Box Cars and One-Eyed Jacks MATH GAME GA MES S FOR TEACHING PLACE VALUE,
OPERATIONAL
FACT FLUENCY AND FRACTIONS
John Felling Our Lady of the Assumption School Atlanta, GA
October 2014
[email protected] phone 1-866-342-3386 / 1-780-440-6284 fax 1-780-440-1619
boxcarsandoneeyedjacks.com BoxCarsEduc BoxcarsEducation
Teaching Tips from Box Cars And One-Eyed Jacks Box Cars And One-Eyed Jacks Inc.
Organizing Your Cards & Card Management Management Use three large buckets (1 gallon or 4 liter liter each}. Gather a lot of decks of cards. cards. Approximately 1 deck per student but 1 deck per 3 students is a good start (purchase, donated, brought from home}. The joke "not playing with a full deck" applies here. We don't play with full decks as it's not important important to the math of the games. Full decks are not necessary when organizing the cards, and not wor rying about full decks speeds getting cards out and putting them away (as seen below) at the beginning and end of classes. In the first bucket, put your low cards. For example, John likes to put his 1's, 2's, 3's, 4's and 5's. The cards match the fingers on the hand, keeps sums to 10, products to 25, denominators to 1/5s. On the other hand, Jane likes to have 1's through 6's as this allows matching the cards to a typical 6-sided die. This also allows sums to 12 , products to 36 and fraction denominators to 1/6s. The key here is that as teacher, decide what cards go into your buckets based on your classroom routines. In the second bucket, put the rest of your single-digit cards. John John - 6's, 7's, 8's, 9's, and 0's (Kings for 0 if using using a regular deck). Jane - 7's, 8 's, 9's, and 0's (Kings for 0 if using a regular deck). The cards in this bucket along with cards in the first bucket allow for P lace Value (0-9 digits), sums to 18, products to 81 and fraction denominators to 1/9s. In the last bucket, put everything else- 10's 11's 12s (Jacks for 11, Queens for 12 if using re gular decks) and any wild cards or jokers . GETTING CARDS OUT Once a teacher has identified a game and shown how to play,the students are t old to get a "small" or "big" handful of cards from either a specific bucket or buckets SHUFFLING AND DEALING Cards are "mushed up" and quickly separated into as many groups as players (typically 2 for 2 players, 3 for 3 players). The player Mushing the cards is the last to pick a pile (piles (piles do not have to be exactly equal. If "winning" is important, the winner is whoever has the most cards in their "point pile" at the end}. CLEANING UP Players quickly place the cards into 3 piles. First pile has 1s 2s 3s 4s and 5s. Second pile has 6s 7s 8s 9s and 0s. Last pile has 10s 11s 12s Wild Cards,Jokers,etc. The piles are then placed into the ir corresponding bucket
Organizing Your Dominoes & Dominoes Management A typical class will need a minimum of one set of dominoes for every two students (about 12 sets). If feasible , 1 se t per student is even better. First and Foremost Use Dominoes of Differe nt COLORS! This makes it easier to determine each student's or group's set while playing and when putting dominoes away. If you already have sets of the same color, get an adult (parent?) volunteer with 6 colors of permanent spray paint. The adult volunteer takes one set, lays them face-down on newspaper (outside or other well-ventilated area) and sprays t he back of the set all one color (for example "green"). The volunteer then takes the other sets and repeats the same process but with a different color for each set until the first 6 sets are done. The volunteer continues to do sets of 6 in this way until the entire collection of dominoes has been done. Keep the dominoes in their sets inside easily opened and closed see-through containers such as Mesh Bags, Traveling Soap containers, heavy duty sandwich sized freezer bags etc.
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For each week that the students are using the Dominoes, have the students make sure they have a complete set by using their set to fill in the Dominoes Outcomes Chart (page 78 in Domino Games - Connecting The Dots, page 77 in Domino Games - Linking The Learning). When students are done using the dominoes for the class, have t hem make stacks of 4 dominoes (a complete set of 28 double-6 dominoes will have 7 stacks). If they have a complete set, they put the dominoes into the container and then put the container away. If a set is missing a domino, it is important that the teacher knows so it can either be found or, if all else fails, the container for the set is marked as "incomplete" until a replacement can be found. Younger students may find it easier to put them into stacks of 2 (14 stacks for a complete set).
Organizing Your Dice & Dice Management Keep dice that are the the same together together in one container (for example 0-9 dice in one containe r, + and - dice in another container, 1-12 dice I in a third container, etc.). See-through re-sealable Tupperware containers or heavy duty mid-sized freezer bags work well. One student per group or game gets the dice for the game and returns the dice at the end of the game. Have the students roll the dice into their hands! Roll their dice into the "Hockey Net", "Soccer Goal", "Dug out" etc. In other words the dice rolled by one hand and are blocked from going too far by the other hand. Another effective example is to have the students roll the dice with both hands, "trap" the dice in both hands and then "hide" the dice as they fall the 2 cms from their hands onto the playing surface. The roll is "revealed" when they remove their hands from over the dice. For noisy dice -roll on somethi ng " soft" Fun Foam, Felt liners or pads, table setting mats etc all work well. In a pinch, have the students roll on 5-10 sheets of paper stacked on top of e ach other. The stacked paper muffles a lot of the sound.
Organizing & Managing Your Dice Trays (36 dice in a tray) When taking the dice out of the tray. Remove the tray from the bag, turn the tray upside-down (black (black on top) and take the black tray off of the clear lid (the dice remain in the lid). The dice are now easily "poured out" of t he lid onto the playing surface. Play on the floor when possible. The dice don't "fall off' the floor and most students enjoy the experience of playing on the floor as it gives t hem room to "spread out".
the "Hockey Net", "Soccer Goal", "Dug Out" etc. Have the students roll the dice into their hands! Roll their dice into the In other words the dice rolled by one hand and are blocked from going too far by the other hand. Another effective example is to have the students roll the dice with both hands, "trap" the dice in both hands and then "hide" the dice as they fall the 2 cms from their hands onto the playing surface . The roll is "revealed" when they remove their hands from over the dice. For noisy dice - roll on something "soft". Fun Foam, Felt liners or pads, table setting mats etc all work well. In a pinch, have the students roll on 5-10 sheets of paper stacked on top of each other. The stacked paper muffles a lot of the sound. When putting the dice back into the trays at the end of a class have the students start with the lid, using one hand to "separate" one half of the lid from the other. The students take all of ONE COLOR of the dice and pour t hem into ONE HALF of the lid. They spread the dice into the half, "patting down" the dice so t he dice are flat and in place. Then all of the dice of t he OTHER COLOR are poured into the other half of the lid. Again, the st udents "pat down" the dice so the dice are flat and in place. The black tray is then fitted on to the top of the dice in the lid. The tray is now complete and can be slipped back into the ziplock bag. Use rubber bands to separate parts of the tray. This is useful when using the trays for place value and you want to limit size to less than 100,000 or you want to have a "decimal place".
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PRIMARY PRIMA RY SUPER MUSH ______ ___ _______ _______ ______ ____ _
_________________
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HORSE HORSE RACE RA CE - PRIMARY ADDITI A DDITION ON LEVEL:
K-2
SKILLS:
adding to 12, commutative commutative property of addition, fact families
PLAYERS:
2 (1 vs 1)
EQUIPMENT: GOAL:
tray of dice (each player needs 18 of their own own color), gameboard
to have the greatest number of dice on your side of the the “racetrack” at the end of the the game
GETTING GETTING STARTED: Each player takes 18 dice of one color and picks a side of the dice tray to to be their “racetrack”. Each player picks up a pair of dice, rolls, and calculates their sum. The player with the greatest sum puts their dice into their side side of the racetrack. Both players verbalize their sums. EXAMPLE:
+ +
= 8
PLAYER PLA YER ONE MATH TALK TALK
+
+
=
6
PLAYER PLA YER TWO
Player One says “8 is a greater sum than 6”
The player with the greatest sum places their their dice in their side of the racetrack. The player with the least sum tosses their dice into the lid. Players each pick up another pair of dice, roll roll and compare their next sums. In the event of a EQUAL SUM – both players put their two dice into their side of the racetrack.
TIE
or
Play continues until both players’ 18 dice have been rolled out. The player with the greatest number of dice on their side of the racetrack wins.
Level 1 : Addition to 12 - Players roll two dice and add them
Player One
Player Player Tw o
Level 2 : Addition to 18 - Players roll three dice and add them. Level 3 : Multiplication to 36 - Players roll two dice and multiply them Level 4 : Multiplication to 72 - Players roll three dice, choose two to add together, then multiply the sum by the third.
Add dice to the track along a curving path to simulate the race! 5
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KNOCK YOURSELF OUT LEVEL: 2 – 6 SKILLS: adding, subtracting, probability, problem solving, multiplication, division for variation, creating outcomes charts, analyzing outcomes
PLAYERS: 2 (1 vs 1) or 4 (2 vs 2) EQUIPMENT: tray of dice (each player needs 6 dice of their own color plus 2 of their opponent’s color, and one half of the tray for their gameboard) player to remove all six of their dice from their their side of the tray. GOAL: to be the first player
GETTING GETTING STARTED: STA RTED: Players set up the gameboard as follows:
PLAYER ONE
PLAYER TWO
The dice in the tray are arranged in a numeric sequence 1 – 6 and remain in that order for the entire game. Once the tray is set up, play can begin. Players alternate turns and play as follows: The two extra dice are rolled on each player’s turn. The dice may be either added for a sum OR subtracted for a difference. The answer must must be a number from one to to six. A player can choose which operation to perform and remove only one die per turn. The removed die must not be changed, i.e. i.e. if the die removed is the (three), it must remain a three, and it must be placed back into the third position if required during the course of the game.
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KNOCK YOURSELF OUT If a player is unable to either add or subtract to equal any of the numbers left on their side of the tray, the player receives a STRIKE and they must CHOOSE and REPLACE any die that has been earlier removed. If there are no dice to replace, the player simply misses that turn. ROLL WARNING: Double 6’s, double 5’s and double 4’s are automatic strikes. The player will either
miss a turn or put a die back if these rolls occur. EXAMPLE:
Player One only Roll 1: 6 & 2 6 – 2, removes 4 5
4
3
1
2
Roll 2: 3 & 2 3 + 2, removes 5 Roll 3: 2 & 1 2 + 1, removes 3 Roll 4: 6 & 5 6 – 5, removes 1 Roll 5: 6 & 1 6 – 5 = 1, which is already out 6 + 1 = 7, which is not an option Player must now put a die back. Player chooses 1
Players continue to alternate turns rolling, analyzing, adding and subtracting combinations until one player has successfully removed all six of their dice at once.
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Multipl ult iplic ica ation tio n Board Board 1
2
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10 10
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1
1
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24
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3
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36
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32
36
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48
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5
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60
6
6
12
18
24
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36
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48
54
60
66
72
7
7
14
21
28
35
42
49
56
63
70
77
84
8
8
16
24
32
40
48
56
64
72
80
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96
9
9
18
27
36
45
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63
72
81
90
99
10 1 08
10
10 10
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120
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11 11
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66
77
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132
12
12
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36
48
60
72
84
96
108
12 120
13 132
14 144
Box Cars & One-Eyed Jacks inc Multiplication Tic Tac Toe Player one rolls 2 x 0-9 or 2 x 1-12 dice and finds the product (eg 4x6=24; 6x4=24) Cover spaces with bingo chips (one space only would be covered if doubles are rolled) Player Two takes their turn. Players continue to alternate turns Build Tic Tac Toe, three or more in a row horizontally, vertically or diagonally One point per chip and remove from board so spaces are open again Roll your partner's space and capture for 2 points per chip Play for a set period of time 9
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the instruction of place value concepts with baseten manipulatives. so they are reading numbers properly; use tens bracelets, bracelets, thousands bracelets, bracelets, playing mats mats / fun foam for building place values. sort out all tens, Jacks, Queens and Kings and use cards from 0-9 only. which you can use to build differentiation and a variety of concepts into your instruction. 0 - 9, 0-100, or tape ten together for a 0-1000
line. with regular dice or in 3-
in-a-cube dice.
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Betweeners © Box Cars And One-Eyed Jacks.
4 Player Player Versio n – Highest doesn't win. Lowest doesn't doesn't win. The two between numbers win.
Betweeners
Variation of Betweeners Betweeners From Math Attack © Box Cars And And One-Eyed Jacks
Concepts: Number Concepts: Number Sense, Ordering Numbers (whole and decimal) Equipment: One 3inCube die / player Goal/Object: record a number that is between the highest and lowest for the round TraditionalTraditional - Each player shakes their own 3inCube die and secretly looks at it, mentally determining the possible answers they could use. Each player player then secretly records one of their possible answers. Once all the players have recorded their answer, they reveal it to the other players. All players copy all all other players' answers onto their own score sheet. The answers are compared, lowest doesn't win, win, highest doesn't win, between number (or numbers if 4 player game) wins. Variations: (1) Players are allowed to create numbers with decimals meaning answers can range from 0.111 to 666. (2) Players create multi-operation m ath sentences trying to have the between answer example 3+2x1=5 (3) Players create mixed fractions example example 3 2 1 makes 3½ or 1⅔ or 2⅓ 2 1 1 can only make 1½ (4) For sim pler version of the gam e, each player can use a 1-12 die ( or 1-20 die/player or 1-30 die/player ) (5) Division: Make 2-digit number, divide it by the remaining number. (Rolled 2, 3, 5 made 35 ÷ 2 = 17.5)
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t e e h S g n i d r o c e R – n o i t a m i t s E n o i t a c i l p i t l u M
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ : e t a D _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ : e m a N
e c n e r e f f i D
l a u t c A
e t a m i t s E
0 1
= s e c n e r e f f i D
1 9 3
l a t o T 0 8 3
s l l o R
3 2 X 7 1
X
X
X
X
X
X
X
X
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d n u o R
e l p m a x E
1
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0 1
1 1
2 1
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6 w R o 2 h . = e e n e l i 2 s 1 o r ÷ e 0 t t b 3 h . g m u 2 i r 1 o n d t a n s n a e o 0 r i u s 3 t h c t d i e p o l d l o e e o R s t
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100 Board Wi pe Out Level:
Grade 3 and up
Skills:
Multi-operations ( + - x ÷ √ X2 ), Order of Operations
Players:
2-3 players working together as a team
Equipment:
Dice Tray, pencil, recording sheet per player/team
Objective/Goal:
To make equations for 1-100 in fewest rolls
Getting Started: Team One One decides whether to to roll 3, 4 or 5 dice and records the roll in the Roll 1 space on the recording sheet. Team One then creates math sentences using the numbers rolled that have the numbers 1-100 as answers. They record each math sentence on the recording sheet in the space for the answer. answer. Each math sentence must use each number rolled. For example, ifif 4, 4, 2 and 6 are rolled then each math math sentence must contain 4, another 4, 2 and 6. Once the team has exhausted all the possibilities for Roll 1, they can take Roll 2. 2. At the beginning of each roll, the team can decide to roll 3, 4 or 5 dice. In other words, they don’t always have to roll the same number of dice for every roll. Example: The team rolled 4, 4, 2 and 6 and made the following math sentences, (utilizing the rules for Order of Operations where necessary - see examples with answers = 10 and = 12): 4 x 4 x 2 + 6 = 38
(6 – 4 + 4) x 2 = 12
6 – 4 + 4 x 2 = 10
4 2 x 4 + 6 = 70 etc
In the examples, the team first rolled 4 dice and using those numbers, made equations for 30 answers before rolling a second time. For the second and third rolls, they rolled 5 dice and had written math sentences for 61 answer before the math period ended (they said they could have kept going).
Variation: (1) Teams can use dice other than regular spotted dice, such as 10-sided 0-9, 12-sided 1-12, 20-sided 1-20 or 30-sided 1-30 dice. (2) Teachers may place restrictions on equations to make it more challenging such as “Every math sentence must include at least one multiplication component”. 15
100 Board Bo ard Wipe Wip e Out Out – Re Record co rdii ng Sheet heet Team Members _______________
_______________
Roll One: __________
Roll Two: __________
Roll Five: __________
Roll Six: __________
_______________ Date: __________
Roll Three: __________ Roll Seven: __________
Roll Four: __________ Roll Eight: _________
= 1
= 2
= 3
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ROLL ON PLACE VALUE
E PLAYER N ONE O D N U O PLAYER R TWO
O PLAYER W ONE T D N U O PLAYER R TWO E E PLAYER R ONE H T D N U PLAYER O TWO R
Roll on Place Value (from Stratedice)
The goal of the game is to create the largest number. Players take turns rolling a die, placing it into the tray and announcing its place value for that roll. After 6 rolls, players compare numbers. A point is earned by the player with the largest number. A Place Value Systems die is rolled to identify a specific place value (for example 100's) A second point is earned earned by the player player with the highest highest value value in that that place. A third "upside "upside down" down" bonus point point is awar ded to the player with the biggest number when the tray is turned upside down and the numbers are compared. 17
ROLL REGULAR DICE TO BUILD PLACE VALUE AS FOLLOWS
2 DICE: 3 DICE: 4 DICE: 5 DICE: 6 DICE:
HUNDRED THOUSANDS
/
TENS /
ONES
HUNDREDS /
TENS /
ONES
THOUSANDS
/
HUNDREDS /
TENS /
ONES
TEN THOUSANDS
/
THOUSANDS
/
HUNDREDS /
TENS /
ONES
TEN THOUSANDS
/
THOUSANDS
/
HUNDREDS /
TENS /
ONES
Roll dic e, arrange for greatest greatest p ossibl e number First to c all ROCK ROCK & ROLL s cor es 5 POIN POINTS TS All Al l o ther th er pla p layer yers s mus m us t freeze f reeze thei t hei r dic d ic e when wh en ROCK & ROLL i s call c alled. ed. If a player's n umber umb er is g reater than th e player who c alled ROCK ROCK & ROLL, they also g et 5 POI POINT NTS S
ROLL
NUMBER
EXPA EXPA NDED NUMBER
1 2 3 4 5 6 7 8 9 10
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Batters Up! Skills:
Place Value to 100 100 000s, 000s , Addition with Expanded Notation
Equipment : Cards 0-9. 0-9 . Place Value System die, die , paper/pencil Goal:
Greatest total sum after ten rounds wins
Gett Ge tt i ng Started: Started: Each player builds a number in the 100 000s with their cards Build in order from 100 000s place to 1s place (Example 230 516) Each player reads their number to the other players. One player rolls the PV System die and calls out t he place value Players identify the value at that place value in their number (this is their score for the round) and record their score for that round. Example: ten thousands is rolled, 3 is in the 10 000s place, score for that round is 30 000 Play 10 rounds, (rotate roller) then total your score. BATTERS UP! Round
Number
Roll
Value/Points/Score
1 2 3 4 5 6 7 8 9 10
Total Score = Copyright Box Cars and One Eyed Jacks Inc.
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r e b m u N y M
s e n O
r e b m u N y M s ' t a h W
s n e T
s d e r d n u H s d n a s u o h T
s d n n a e s T u o h T s d d e n r a d s n u u o h H T s n o i l l i M
s n n o e i l T l i M
d s e n r o d i n l l i u M H
. s n i w r e b m u n t s e g r a L . d n u o r f o d . n s e i n t a w r t n e e b n m o u p n p t o s e h t g i r w ) a s t s L r . e t e l b l n a m m e u s n n r o e o p p r o a t p s e h t g i m r o a w C l e r . t o a r e n p b i e m ( o m u s c , n i n e d l u w l i r u e a b b v e o c t t m a l e u p e n h n c s e i f e i c n w o t e e p d r b s o e e c h e t s o r , o n s h e c e r i e c h y t y D a l d l m 9 - n p o 0 a 3 d l n e l s o r o a U R F R • • • •
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Fraction Horse Race Race
Middle Muddle
Box Cars Stratedice Book page 34 (Adapted)
Box Cars "Piece It Together With Fractions" page 28
Concepts: Comparing Fractions Equipment: Stratedice Tray, Chart, Fraction Pieces Goal/Object: To have the smallest fraction, have most dic e in the racetrack at the end Each player has their own color color of dice. Players roll 2 dice and create a proper fraction. Players build their fraction with fraction pieces (or find their fraction on the chart) and compare. Player with the SMALLEST fraction wins the round and places their dice in the "racetrack" (black grid). Losing player places their dice into the lid (clear grid). In the case of a tie or equiv alent fraction, both players put their dic e into th e of the dice black tray. Play continues until all of have been used. Player with the most dice in the black tray at the end wins. Variation: Each Variation: Each player rolls 3 dice and creates a mixed fraction (whole number and fraction) like 2¾.
Concepts: Comparing & Ordering Fractions Equipm ent: Stratedic e Tray Tray / Player Goal/Object: Goal/Object: to be the between fracti on, have the most dice in the racetrack racetrack at the end. Players roll 2 dice and create a proper fraction. Players build their fraction with fraction pieces (or find their fraction on the chart) and compare. Player with the SMALLEST fraction DOES N OT WIN. Player with the the LARGETS LARGETS fraction DOES DOES NOT WIN. Player with the IN-BETWEEN IN-BETWEEN FRACTION WINS THE ROUND. ROUND. Winner places places their dice into their black tray, losers place their dice into their lids. In the case of a tie of 2 or 3 players or equivalent fractions for 2 or 3 players, all players put their dice into their li ds (they all all lose because no one is " between"). between"). Play continues until all of the dice have been used. Player with the most dice in the black tray at the end wins. Variation: Each player rolls 3 dice and creates a mixed fraction (whole number and fraction) like 2¾.
Rainbow Rainbow Fractions
Order In The Court Court
Box Cars "Piece It Together With Fractions" page 49
Box Cars "Double Dare You" page 15 (Adapted)
Concepts: Fraction Number Sense, Equivalent Equivalent Fractions Fractions Equipment: Fraction Pieces Pieces (circ les) Goal/Obje Goal/Object: ct: Find as many w ays as possi ble of cr eating eating the whole (1) (1) using at least two diff erent erent ki nds of fraction pi ece sizes.
Players create a circle using at least two different colored fraction pieces. They then color in in a circle on their page showing the different color pieces used and record the size of fraction pieces used (ie keep track of what sizes are used on the sheet). EACH "Rainbow" must be different for other "Rainbows" on the answer page.
Fraction s Concepts: Comparing and Ordering Fraction Equipment: 1 double regular die & gameboard per player
Goal/Object: To place all all 5 fractio ns in o rder in 7 or less rolls.
Each player has a gameboard showing 5 places (left to right) to place fractions and 2 places for rejected fractions. Player one rolls a double die and makes a proper fraction from the roll. Player one records the fraction on their their gameboard. Player two rolls their their double die, makes a proper fraction and records it on their gameboard. Player one rolls again and makes another proper fraction and records it on their gameboard. Player two rolls again again and records their second fraction as well. Players continue to roll and record fractions IN ORDER FROM LEAST to GREATEST on their gameboards until one player wins in even turns or both players bust. Player One 1/6 1/4 1/2 ___ 3/3
rolls 3/4 "OK"
Previous Rejects = 1/5
Player Two 1/5 2/5 ___ 3/6 5/6
rolls 1/3 "Reject"
Previous Rejects = 4/4
Player One wins the game, Player two can't play 1/3 between 2/5 and 3/6 (it's sm aller than 2/5)
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B A SIC FRA FRA CTION CTION HORSE HORSE RACE B ASIC FRACTIONS WORK WORK AND SCORE SHEET SHEET
RECORD AND CIRCLE WHICH G AME
MY ROLLED
NUMBER
FRACTION
MY REDUCED
MY
MY
PLAYER HAS THE
FRACTION
P ARTNER' S
P ARTNER' S
LEAST FRACTION
(if necessary)
FRACTION
REDUCED FRACTION
ME
MY P ARTNER
(if necessary)
1
2
3
4
5
6
7
8
9
10
POINT TOTAL TOTAL
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ORDER IN THE COURT
Reject Rolls
Reject Rolls
Reject Rolls
Reject Rolls
Reject Rolls
Reject Rolls
Use Double Sided Dice, 6-sided Dice, or 1-12 Dice Goal: To get as many fractions in a row as possible Roll one die at a time. (Variation: (Variatio n: You may roll all the dice at once and race your partner to line them up) Write the fraction into the chain or put into the reject boxes. Points are awarded at the end of 7 rolls. 1 point for each fraction in the chain. Fraction Bars to check accuracy. accuracy. Use Fraction Circles or Fraction Copyright Box Cars and One Eyed Jacks Inc.
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s 0 0 d r 1 i h 0 T 0 . e 1 e r 3 h / T 3
s % h 0 t r 0 u 1 o F 0 0 . r 1 u o 4 F / 4
s % e 0 v 0 1 l a 0 H 0 . o 1 w 2 T / 2
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s % h 0 8 t f i F 0 . r 8 u 0 o 5 F / 4
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s % h 0 t r 5 u 0 o . F 5 o 0 w 4 T / 2
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s % 7 h 6 t x 6 i S 6 r 6 . u 0 o 6 F / 4
s % h 0 t x 5 i S 0 . e 5 e 0 r h 6 T / 3
s % 0 h 4 t f i 0 F 4 . o 0 w 5 T / 2
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s % h 6 t 8 n e 7 v 5 e 8 . S 0 x i 7 S / 6
s h % 1 t n 7 e 4 v 1 e . S 7 e 0 v 7 i F / 5
s h % 7 t n 5 e 1 v 7 e S 5 . r 0 u 7 o / F 4
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s h % 9 t n 2 e 6 v 8 e . S 2 o 0 w 7 T / 2
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s % h 0 0 t n 1 i N 0 . e 0 n 1 i 9 N / 9 s % h 9 8 t n 8 i N 8 t 8 . h 0 g i 9 E / 8 s % h 8 t n 7 i N 7 7 n 7 . e 0 v e 9 S / 7 % s 7 6 h t n 6 i 6 N 6 . x i 0 S 9 / 6 % s 6 h t 5 n 5 i N 5 5 . e 0 v i 9 F / 5 s % 4 h t 4 n i 4 N 4 r 4 . u 0 o 9 F / 4 s % h 3 t 3 n i N 3 3 e 3 . e r 0 h 9 T / 3 % s 2 h 2 t n 2 i N 2 2 . o 0 w T / 9 2 % h 1 1 t n i 1 N 1 . e 1 n 0 O 9 / 1
% 0 s 0 h 1 t n 0 e . T 0 1 n e 0 T / 1 0 1 s % h 0 9 t n 0 e 9 T . e 0 n 0 i 1 N / 9 s % h 0 t 8 n e 0 T 8 . t 0 h g 0 i 1 E / 8 s % h 0 t n 7 e T 0 7 . n 0 e v 0 e 1 S / 7 % s 0 h 6 t n 0 e 6 . T 0 x i 0 S / 1 6 s % 0 h 5 t n 0 e . T 5 e 0 v i 0 1 F / 5 s % h 0 4 t n 0 e 4 T . r 0 u o 0 1 F / 4 s % h 0 t 3 n e 0 T 3 . e 0 e r 0 h 1 T / 3 % s 0 h 2 t n 0 e . T 2 o 0 w 0 1 T / 2 % h 0 t 1 n e 0 T 1 . e 0 n 0 O 1 / 1
s h % t 0 n 0 e 1 v e 0 l . E 0 1 n e 1 v / 1 e 1 l E 1 s % h 1 9 t n 9 e 0 v 9 e . l E 0 n 1 e 1 T / 0 1 s h % 2 t n 8 e v 8 e 1 8 l . E 0 e 1 n 1 i N / 9 s h % 3 t n 7 e v 7 e 2 l 7 E . t 0 h 1 g / 1 i E 8 s h % t 4 n 6 e v 6 e 3 l . E 6 n 0 e 1 v / e 1 S 7 s % h 5 t 5 n e 5 v 4 e 5 l . E 0 x 1 i 1 S / 6
s % h 5 t n 4 e v 4 e 5 4 l . E 0 e 1 v i 1 F / 5 s h % 6 t n 3 e 4 v 6 e 3 l . E 0 r u 1 o 1 F / 4 s h % t 7 n 2 e v 3 e 7 l . E 2 e 0 e 1 r 1 h / T 3 s % h 8 t n 1 e v 2 e 8 1 l . E 0 o 1 w 1 T / 2
h % t n 9 e v 1 e 9 0 l . E 0 e 1 n 1 O / 1
s h % 0 t f l 0 e 1 w 0 T 0 . e 1 v 2 l e 1 w / T 2 1 s h % 2 t f l 9 e 2 w . T 9 n 0 e 2 v 1 e / l E 1 1 % s 3 h 8 t f l 3 e 8 w . T 0 n 2 e 1 T / 0 1 s % h 5 t f l 7 e 5 w 7 . T 0 e 2 n i 1 N / 9 s % h 7 t 6 f l e 7 w 6 T 6 . t 0 h 2 g i 1 E / 8 s h % 8 t f l 5 e 3 w 8 T 5 . n 0 e v 2 e 1 S / 7 s % 0 h 5 t f l 0 e 5 w . T 0 x 2 i 1 S / 6 s % h 2 4 t f l 7 e 1 w . T 4 e 0 v 2 i 1 F / 5 s % h 3 t f l 3 e 3 w 3 . T 0 r u 2 o 1 F / 4 s h % 5 t f l 2 e 5 w . T 2 e 0 e 2 r 1 h / T 3 s % h 7 1 t f l 6 e 6 w . T 1 0 o w 2 1 T / 2 h % 8 t f l 3 e 8 w . T 0 e 0 n 2 1 O / 1
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Fractions ractions “ Cents” copyright 2014 Box Cars And One-Eyed Jacks
Grades: Concept: Players: Equipment: Object / Goal:
Grade 6 and up Converting fractions to equivalent percent or decimal, mental math, division, estimation 1 vs 1 Cards 1 to 12, Number Line 0-100, fraction/decimal/percent chart Earn points by having the most accurate answer when converting a fraction to its decimal or percent equivalent.
Set Up and Play: Each player begins with a deck of about half the cards in the game. Play begins with each player turning turn over the top card of of their deck at the same time. Players count out loud “1, 2, 2, 3 point”. While they are counting, they are mentally arranging the cards into a “Proper Fraction (numerator/top smaller than or equal to denominator/bottom), and calculating the percent equivalent. When they say “point” each player places one finger on the number line at the percent equivalent they think is correct (it is possible for both players to be on the same point) and says what their answer is. They check their accuracy by referring to the Fraction/Decimal/Percent chart or by using a calculator to divide the numerator by the denominator. If a player is exactly correct, they collect the cards from that round and place them into their point pile. In the case of a tie both players place the card they turned over into their point pile. If neither player is exactly correct, the player closest to the correct answer wins the round and places the cards into their point pile. Example: Player One turned over over a 5 and Player Two Two turned over an 8. When they said “point” Player One pointed to 63 and said “five eighths of 100 is 63”. Player Two Two pointed to 65 and said “five eighths of 100 is 65. 65. 5 divided by 8 is 62.5. Player One was the closest and wins, placing both cards into their point pile. Variation: 1. The number number line is conside considered red “1”. Players say the decimal decimal equivale equivalent nt when they they voice their answer. answer. In the example, Player One would have pointed to 63 and said “Five eighths of one is 0.63”. Player Two Two would have pointed to 65 and voiced “Five eighths of one is 0.65”. Exact answer is 0.625, Player One wins. 2. The number number line is consider considered ed 100%. Players Players say the percent percent equival equivalent ent when they they Voice their answer. answer. In the example, Player One would have pointed to 63 and said “Five eighths of 100% is 63%.” Player Two would have pointed to 65 and voiced “Five eighths of 100% is 65%.””. Exact answer is 62.5%, Player One wins. Round
Fraction
Equivalent
Example
5 8
62.5
Player 1
Player 2
63
65
Observations / Comments Both of us were close!
1 2 3 4 5 6 7 8 9
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Balanced Equations © Box Cars And One-Eyed Jacks Inc.
Concepts: Problem Concepts: Problem Solving, Linear Equations Equipment: Two Equipment: Two 3-in-a-Cube Dice / Game Goal/Object: Be Goal/Object: Be the first player to create a balanced equation. A player shakes both 3-in-a-Cube dice and places them on the table so all players can see them. Each player (or team of two - if that is the way the teacher has set them up) races to create a balanced equation with the numbers from one die on one side of the equation and the numbers from the other die on the other side of the equation. A player says "Balanced" when they have a balanced equation. Other players verify the the "Balanced" player's equation. If correct, that player earns a point. In the case of a tie, if both players have a balanced equation (they could be different but still correct) they both earn a point The player with the most points at the end of the time wins. All players record all the winning answers for each round.
Example: 3, 2, and 6 as well as 1, 2, and 5 2 3 - 6 = 5 - (1 x 2) OR 6 - 2 + 3 = 1 x 5 + 2
Betweeners Betweeners (Tradit (Tradition ion al) Concepts: Number Concepts: Number Sense, Ordering Numbers (whole and decimal) Equipment: One 3inCube die / player Goal/Object: record Goal/Object: record a number that is between the highest and lowest for the round Each player shakes their own 3inCube die and secretly look at it, mentally determining the possible answers they could use. Each player then secretly records one of their possible answers. Once all the players have recorded their answer, they reveal it to the other players. All players copy copy all other other players' players' answers onto onto their own score sheet. The answers are compared, lowest doesn't win, highest doesn't win, between number (or numbers if 4 player game) wins. Variations: (1) Variations: (1) Three addend addition. The between sum (add all 3 numbers) wins. (2) Use 12-sided die on a ruler, 30-sided die on a yardstick, 10s 1's on a meter stick (1-100) Variation of Betweeners From Math Attack © Box Cars And One-Eyed Jacks (unpublished)
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TIC TAC OH NO! Box Cars And One-Eyed Jacks 2014
©
6
(1,6)
(2,6)
(3,6)
(4,6)
(5,6)
(6,6)
5
(1,5)
(2,5)
(3,5)
(4,5)
(5,5)
(6,5)
4
(1,4)
(2,4)
(3,4)
(4,4)
(5,4)
(6,4)
3
(1,3)
(2,3)
(3,3)
(4,3)
(5,3)
(6,3)
2
(1,2)
(2,2)
(3,2)
(4,2)
(5,2)
(6,2)
1
(1,1)
(2,1)
(3,1)
(4,1)
(5,1)
(6,1)
5
6
Y
Use The Clear Lid
X
1
2
Dice are placed on the X and Y to the right to verify which will represent the X coordinate and Y coordinate
3
4
(X,Y)
Roll 2 dice Place "Y" coordinate into clear lid. "X" goes back into pile. Game ends when one player has less than 2 dice remaining. st If you land on a space already occupied, pull out the 1 die and and discard into black black tray. Put your "Y" in clear lid in its place. Scoring dice in play = 1 point each. Dice in Tic Tac Toes also count 2 points each.
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TIC TAC OH NO! Player One Type of Tic Tac Toe
Game
________
Game
________
Score
1 2 3 4 5 6 7 8 Total Dice (1 point/die)
Total Score
Player Two Type of Tic Tac Toe
Score
1 2 3 4 5 6 7 8 Total Dice (1 point/die)
Total Score
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COMMIT COMMIT AND A ND CAPTU CA PTURE RE 1.
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Quick Version: Teams Version: Teams of two competing against other teams of two. Each team has their own gameboard, there can be a variety of dice to use or just use standard 6-sided dice. Teams take turns choosing a die and rolling it. They must fill in an open space of the math sentence with the number they rolled. Teams fill in one math sentence at a time. When the sentence sentence is complete complete for both teams, the team with the greatest value as an answer wins the round. Quicker Version: Played Version: Played the same as above but the roll that that one team makes must be used by both teams. There is a possibility for a lot of ties with this method. Most Math Version: Played the same as Quicker Version except each team may place the roll on any open space on any math sentence. Scoring is not performed until the entire sheet has been filled in. Thought Provokers: 1. Since it is possible for negative answers answers who wins wins when the outcome is -34 for one team and +19 for the other team (-34 (-34 has a greater absolute value compared to +19)? 2. What What about about playin playing g for the the smalles smallestt possib possible le value value? ? 3. What about playing playing for for the the middle middle value value in a game game of of 3 teams?
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What's My Number Concepts: Place Concepts: Place Value to 100,000.000s Equipment: One Equipment: One 0-9 die and gameboard Goal/Object: build Goal/Object: build largest number Players take turns rolling a 0-9 die. All players use the number rolled and record it on their gameboard (or blank paper with 9 dashes). Players continue to take turns rolling the die with all players recording each roll in such a way that they build the largest number they can (their numbers will likely be different as each player may record their rolled number in a place different than the other players). Once all of of the spaces have been filled in (after 9 rounds), the players compare their numbers. The player with the largest number wins the round. Variations: (1) Variations: (1) Roll the die 9 times quickly to create a target number. Players then play the normal way but try to create a number closest to the target number. (2) Three players but trying to create the “between” value ie between other two players
Salute Box Cars "All Hands On Deck" Mystery Number (adapted)
Concepts: Missing Concepts: Missing Addend, Factor Equipment: Cards Equipment: Cards 0-12 (J=11 Q=12 K=0) Goal/Object: Figure Goal/Object: Figure Out value of the card on your head Usually 3 players with one player taking the role of "General". The General says "salute". The other two players take the card from the top of their deck and WITHOUT LOOKING AT IT place it on their forehead so everyone else can see what the card on their forehead is. The General Adds the two cards together together and and says "The sum of your two cards is...." The two players then use the sum and the card they can see on their opponent's forehead to try and figure out their own card. Variations: (1) Multiplication (take out 0s) (2) 4 Players (one General, 3 soldiers) (3) Red = neg integers / Black = pos integers
From: All Hands On Deck - Family Edition
Balanced Equations © Box Cars And One-Eyed Jacks Inc.
Concepts: Problem Concepts: Problem Solving, Linear Equations Equipment: Two Equipment: Two 3-in-a-Cube Dice / Game Goal/Object: Be Goal/Object: Be the first player to create a balanced equation. A player shakes both 3-in-a-Cube dice and places them on the table so all players can see them. Each player (or team of two - if that is the way the teacher has set them up) races to create a balanced equation with the numbers from one die on one side of the equation and the numbers from the other die on the other side of of the equation. A player says "Balanced" when they have a balanced equation. Other players verify the "Balanced" player's equation. If correct, that player earns a point. In the case of a tie, if both players have a balanced equation (they could be different but still correct) they both earn a point. The player with the most points at the end of the time wins. All players record all the winning answers for each round.
Example: 3, 2, and 6 as well as 1, 2, and 5 2 3 - 6 = 5 - (1 x 2) OR 6 - 2 + 3 = 1 x 5 + 2
Throw an Equation Equation Concepts: Solving Concepts: Solving Linear Equations Equipment: Solve Equipment: Solve for X dice, Exponent Dice and various other dice. Goal/Object: Create Goal/Object: Create an equation that you can solve that is hard for your opponent to solve. Two teams of 2 players each. Each team selects some dice (number, operation, and either Solve for X or Exponent dice). The team then rolls the dice and using the ALL the items rolled, create a linear equation and solve it. Meanwhile, the other team chooses their own dice, creates their own sentence with their roll and solves their own equation. Once each team has solved their own equation, they make a new copy of the equation (unsolved) on a separate piece of paper. paper. On "go", teams hand their equation to the other team. Teams race to solve the other team's equation first.
Variation of game in Radical Math © Box Cars And One-Eyed Jacks (unpublished)
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Rolling oll ing 6's copyright 2013 Box Cars And One-Eyed Jacks
Grades: Concept: Players: Equipment: Object / Goal:
Kindergarten or greater (best fit is grade 6 and higher) Comparing Theoretical and Experimental Probability 2 to 3 players working together Dice Tray with 36 dice, Chart (or blank paper) and pencil To predict number of 6's rolled each round.
Set Up and Play: Players start out with 36 dice and predict how many of the dice will end up as 6 once they have been "rolled" by mixing them. They write their prediction for that round on their chart. Players then mix the dice (super mush). The dice that show 6 are counted. The score is recorded next to the prediction and then the dice are placed into the tray. tray. The players now predict how many of the REMAINING dice will show 6 in the next round of rolling. The prediction for the next round is recorded, then the dice are mixed (super mush). The dice that show 6 are counted. The score is recorded next to the prediction and then the dice are placed into the tray. tray. The sequence of predicting 6's for the remaining dice, writing the prediction, mixing the dice, counting 6's, recording the score and placing the dice into the tray continues until all the dice are in the tray. Variation: 1. The players players build a graph each each round by lining the dice dice up (similar (similar to a bar graph). The graph builds builds as each round round is completed. Thought Provokers: 1. How did you you figure out out your prediction prediction before each each roll? 2. Do you think it matters matters if you rolled rolled each die individua individually lly for a round as opposed opposed to "mixing" "mixing" using using a super mush? mush? Why do you think that? Play ers : ____________________ ____________________ ____________________ Round Prediction
Actual
Difference
Observations / Comments
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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Salute
Sweet 16
Box Cars "All Hands On Deck" Mystery Number (adapted)
Concepts: Missing Concepts: Missing Addend, Factor Equipment: Cards Equipment: Cards 0-12 (J=11 Q=12 K=0) Goal/Object: Figure Goal/Object: Figure Out value of the card on your head Usually 3 players with one player taking the role of "General". The General says "salute". The other two players take the card from the top of their deck and WITHOUT LOOKING AT IT place it on their forehead so everyone else can see what the card on their forehead is. The General Adds the two cards together together and and says "The "The sum of your two cards is...." The two players then use the sum and the card they can see on their opponent's forehead to try and figure out their own card. Variations: (1) Multiplication (take out 0s) (2) 4 Players (one General, 3 soldiers) (3) Red = neg integers / Black = pos integers
Concepts: Mixed Operations, Order of Operations Equipment: 1x1-30 die, Cards 0-12 (J=11 Q=12 K=0) Goal/Object: Remove Goal/Object: Remove all your cards 1st Each player makes a grid of 4 cards by 4 cards. One player rolls a 30-sided die to identify a target answer that both players must try to get. Each player takes turns creating math sentences that equal the target answer, using cards in their own grids. Players can add, subtract, multiply, divide, and use square roots or exponents. Players may use a few as 2 cards and as many as 5 cards per math sentence. sentence. First player player to completely remove all their cards (in equal turns). If neither player can remove all their cards, then the player with the fewest cards left wins.
From: Math Attack
Flippin' Out Box Cars series "Deca Dice" page 86
Concepts: Rounding, Concepts: Rounding, Probability Equipment: Cards 0-9, 00-90 die, 2 Bingo Chips and gameboard Goal/Object: To be the closest to the target number and to have the most cards in their point pile. Each player turns over 2 cards and arranges them to make their number. They round their numbers to the nearest 10's place and place their own bingo chip on the 10's place they rounded to. After the bingo chips are placed, one player rolls the decade (00-90) die to get their target and places the die on the 10's place target. Whomever has their bingo chip closest to the target die, wins all the cards and places them into their point pile. If there is a tie, both players keep their own cards. Example: Player one's cards are 4 and 7 makes 47 (could have made 74). Player two's cards are 9 and 3 makes 39 (could have made 93). Player one rounds to 50 player two rounds to 40. The decade die was rolled and showed 30. 30. Player two was closest. Player two wins all 4 cards. Thought Provoker: What would have happened if one or both players chose to go with their other possibility and the decade die still rolled 30?
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