Integrating Games in Math Class to Build Concepts

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Integrating Games in Math Class to Build Concepts

• Jim Rahn
• LL Teach, Inc.
• www.llteach.com
• www.jamesrahn.com
• james.rahn_at_verizon.net

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Mean and Median Game

• Materials
• Regular deck of cards with kings and queens
  removed (red cards are negative, black cards are
  positive, jokers and jacks are zero)
• 3-9 spinner with paper clip
• Counter, tiles, or cubes for keeping score
• Players two
• Objective To find and compare the mean and
  median for a set of randomly generated data.

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Rules

• Each player spins the spinner to determine how
  many pieces of data they must select from the
  deck of cards.
• Players select cards alternately from the deck of
  cards until they have the number of required
  data.
• Each player calculates their median and mean of
  their data.
• The player whose median is closer to their mean
  wins the game and takes a counter, tile or cube.
• Play continues for an pre-determined amount of
  time.
• The player with the most counters, tiles, or
  cubes wins the game.

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Example

• Violet spins a 6 and draws
• The median is 0.5 and the mean is 0.17

• Victor spins a 5 and draws
• The median is 3 and the mean is 2.2

Violet take the counter, tile, or cube as winner.
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Alternate Form

• Play the same game, but only calculate the means.
  The person with the highest mean wins the game.

• Play the same game, but only calculate the
  median. The player with the highest median wins
  the game.

Write a journal entry that describes your
strategies to find the mean and the median of
your data.
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Earning an 80 game

• Materials
• 0-9 spinner or a regular deck of cards with all
  red cards, tens, kings and queens removed (jacks
  and jokers are zero)
• Tiles, counters, or cubes for keeping score
• Players two
• Objective To find the scores needed on a set of
  tests to earn an average (or mean) of 80.

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Rules

• Each player randomly generates 10 digits and uses
  all the digits to create 5 grades.
• A number is then generated that represents the
  number of tests that will still remain to be
  taken and will count toward the mean grade for
  the set of scores.
• The winner is the player who needs the the lesser
  mean of the remaining tests to earn an 80. They
  get a marker.
• Players who need greater than 100 lose their
  turn.
• If a mean of 80 cannot be earned by either
  player, no one receives a marker for the game.
• Play continues for a pre-selected amount of time.

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Examples

• Bernard generates the following numbers
• 9, 0, 6, 5, 8, 8, 1, 2, 4, and 6
• He forms the following grades
• 95, 84, 82, 61, and 60

• Bette generates the following numbers
• 7, 5, 3, 3, 7, 5, 4, 2, 1, and 5
• She forms the following grades
• 74, 73, 53, 52, and 51

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• Bernard generates a 4, which means he has four
  more tests to take to average 80.
• To get an average of 80 on the 9 test, he will
  have to have an average of 84.5 on the four
  tests.
• This is possible.

• Bette generates a 3, which means she has three
  more tests to take to average 80.
• In order to average 80 on the eight tests, she
  will have to have an average of 112 1/3 on the
  three tests.
• This is impossible

Bernard wins the game.
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Shady Deal Game

• Objective To create as many polygons as
  possible within a given figure. The winner is the
  player who ends up with the smaller area of the
  given rectangle not covered by other rectangles
  or polygons.
• Materials
• Communicators, markers, graph paper, rulers, 2
  dice or spinners, and counters

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Rules

• Each player uses graph paper in their
  communicator to create a playing board that has
  100 square units.
• Alternately, players roll two dice or spin two
  spinners to find the dimensions of a rectangle or
  polygon and then draw the figure inside the 100
  square playing board.
• As more rectangles or polygons are added, they
  may be adjacent, but may not overlap.
• When a player cannot add another figure on their
  playing board, the area of the playing board that
  is not covered by the rectangles or polygons is
  their score.
• The player with the lower score wins the marker.
• Play continues for a pre-determined amount of
  time.

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Alternate Game

• When the spins their two numbers, they can form
  any polygon whose area equals the product of the
  two numbers spun.

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Straight Angle Game

• Objective To create three angles that sum to
  180o.
• Materials
• 0-9 spinner or a regular deck of cards with all
  red cards, tens, kings and queens removed (jacks
  and jokers are zero)
• Markers, tiles, or cubes for keeping score
• Players two or three
• Play continues for a pre-determined amount of
  time

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Rules

• Spin the spinner 6 times
• Use all six numbers to generate the measure of
  three angles
• The player that comes closest to 180 degrees
  without going over wins a marker.
• The players that can make exactly 180 degrees
  wins two markers.

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Examples

• Elvira generates 6, 6, 1, 3, 1, and 0
• She creates angles that measure 110, 66, and 3
  degrees
• Her total is 179 degrees.

• Elvis generates 7, 8, 0, 2, 2, and 3
• He creates angles that measure 80, 72, and 23
  degrees
• His total is 132 degrees

Elvira wins a marker
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Examples

• Elvira generates the numbers 3, 4, 0, 0, 2, and 6
• She forms the angles 60, 40, and 32 degrees
• Her angles total 175 degrees

• Elvis generates the numbers 1, 1, 0, 6, 3, and 7
• He forms the angles 106, 73, 1 degrees
• His angles total 180 degrees

Elvis wins 2 markers
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Alternate Form

• Generate ten numbers to create a set of angles
  that will sum as close to 360 degrees.

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Angle Roulette Game

• Objective To compute angle values which sum to
  180 degrees
• Materials
• 0-9 spinner or a regular deck of cards with all
  red cards, tens, kings and queens removed (jacks
  and jokers are zero)
• Dice
• Communicators
• Markers, tiles, or cubes for keeping score
• Players two or three

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Rules

• Each round begins by players draw a straight line
  on their communicators
• Each player generates two digits 0-9 to create
  the measure of an angle less than 180 degrees
• Each player uses their estimation skills to draw
  and label the given angle. Two supplementary
  angles are formed.
• Each player rolls the dice to generate a number
  from 1-6. They divide the supplementary angle
  into that number of equal parts. They determine
  the measure of each of these equal angles.
  Record this angle measure.
• Play continues until the sum of their individual
  angles measures is equal to or greater than 180
  degrees.

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Example

• Mary generates a 4 and 5 and creates, sketches,
  and labels an angle that measures 54 degrees.
• She generates a 4 with the dice.
• Her supplementary angle of 126 degrees is divided
  into 4 equal angles or 31.5 degrees.

• Manny generates a 3 and 6 and creates, sketches,
  and labels an angle that measures 36 degrees.
• He generates a 2 with the dice.
• His supplementary angle of 144 degrees is divided
  into 2 equal angles or 72 degrees.

Manny is currently winning because his angle is
closest to 180 degrees.
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Alternate Form

• Use a circular angle instead of a straight line
  and play the game to total to 360 degrees.
• Measure the angle with a protractor and receive a
  marker if the angle is within 5 degrees of the
  correct measure.

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Steepness Sleuth

• Objective To create slopes from randomly
  generated coordinates that will yield the
  steepest slope
• Materials
• -10 to 10 spinner or a regular deck of cards
  with kings and queens removed (jacks and jokers
  are zero, red cards are negative, and black cards
  are positive)
• Communicators and recording sheet
• Markers, tiles or cubes for scoring
• Play continues for a pre-determined amount of
  time.

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Rules

• Each player alternately generates four numbers
  with the spinner or cards and records them on the
  record sheet as coordinates.
• Each person calculates the slope of the line that
  passes through the two points.
• The person with the steepest slope (regardless on
  sign) wins the round.

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Example

• Emilio generates the numbers -4, 3, 0, and -10.
• The coordinates are (-4, 3) and (0, -10)
• The slope is -13/4

• Espanaro generates the numbers -9, -6, 3,and 2
  .
• The coordinates are(-9,-6) and (3,2)
• The slope is 8/12 or 2/3.

Emilio takes a marker for the steepest line.
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Alternate Form

• Players rearrange the four randomly generated
  numbers to create the slope.
• Additional points are given for negative slopes.

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Intersection Game

• Objective To visualize lines from randomly
  generated slopes and collect markers based on the
  location of the intersection of the lines.
• Materials
• -10 to 10 spinner or a regular deck of cards
  with kings and queens removed (jacks and jokers
  are zero, red cards are negative, and black cards
  are positive)
• A coin for flipping
• Markers for scoring
• Players two

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Rules

• One player tosses the coin. If it is heads, he
  or she is assigned even numbered quadrants or odd
  numbered quadrants if it tails.
• The other player is assigned the other quadrants.
• Players generate four random numbers using the
  spinner or cards.
• First number change in y-values
• Second number change in x-values
• Third and fourth numbers point through which
  the line passes

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Rules

• The players determine in which quadrant the point
  of intersection occurs.
• The player whose quadrant wins get the marker.
• If the lines are parallel or the intersection
  point is on an axis, then the round is scored
  zero.
• Game is played for the pre-determined amount of
  time.
• The player with the most markers at the end of
  the game is the winner.

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Example
Tomasina tosses a dime and it lands on heads.
She is assigned quadrants II and IV.

• Tomasina generates 4, 0, 4, and -7
• The slope is undefined.
• The line passes through (4,-7)

• Tomas generates -2, 8, 0 and 2.
• The slope is -2/8 or -1/4.
• The line passes through (0,2).

The lines intersect in the first quadrant. Tomas
receives one marker for this round.
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Balance Game

• Objective To use appropriate cubes to make a
  scale balance and to end with as many black cubes
  as possible.
• Materials
• Balance Scale and communicators
• 10 black cubes, 5 red cubes and 1 white cube
• One opaque container
• Reservoir of red and black cubes
• Players two

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Rules

• Each player places all the cubes in the container
  and randomly selects a handful of cubes. These
  are placed on the left side of the balance scale.
• The remaining cubes are placed on the right side
  of the balance scale.
• Each player must replace the white cube with the
  appropriate number of red or black cubes that
  will keep the scale balanced.
• The player who uses the most black cubes wins the
  round and takes the marker.
• If no one adds black cubes or there is a tie,
  neither player gets a marker.

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Example

• Doris chooses 2 red and 3 black cubes and places
  them on the left.
• The remaining cubes 2 red, 7 black, and a white
  are placed on the right side.

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Example

• Doris determines she needs to replace the one
  white cube with 3 red cubes to make her scale
  balance.
• Her answer in incorrect.

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Example

• Doug chooses a white and 4 black cubes and
  places them on the left.
• The remaining cubes 5 red and 4 black cubes are
  placed on the right side.

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Example

• Doug determines he needs 7 red cubes to replace
  the white cube for the scale to be balanced
• His answer is incorrect.

Neither person gets a marker.
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Example

• Doris chooses 4 red, 5 black and a white cube and
  places them on the left.
• The remaining cubes 1 red and 5 black cube are
  placed on the right side.

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Example

• Doris determines she must replace the one white
  cube with 3 black cubes to keep the scale
  balanced.
• The scale is balanced.

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Example

• Doug chooses 3 red and 3 black cubes and places
  them on the left.
• The remaining cubes 2 red, 7 black cubes and
  the white cube are placed on the right side.

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Example

• Doug determines he needs 5 red cubes to replace
  the white cube.
• The scale is balanced.

Doris wins the round because she required more
black cubes than Doug.
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The Multiples of X Game

• Objective To determine the number os cubes
  needed to make a scale balanced. The player
  whose equation has the larger solution wins the
  round.
• Materials
• Balance scale
• One deck of cards per player
• 10 red, 10 black and 10 white cubes
• Markers for scoring
• Players two

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Rules for Version 1

• Separate the queens and kings, shuffle, and place
  face down.
• Remove the black cards from the deck, shuffled
  and placed face down.
• Each player chooses one card from the
  king-and-queen cards and two cards from the black
  card pile.
• The first black card determines the number of
  white cubes to be placed on the scale.
• The second black card determines the number of
  black cubes that are placed on the scale.
• The king or queen determines which side of the
  scale the white cubes are placed. If a queen is
  chosen, the white cubes are on the left side. If
  the king is chose, the white cubes are placed on
  the right side. The black cubes are placed on
  the opposite side.
• Each player determines the value of the white
  cube. The person with the larger value takes the
  marker.

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Example

• Alicia chose

• Aaron chose

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Example
Alicia wins the round and gets a marker.

• Alicia determines the white cube is 2 ½

• Aaron determines the value of the white cube is
  1/3

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Version 2

• All the kings and queens are grouped together,
  shuffled and placed face down.
• The rest of the cards are separated into two
  groups red cards and black cards. Cards are
  placed face down.
• Each player choose one king-queen card, one
  black card and one red card.
• The black card determines how many white cubes
  are placed on the scale.
• The red card determines how many red cubes are
  placed on the scale.
• The king or queen determines which side of the
  scale the white cube is placed. Kingswhite cube
  on right, Queenswhite cube on left. The red
  cubes are placed on the opposite side.
• The player with the fewest number (largest value)
  of red cubes is the winner.

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Example

• Alicia chose

• Aaron chose

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Example
Aaron wins the round

• Alicia determines the value of the white is -2
  1/3.

• Aaron determines the value of the white is -1/2.

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Version 3

• All the kings and queens are groups, shuffled and
  placed face down.
• The red cards are separated, shuffled, and placed
  face down.
• Each player chooses one king-queen card and two
  red cards.
• The first red card determines number of white
  cubes that are snapped to a red cube and placed
  on the scale.
• The second red card determines the number of red
  cubes to be placed on the other side of the
  balance scale.
• The king or queen decides which side the snapped
  cubes are placed Kingswhite cube on right,
  Queenswhite cube on left.
• Each person decides the value of their white
  cube.
• The player with the larger value wins and gets a
  marker.

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Example

• Alicia chooses

• Aaron choose

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Example
Alicia wins the round.

• Aaron determines the value of the white cube to
  be 5/9 of a black cube

• Alicia determines the white cube to be equal to
  3/5 of a black cube.

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Finding the Percent

• Objective To obtain as many points as possible.
• Materials 12 to 12,000 and a regular deck of
  playing cards with the face cards removed (aces
  count as 1).

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Rules

• Each player must have their own board and
  Communicator clearboard.
• Players alternately draw two cards from the
  shuffled deck.
• The first card indicates the percent.
• The second card indicates the number.
• Once the values are determined, the percentage is
  calculated mentally or with some paper and pencil
  assistance. It is then recorded on the Game
  Record Sheet. When five rounds have been
  completed, the players add the numbers they have
  recorded.

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• The winner of the game is determined by the next
  card that is drawn.
• If the card is a red card (a heart or a diamond),
  the player with the greatest value wins.
• If the card is a black card (a club or a spade)
  the winner is the player with the least value.
• In the event of a tie, the answer on the first
  entry is compared.

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Example

• Player 1 draws a
• The player must determine the answer to 125 of
  1200.
• Mental math, number sense and problem solving
  skills are applied, and the answer is determined
  to be 1500, which is recorded on the first line
  of the game record sheet.

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• Player 2 draws
• The player must determine the answer to 10 of
  1200. Mental math, number sense and problem
  solving skills are applied, and the answer is
  determined to be 120, which is recorded on the
  first line of the game record sheet.
• Play continues for four more rounds each, and the
  answers are added and a card is drawn to
  determine the winner.

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Whats the Number

• Objective To obtain as many points as possible.
• Materials
• The 12 to 12,000 game board
• Form a deck of cards from a regular deck of
  playing cards by removing all face cards and the
  5, 8 and 10 of diamonds, 3, 5, 8, 9, 10 of hearts
  and the ace of spades (aces count as 1).

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Rules

• Players alternately select two cards.
• The first card is the percent that will be used
  for the round
• The second card is the value of the percent.
• The player must determine the number of which the
  percent being used was taken to get the value
  selected through the second draw. Mental math,
  number sense and problem solving skills are
  applied to determine answers. The answer is
  recorded on the game record sheet.
• When five rounds have been completed, the players
  total the numbers they have recorded.

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• The winner of the game is determined by the next
  card that is drawn.
• If the card is a red card (a heart or a diamond),
  the player with the greatest value wins.
• If the card is a black card (a club or a spade),
  the winner is the player with the least value.
• In the event of a tie, the answer on the first
  entry is compared.

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Examples

• Player one chooses a
• The player solves the problem Five percent of
  what number is 12?
• Using mental math and problem solving the answer
  240 is found. 240 is recorded on the record
  sheet for game 1.

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• Player two chooses
• The player must solve the problem, ¼ of what
  number is 12,000?
• If ¼ of 1 is 12,000, 1 must be four times as
  large, or 48,000. Therefore the number is 100
  times larger or 4,800,000.
• This number is recorded on the game record sheet.
• Play continues for four more rounds each, and the
  answers are added and a card is drawn to
  determine the winner.

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Psychic Math

• This activity has been designed as a review.
• If necessary, however, you may want to review
  basic vocabulary such as x-axis, y-axis,
  coordinates, quadrants, mirror image, and
  horizontal and vertical lines.
• To start the activity, tell students that when
  you tell them to do so, they are to turn to
  Analyzing Ordered Pairs on a Coordinate Grid
• Tell them to randomly plot eight points on the
  graph and label the coordinates of each.
• They will receive points if their ordered pairs
  meet the criteria you have set up in advance.
  They do not know the criteria they must become
  psychics and try to read your mind.
• After students have finished plotting the points,
  go through the following rules and have the
  students determine their scores.

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Game Rules

• 5 points for every point in the third quadrant
• 5 points for every point with coordinates that
  yield a negative product
• 10 points if a zero serves as either an x- or a
  y-coordinate
• 10 points if two or more points lie in a
  horizontal line
• 25 points if in any pair of coordinates the
  x-coordinate is twice as great as the
  y-coordinate
• 25 points if two points are mirror images of each
  other
• 25 points if the distance between two points is
  five units

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• As a homework or in-class activity challenge
  students to graph eight points that will yield a
  top score according to the criteria above.