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Meeting 2 Student’s Booklet
Games Galore
October 6, 2016 @ UCI
Contents
0 Warm-up
1 The fantastic four
2 The incredible five
3 Fraction war
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http://www.math.uci.edu/mathceo/
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• Meeting 2 (October 6,, 2016)
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)+7
● 7 + (13*13) - (7:13).
You do not need to necessarily use all the
numbers.
=13
Write 2 expressions using the
numbers 8, 5 and 3.
What is the biggest expression
you can make with these 3
numbers?
Jack = 11
Queen = 12
=
Ace
1
King = 13
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• Meeting 2 (October 6,, 2016)
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 2
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.
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●
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 2, 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.
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• Meeting 2 (October 6,, 2016)
Example:
The 4 cards
Valid expressions
●
●
●
●
●
8*1
8 + (1-1)
(8 + 8) : (1 + 1)
(8 * 1) : 1
8 + 8 * (1 - 1)
The goal card
Invalid expressions
●
●
●
The expression
does not equal 8
8+8-1-1
8+8:1+1
8
Only uses 1 card
No parentheses
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Scoring
★
Every correct expression gives you points, as follows:
○ An expression using 2 cards gets 2 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 2 points.
★
If two expressions are related by some arithmetic properties of
numbers, then you only get credit for one.
For example:
2 + (4 - 3) and (2 + 4) - 3 count as the same expression.
( 3 + 4 ) -2 and ( 4 + 3 ) - 2 count as the same expression.
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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…
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2 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.
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Example:
There are 2 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) - (7 + 13 + 13).
Use the properties of arithmetic to your
advantage, and rewrite this as
(7 - 7) + (13 - 13) + 13.
The sum is 13.
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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 2 points.
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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 = 12 points
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2. The “sum” of the 5 cards is -10.
?
King = 13 points
Queen = 12 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.
?
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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 -22? (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.
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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 2 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.
1/13
1/13
1/12
1/13
1/12
1/11
1/12
1/11
1/10
1/7
1/10
1/6
1/4
1/13
1/12
1/10
1/9
1/7
1/6
1/5
1/6
1/5
1/5
1/4
1/4
1/3
1/2
1/10
1/8
1/7
1/6
1/11
1/9
1/8
1/7
1/12
1/11
1/9
1/8
1/13
1/12
1/10
1/3
1/2
1/13
1/12
1/11
1/10
1/9
1/7
1/4
1/3
1/13
1/11
1/8
1/6
1/5
1/11
1/10
1/8
1/6
1/13
1/12
1/9
1/7
1/5
1/12
1/10
1/8
1/13
1/11
1/9
1/7
1/13
1/12
1/11
1/9
1/8
1/13
1/12
1/11
1/10
1/9
1/8
1/13
1/12
1/11
1/10
1/9
1/13
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UCI Math CEO
• Meeting 2 (October 6,, 2016)
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 2 points.
★
The first person to identify the next highest fraction correctly
receives 2 points, and leaves the game. If the answer is
incorrect, he/she loses 1 point.
And so on…
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• Meeting 2 (October 6,, 2016)
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? 20? more than 30?
Next, think of all possible ways to get the fraction ½.
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More Challenges
1. Same game, but allow cards to have a
sign. Black cards are positive, red cards are
negative.
2. 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 2 (October 6,, 2016)