Close or closer
To provide practice finding fractions of a whole number. Students find fractions (including 3/4 , 7/12, 5/6, 3/10, 3/5, and others) of 120 and use the results to match a target amount.
A game for two players
- One set of nine digit-cards, each containing a single digit from 1 through 9. Two cards drawn from this set will be used to form a single two-digit number (12 through 98, excluding the multiples of 10 or 11).
- A set of fraction cards cut out from Activity Master 27: Fraction Cards 1.
- Mix the digit cards. Select two randomly and turn them face up to make a two-digit number. This is the "target number." Put the rest of these cards away until next game; they will not be used during this round.
- Mix the fraction cards and stack them face down on the table. Turn two of these face up on the table to start the game.
Object of the game: to collect the set of one or two fraction cards (no more) that allows you fraction of 120 that matches, as closely as possible, the target number.
For example, if the target number is 91, then the fraction 3/4 gets quite close (because 3/4 of 120 is 90). The pair of fractions 1/2 and 1/4 gets the same result (because, together, they are 3/4, or because 1/2 of 120 is 60 and 1/4 of 120 is 30, and together 60 + 30 make 90.) The combination of 3/5 and 1/6 gets a different result (1/5 of 120 is 24, so 3/5 of 120 is 72, and 1/6 of 120 is another 20 for a total of 92), but is equally close to the target of 91.
While you are waiting for your turn...
Figure out what fraction of 120 your hand represents.
You start the game with no fraction cards in your hand, so your hand is worth 0. As you play, you will collect one or two fraction cards in your hand. If you have 1/10 in your hand, your hand is worth 12, because 1/10 of 120 is 12. If you have 3/10 and 1/6, your hand is worth 3x12 (three times as much as 1/10 of 120) plus 20 (one sixth of 120), for a total of 56. Your object is to get your hand's value as close as possible to the target number.
On your turn...
- You may choose one fraction card from the face-up pair and add it to your hand. (If no cards are left on the table, the game is over.)If you then have more than two fraction cards in your hand, you must discard one of them by placing it face down under the stack of fraction cards. (If you have two cards, you may discard one, but do not have to.) Replace the table-card by turning up a new one from the stack. It is now the other player's turn.OR...
- You may pass, and announce that you like your hand as it is.You have decided that your hand's value is as close to the target number as you expect to get. Do not take a new fraction card. You must now keep your hand as is for the rest of the game. The other player may now continue to choose new cards from the table, as long as there are such cards, until he or she is satisfied. The game is then over.
Ending and scoring
Whoever has the hand with the value closer to the target number wins.