Pick a card, not just any card: a game for exploring number combinations and probability

Instructor, Nov-Dec, 1995 by Rusty Bresser, Stephanie Sheffield

Have you ever watched children play the card game War? In the throes of concentration, they rapidly slap down cards, check which has the greater value, and - after they've gone through the deck - eagerly count cards to see who won. Because in our math classes we strive for this kind of total focus, we thought, Why not build on children's interest in card games to help them focus on math concepts? "Is It 10?" is a card game that does just that, captivating kids while they practice addition, learn beginning probability concepts, and more.

STEPHANIE'S PRIMARY LESSON

Step 1

I give each pair of students a deck of cards and have them remove all the cards that are greater than 6. This can be a challenge for first graders.

Step 2

I draw the chart below on the chalkboard and direct each pair to copy it:

Less Than 10     10     More Than 10

Step 3

I ask a volunteer to help me demonstrate the game. First, I deal all the cards, facedown, to the two of us. Then we each turn over our top card. Together we decide if the sum of the numbers is less than 10, 10, or more than 10. One of us records the number sentence (like above) in the appropriate column on the chart on the chalkboard. After we've turned over several pairs of cards and recorded each sentence, I tell the children that they are to play until they use all of their cards, recording their results on their charts.

Step 4

After students have finished playing at least one game, we gather for a class discussion. I ask them to report what happened during play. (Children report that most of the number sentences fall in the "less than 10" column.)

Step 5

To help children think about why sums of less than 10 come up most often, I ask them to tell me possible pairs of cards each, less than 6, that give a sum that's more than 10. We record their suggestions in the "more than 10" column on the chart on the board. (I erase what the volunteer and I recorded during our demonstration game.) When children can't think of any more combinations, I ask them to think of cards that add exactly to 10, and finally, that add up to less than 10. Typically, children this age don't have an organized way to think of all the possible combinations for each column, but the discussion still helps them see that there are more sums for less than 10 and, therefore, they are more likely to get those sums when playing.

If you wish to take the activity further with your students, try intermediate steps 1 and 2.

RUSTY'S INTERMEDIATE LESSON

Step 1

For older students, follow primary steps 1 to 5. Then help students find an organized way to be sure they have found all the combinations for less than 10, 10, and more than 10. Explain that mathematicians use organized lists to help them keep track of data they're gathering and examining.

To get started, I say, "If I turn over an ace, what are all the possible cards my partner could turn over?" As students suggest cards, I show them how I record the combinations in list form on the board. We continue in this way until all the combinations are recorded. The chart will look like the one above.

Step 2

I ask, "What patterns do you notice when we record our data this way?" Students may respond: "All the answers count up by ones but they start with different numbers" or "The answers get bigger when you go across a row."

Step 3

I use three different colors of chalk and circle the combinations that add to less than 10 in one color, those that add exactly to 10 in another, and those that are more than 10 in the third color. I ask students to use this information to explain why it's more likely to get a sum of less than 10.

Step 4

I pose this question: If two people play this game so that player A scores a point for all sums less than 10 and player B scores a point for all sums greater than 10, do both players have the same chance of winning? If they do, that makes the game fair. If not, it's unfair.

After students come to a consensus that the game is not fair, I ask: How can you revise or change the game - or invent a new one - so that it would be fair for both players? Students may suggest, for example, giving two or more points to some cards. They may also suggest adding the sevens to the deck. If they do, add this combination to the chart. Then ask children for their prediction for combinations on the chart if you add 8, 9, and 10.

Editor's Note: A version of this activity by Bonnie Tank, a Math Solutions instructor, appears in Math By All Means: Probability, Grades 1-2, available in January 1996 from Cuisenaire.

STEPHANIE SHEFFIELD, a first-grade teacher in Houston, Texas, and RUSTY BRESSER, a fifth/sixth-grade teacher in San Diego, California, are the authors of Math and Literature books, published by Math Solutions Publications, available from Cuisenaire. MARILYN BURNS is the creator of Math Solutions inservice workshops.