# Target Number (use all binary operations to = target card)

Preparation:  Take a deck of cards and separate out all of the face cards (eliminate Jacks, Queens, and Kings);You should have 40 remaining cards from Ace to 10 in four suits. Ace counts as one.

Play by yourself or in groups of two or more.

1. draw 5 cards face up.

2. draw a 6th card face up and place separately from the first 5.

3. begin combining ALL 5 cards using addition, subtraction, multiplication and/or division to result in the 6th card; there will be multiple methods to reach your solution.

Note: Younger children in second grade or below can win if they use three or more of the five cards. When they get comfortable enough with using all five cards, they should play by the advanced rules.

For example, if you draw 1, 4, 10, 8, 7 and your target number is 8, one solution might be: 10-7=3; 4-3=1;1x1=1;1x8=8

Another example, you draw the 5 cards:  2,  3,  8, 8  and 9; the 6th card is a 4.

You find that 8 ÷ 8 = 1; 9 - 3 = 6; take the result from the previous two calculations with the first 4 cards and combine 6 x 1 = 6; finally 6 - 2 = 4.

Another example, you draw the 5 cards:  4, 7, 2, 3, and ; the 6th card is a 3.

You find that 7 x 3 = 21; 3 ÷ 1 = 3; and 21 ÷ 3 = 7; 7 - 4 = 3.

4. if you are playing with two or more people, the first one to find the solution keeps the 6 cards.

5. the player with the most cards wins (since there are 40 non-face cards in a deck, there are 6 rounds in a deck).  Once the deck is finished, you can reshuffle and start again or keep a running total.

6.  NOTE: Sometimes you will see the solution instantaneously, and sometimes, it
may take you 15 minutes to find a solution (HINT: go into negative numbers).

7. Special hints: stay away from high numbers; try to get zero by subtracting a number from itself; try to get a one by dividing a number by itself; add zero to get the number added to; multiply by one to get the number multiplied by.

The algebraic properties of addition, subtraction, multiplication and division are as follows:

a + 0 = a this is the identity property of zero

a x 1 = a this is the identity property of multiplication

a / a = 1 this is the identity property of division

a x 0 = 0 this is the multiplicative property of zero

As an advanced method, you can use exponents and factorials. For example, if you have a 3 and a 2, 3 to the second power is 3 x 3 = 9. 3! = 3 x 2 x 1 = 6 and 4! = 4 x 3 x 2 x 1 = 24.

This game can be played online at http://illuminations.nctm.org/ActivityDetail.aspx?id=173. The game on line is called Primary Krypto.

I also gave everyone a printed deck of 40 cards if they do not have playing cards. They can cut them out.

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Target_Number_all_5_cards.pdf747.37 KB
Target_Number_3_or_more_cards.pdf735.5 KB