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Introduction to Exactly 20

This post might be slightly out of order with the post Exactly 20 already up and out, but it wasn’t out of order the day we were working on the task.  After we tried Exactly 20 ourselves, we talked about what support or scaffolding we might need to put in place so that the kids can play the game independently and, as they play, are also working on using strategies efficiently and building computational fluency.

So, this was our idea for an introduction to Exactly 20.

We wanted to create some pre-determined sets of cards to use as the basis for a whole class conversation.  We selected a set of 4 cards to see what combinations were possible.  Then, we checked to see if we could use make 10 as a strategy and if we used the pair as 2 of our 3 cards, would the 3 cards result in a sum closest to 20 or a sum that was close to 20.

Here is the set of cards we started with:  4, 7, 3, 7.

IMG_2025

The set has a pair cards that make 10, the 3 and the 7, and when the second 7 is added to the 10, results in 17, a sum pretty close to 20:  7 + 3 + 7.  But…there is a second set of cards that results in a sum of 18: 7 + 7 + 4.  You can use doubles to find the sum. You can also use a make 10 strategy, if you split the 4 into a 3 + 1, and then, add the 3 + 7 to make 10 and then add the 7 and the 1, you get a sum of 18.  You are using make 10, but it is not as obvious as 3 + 7 that make 10.  We were looking for an obvious pair that made 10 for the first set.  So, we replaced one of the 7s with a 5.  The next set we tried was 4, 5, 2, 7.  It did not contain an obvious pair that makes 10.  What were we thinking!!!  The third set was the charm:  4, 3, 2, 7.  It made for great conversation as we found that we had to generalize a bit:  look at the three largest to see if they resulted in a sum that was 20 or less, and then check to see if we had an obvious pair that would let us use the make 10 strategy.  As you can guess, we needed to do some adjusting to some of the sets of cards we chose.

We found three sets that fit our criteria:  close to 20 or 20 exactly and an obvious pair that let kids use make 10. We then decided we wanted to stretch kids a bit and include, in the last 2 sets, some combinations that obviously made 10, to which a third card could be added, but would not have the sum closest to 20 or exactly 20.  We wanted to see what the kids would notice; who would use the make 10 strategy and who might would find other combinations of cards that would actually be closer to 20.

Our final list:

IMG_2029

We used this as a whole class lesson, with some partner conversation and partner work, to introduce the game Exactly 20 and to provide additional opportunities for kids to use the strategies we had been working on.  Our ultimate goal:  we want the kids to be so good at this game that it can be sent home for homework:  teach someone at your house how to play Exactly 20.

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