Games Galore. Meeting 2 Student s Booklet. Contents. October 6, UCI. 0 Warm-up 1 The fantastic four 2 The incredible five 3 Fraction war

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1 Meeting Student s Booklet Games Galore October 6, UCI Contents 0 Warm-up 1 The fantastic four The incredible five 3 Fraction war UC IRVINE MATH CEO

2 Meeting (October 6,, 016) 0 Warm-up Given any numbers, we can combine them into a mathematical expression by using any of the 4 basic operations: +, -, : and *, and parentheses. Look, for example, at the cards in the picture. There are many mathematical expressions we can form with the numbers 7,7, 13, 13 and 13. For example: (13-7) (13*13) - (7:13). You do not need to necessarily use all the numbers. =13 Write expressions using the numbers 8, 5 and 3. What is the biggest expression you can make with these 3 numbers?

3 Jack = 11 Queen = 1 = Ace 1 King = 13

5 Meeting (October 6,, 016) 1 The Fantastic Four (*) Get a deck of cards, without the jokers. Choose a dealer (who will pass the cards). Divide the remaining players into teams. Give to each player scratch paper and pencil. The dealer chooses 4 cards and a goal card from the deck. The 4 cards are displayed face up, but the goal card is kept secret. Every player writes down the numbers on the 4 cards. (*) Adapted from THE MATH EXPLORER: Games and Activities for Middle School Youth Groups, by Pat Murphy, Lori Lambertson, Pearl Tesler, and the Exploratorium.

6 Meeting (October 6,, 016) Once players are ready, the goal card is turned face up and the timer starts Players have 6 minutes to use the 4 cards to make math expressions that equal the goal card. You do not need to use all the cards, and you can not use the same card twice. Work as a team, and collect as many expressions as you can. If needed, a team can draw one more card in order to make an expression, but they lose one point for drawing the extra card. Write as many expressions as you can, using, 3 or 4 of the numbers from the given cards. You can use any math operation that you want, but you cannot use the same card more than once in the same math expression. Make sure to include parentheses as needed! (*) Adapted from THE MATH EXPLORER: Games and Activities for Middle School Youth Groups, by Pat Murphy, Lori Lambertson, Pearl Tesler, and the Exploratorium.

7 Meeting (October 6,, 016) Example: The 4 cards Valid expressions 8*1 8 + (1-1) (8 + 8) : (1 + 1) (8 * 1) : * (1-1) The goal card Invalid expressions The expression does not equal :1+1 8 Only uses 1 card No parentheses

8 Meeting (October 6,, 016) Scoring Every correct expression gives you points, as follows: An expression using cards gets points. An expression using 3 cards gets 3 points. An expression using 4 cards gets 4 points. If you draw an extra card, you lose 1 point. If the expression you make is incorrect, you lose points. If two expressions are related by some arithmetic properties of numbers, then you only get credit for one. For example: + (4-3) and ( + 4) - 3 count as the same expression. ( ) - and ( ) - count as the same expression.

9 Challenges Is it always possible to combine the 4 cards into an expression which gives you the goal card? For example, given any 4 cards, can you always get an expression equal to 1? Try it out Meeting (October 6,, 016)

11 Meeting (October 6,, 016) The Incredible Fives (*) Get a deck of cards, and remove the jokers. Give every player scratch paper and pencil. The dealer draws 5 cards, and places them face down on the table. When everybody is ready, the dealer turns the cards and all players rush to add their cards with a twist! Convention for the game: Numbers in black cards are regarded as positive, whereas numbers in red cards are regarded as negative. For example, the 7 counts as a 7, and the K counts as +13. When everybody is ready, the timer starts The dealer turns the cards. Players have 3 minutes to compute the sum of the 5 cards and write down their answer (without saying it loud.) The first person who computes the sum should tap the table. At the end of the 3 minutes, the players compare their answers. (*) Inspired from PLAYING WITH MATH, edited by Sue VanHattum.

12 Example: There are black cards (7 and 13) and three red cards (7, 13, 13). Recall that the black cards are positive, and the red cards are negative. So we need to compute the expression: (7 + 13) - ( ). Use the properties of arithmetic to your advantage, and rewrite this as (7-7) + (13-13) The sum is 13. Meeting (October 6,, 016)

13 Meeting (October 6,, 016) Scoring Every person that computes the sum correctly gets 1 point. Every person that computes the sum incorrectly loses 1 point. The first person who taps the table gets 3 points (but only if the sum is correct). If you scream your answer you ruin the other people s game, so you lose points.

15 Meeting (October 6,, 016) Some challenges 1. The sum of the cards below is -5.? Jack = 11 points King = 13 points Draw the mystery card. (Recall that red cards are negative, and back cards are positive.) Queen = 1 points

16 Meeting (October 6,, 016). The sum of the 5 cards is -10.? King = 13 points Queen = 1 points Jack = 11 points Draw the two mystery cards. Can you think of other solutions? How many? BIG challenge Get together with your group and brainstorm how many possible solutions are there *The dealer has only 1 deck.?

17 Meeting (October 6,, 016) More Challenges The dealer has 3 decks of cards. It gives you 5 cards. What is the biggest sum can you get? (Try it out ) Can the sum ever be 70? (Try it out ) Can the sum be 31? (Try it out ) Can the sum be -? (Try it out ) Can the sum be any number between -65 and +65? BIG challenge: What if the dealer only has 1 deck? Explain your answers.

19 Meeting (October 6,, 016) 3 Fraction War (*) Get a deck of cards, and remove the jokers. Give every player scratch paper and pencil, and pass out the fractions wall hand-out. The dealer gives cards to each player. All cards are displayed on the table, face up. Every pair of cards gives rise to a (proper) fraction = (smallest number)/(biggest number) so, for examples, the two cards 7 and 3 give the fraction 3/7. (For now, we ll think of every card as positive.) Each player should write down all the fractions. The purpose of the game is to order all the fractions, from the biggest fraction to the smallest fraction. All players work together, as a team, but the fastest players receive more points. (*) Inspired from PLAYING WITH MATH, edited by Sue VanHattum.

20 1/1 1/1 1/11 1/1 1/11 1/10 1/7 1/10 1/6 1/4 1/1 1/10 1/9 1/7 1/6 1/5 1/6 1/5 1/5 1/4 1/4 1/3 1/ 1/10 1/8 1/7 1/6 1/11 1/9 1/8 1/7 1/1 1/11 1/9 1/8 1/1 1/10 1/3 1/ 1/1 1/11 1/10 1/9 1/7 1/4 1/3 1/11 1/8 1/6 1/5 1/11 1/10 1/8 1/6 1/1 1/9 1/7 1/5 1/1 1/10 1/8 1/11 1/9 1/7 1/1 1/11 1/9 1/8 1/1 1/11 1/10 1/9 1/8 1/1 1/11 1/10 1/9

21 Meeting (October 6,, 016) Scoring (for a group of 5 players): The first person to identify the highest fraction correctly gets 4 points, and leaves the game. If the answer is incorrect, he/she loses 3 points. The first person to identify the next highest fraction correctly gets 3 points, and leaves the game. If the answer is incorrect, he/she loses points. The first person to identify the next highest fraction correctly receives points, and leaves the game. If the answer is incorrect, he/she loses 1 point. And so on

22 Meeting (October 6,, 016) Challenges What is the smallest possible fraction you could get? Can you think of 5 different pairs of cards that give rise to this fractions? How many more pairs of cards do you think would give you the same fraction? 10? 0? more than 30? Next, think of all possible ways to get the fraction ½.

23 More Challenges 1. Same game, but allow cards to have a sign. Black cards are positive, red cards are negative.. Same game, but use with improper fractions: to form a fraction, divide the biggest number by the smallest number. For examples, the two cards 7 give the fraction 7/3. and 3 Meeting (October 6,, 016)

What numbers can we make?

Meeting Student s Booklet What numbers can we make? October 12, 2016 @ UCI Contents 1 Even or odd? 2 New currency A present for Dad 4 A present for Mom 5 Challenges 6 Crystal Ball UC IRVINE MATH CEO http://www.math.uci.edu/mathceo/