Thursday, May 9, 2013

A Quick but effective game for pairs of 20

Yesterday, I wrote about a game and lesson I did with K and 1 kids around pairs of 10.  If you haven't seen it you may want to start there.

Today, I was working with a group of intervention second graders and decided to extend the pairs of 10 game to the pairs of 20.  I wanted to review the idea of compensation but the focus today was more on all possible combinations of 20 and how the combinations of 10 can help you with the combinations of 20.

I started by giving them each a small handful of two sided chips (pennies would also work!) and having them figure out how many I gave them and how many more they would need to have 20.  (I always underestimate.  This gives them one more chance to practice a combination for 20).  Once everyone had 20 chips (actually today we did pairs) we put our chips in a cup and shook and dropped.  We then sorted into yellow and red and had kids count how many of each color and write an equation to match.
 20 two sided chips.

 Sorting the chips into yellow and red and counting them up.  This led to a lot of practice with counting by 2's and counting by 2's then adding one more when the numbers were odd.  A very nice side benefit because that is another skill this group has been struggling with.

 A look at the record sheet of one pair.  Record sheets are great to bring back to the whole group to have kids share things they noticed.
After playing for about 10 minutes, I pulled the group back together and told them I wanted to share what happened when I was playing.  I gave them examples such as I had 8 red chips, how many were yellow?  OR I had only 3 yellow chips, how many were red?  This is a great way to use the context of the game to help kids think about missing addends.  I wrote a question on the board and asked kids to write an equation that went with it.
 I wrote this question on the board and asked kids to find an equation that went with it.  As you can see in the picture, they came up with 13 + ___ = 20.  Then one little boy said, I actually got 20 - 13 but I think they are the same thing.  This led to a great discussion about fact families and the relationship between addition and subtraction.

The kids in this group really understood the idea of compensation and how an equation like 12 + 8 is related to an equation like 13 +7.  They were readily able to demonstrate this with the materials so we moved on from here and talked about how the make 10 facts helped us with the make 20 facts.

I still had 5 minutes left so I asked if any group played the game long enough to find all the possible equations.  The whole group was not sure but one little boy was convinced that there was no way they had enough time.  They started sharing different equations and one student decided to organize the equations so that we would know if we had them all.  Check out his work below!
 One boy's list of the combinations of 20.  Writing this list out himself really helped him process what he had learned and pull together all of the little pieces of knowledge we used in this game.

As the kids were lining up at the end of class, one little boy noticed that the 2 numbers were either both even or both odd.  He said, "it is just like when we were playing if the number of red chips was even so was the number of yellow chips." What a great notice for the end of class.  I took a picture and wrote his idea down so that we can explore it more and he can prove why it is true to his classmates next week.  If only I had 15 more minutes with these kids today......

Are your students fluent with combinations of 20?  Can they extend what they know about combinations of 10 to combinations of 20 or even 100?

1. Wow! Another great lesson. I like how you work in math with every little step (handing out the counters etc.).
I'm glad you're sharing this stuff!
Barbara