here is what we did today

Materials needed
- paper or whiteboards and pencil or markers for record sheet
- 10 small objects that have two distinctive sides.  I have used pennies often in the past because they are cheap and readily available.  You will see my fancy 2 sided counters that I got this year in the pictures.
- A small cup (this is not necessary but it got so hot in here this afternoon that the chips were sticking in their hands so we shook them in the cup and spilled them out rather than shaking them in our hands.

Make sure each player (or pair) has a cup and 10 objects.  Have them shake and dump the objects
The materials needed for one student (or a pair of students)

Have students record how many of each kind they got and write and equation that shows how much altogether.  (you see we used red and yellow in the pictures.  If you were using pennies, you could do heads or tails.)

A look at a student record sheet.  Having students keep a record can help move kids' thinking forward and can be a great jumping off point for discussions about big mathematical properties.  The students who were doing this record sheet noticed that 3 + 7 was the same as 7 +3.  When they shared this during whole group discussion, other kids started sharing similar ideas that they noticed from their own record sheets. 

The kids played for about 7 minutes and then I brought them back together in a discussion circle and had them bring their record sheets with them.  We started sharing things that groups noticed.  Our biggest discussion centered around this idea

We recorded student equations in order.  They noticed that the numbers to the far left were going up by one as the  other number was going down by one.  This was the big idea I wanted to get to with the students today.

So the first thing kids notice when we write the equations on the board in this way is that one number goes up while the other number goes down.  This is a great first step but DO NOT STOP HERE.  I have seen so many classrooms where kids notice this and the discussion is over.  If you do that, you are missing the big idea of compensation in addition.  You are taking one from one number and giving it to the other number.  I have kids pair up and use their counters to explore this idea further.

The student on top is showing 8+2 and the student on bottom is showing 7+3.  They  talked about how one chip got flipped over from the yellow side to the red side and that is why one number got one bigger and the other number got one smaller.

The kids have the counters out so have them model what is going on and prove why it works.  Try to get to the big idea that if you take one from one number and give it to the other, the total amount doesn't change.   If kids get this big idea in the primary grades, it will come in handy when they are doing something like 99 + 69.  They could take one from the 69 and give it to the 99 and make 100 + 68.  That looks like a much friendlier problem.  This is also very helpful with money.  You will see kids in grade 3 need to add $8.99 to $7.55.  If they understand compensation, they might think of it as $9.00 + $7.54 which is a much easier problem for kids to do mentally.

Want to go farther?  Click here to see how I extended this game to pairs of 20

How do you teach the idea of compensation?


  1. This is such an important part to creating a foundation for mathematics! Thanks for sharing a great lesson. I love teaching math and love that you get to teach math all day to little ones-how amazing! :)

    Learning to the Core

    1. Hi Amanda,
      Teaching math all day really is my passion. I was offered a job as a classroom teacher for next year but couldn't take it because it would mean giving up teaching math all day. I wasn't ready for that!

  2. I like the conversations that you're having. I need to continually press myself to do this more and more, otherwise kids just think they're having fun and that's about it.
    ❀ Tammy
    Forever in First

    1. Having the conversations with little kids is something I am doing more and more. If you don't help them pull out the big ideas than they can get lost in playing the games. This whole lesson only took 20 minutes and we got a lot out of it.

  3. That's a great idea for pushing their thinking. Thanks!I'm going to keep that in mind.
    Grade ONEderful
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