Box Cars and One-Eyed Jacks MATH GAMES FOR TEACHING

Box Cars and One-Eyed Jacks
MATH GAMES FOR TEACHING
PLACE VALUE, OPERATIONAL
FACT FLUENCY AND FRACTIONS
John Felling
Our Lady of the Assumption School
Atlanta, GA
October 2014
john@boxcarsandoneeyedjacks.com
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
Use three large buckets (1 gallon or 4 liter each}. Gather a lot of decks of 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 to the math of the games. Full decks are not
necessary when organizing the cards, and not worrying 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 - 6's, 7's, 8's, 9's, and 0's (Kings for 0 if 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 Place 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 regular 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 told 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 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 their 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 set
per student is even better.
First and Foremost Use Dominoes of Different 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 the 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.
2
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 them 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 same together in one container (for example 0-9 dice in one containe r, + and - dice in
another container, 1-12 dice Iin 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 each 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 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 the 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 them room to "spread out".
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 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 them into
ONE HALF of the lid. They spread the dice into the half, "patting down" the dice so the dice are flat and in place. Then
all of the dice of the OTHER COLOR are poured into the other half of the lid. Again, the students "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".
3
PRIMARY SUPER MUSH
_________________
_________________
4
HORSE RACE - PRIMARY ADDITION
LEVEL:
K-2
SKILLS:
adding to 12, commutative property of addition, fact families
PLAYERS:
2 (1 vs 1)
EQUIPMENT:
GOAL:
tray of dice (each player needs 18 of their own color), gameboard
to have the greatest number of dice on your side of the “racetrack” at the end of the game
GETTING STARTED:
Each player takes 18 dice of one color and picks a side of the dice tray 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 of the racetrack. Both players verbalize their sums.
EXAMPLE:
+ +
= 8
PLAYER ONE
MATH TALK
+
+
=
6
PLAYER TWO
Player One says “8 is a greater sum than 6”
The player with the greatest sum places 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 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 Two
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
6
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:
GOAL:
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)
to be the first player to remove all six of their dice from their side of the tray.
GETTING STARTED:
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 be a number from one 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. 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.
7
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.
8
Multiplication Board
1
2
3
4
5
6
7
8
9
10
11
12
1
1
2
3
4
5
6
7
8
9
10
11
12
2
2
4
6
8
10
12
14
16
18
20
22
24
3
3
6
9
12
15
18
21
24
27
30
33
36
4
4
8
12
16
20
24
28
32
36
40
44
48
5
5
10
15
20
25
30
35
40
45
50
55
60
6
6
12
18
24
30
36
42
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
88
96
9
9
18
27
36
45
54
63
72
81
90
99
108
10
10
20
30
40
50
60
70
80
90
100
110
120
11
11
22
33
44
55
66
77
88
99
110
121
132
12
12
24
36
48
60
72
84
96
108
120
132
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
10
Place Value 
Teaching Tips 
 Games support the instruction of place value concepts with baseten manipulatives.
 Always sit players side by side so they are reading numbers
properly; use tens bracelets, thousands bracelets, playing mats / fun
foam for building place values.
 For cards, sort out all tens, Jacks, Queens and Kings and use
cards from 0-9 only.
 Place Value dice come in a variety of values which you can
use to build differentiation and a variety of concepts into your
instruction.
 Use number lines: 0 - 9, 0-100, or tape ten together for a 0-1000
line.
 Use chunking place value strategies with regular dice or in 3in-a-cube dice.
 Foam mats/ Dry Erase Boards
11
Betweeners
© Box Cars And One-Eyed Jacks.
4 Player Version – Highest doesn't win. Lowest doesn't win. The two between numbers win.
Betweeners
Variation of Betweeners From Math Attack © Box Cars And One-Eyed Jacks
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
Traditional- Each player shakes their own 3inCube die and secretly looks 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 all other players'
answers 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) Players are allowed to create numbers with decimals meaning answers can range from 0.111 to 666.
(2) Players create multi-operation math sentences trying to have the between answer example 3+2x1=5
(3) Players create mixed fractions example 3 2 1 makes 3½ or 1⅔ or 2⅓ 2 1 1 can only make 1½
(4) For simpler version of the game, 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)
12
13
Rolls
17 X 23
X
X
X
X
X
X
X
X
X
X
X
X
Round
Example
1
2
3
4
5
6
7
8
9
10
11
12
380
391
Actual
Total Differences =
Estimate
10
Difference
Name: _______________________ Date: ________________
Multiplication Estimation – Recording Sheet
14
Rolled 30 and 12. 30÷12 = 2 R6
see pictures to right to see how
to do this on a number line.
100 Board Wipe 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 decides whether 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. Each math sentence must use each number rolled. For example, if 4, 4, 2 and
6 are rolled then each 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. 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
42 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 Wipe Out – Recording Sheet
Team Members _______________
_______________
Roll One: __________
Roll Two: __________
Roll Five: __________
Roll Six: __________
_______________ Date: __________
Roll Three: __________
Roll Seven: __________
Roll Four: __________
Roll Eight: _________
= 1
= 2
= 3
= 4
= 5
= 6
= 7
= 8
= 9
= 10
= 11
= 12
= 13
= 14
= 15
= 16
= 17
= 18
= 19
= 20
= 21
= 22
= 23
= 24
= 25
= 26
= 27
= 28
= 29
= 30
= 31
= 32
= 33
= 34
= 35
= 36
= 37
= 38
= 39
= 40
= 41
= 42
= 43
= 44
= 45
= 46
= 47
= 48
= 49
= 50
= 51
= 52
= 53
= 54
= 55
= 56
= 57
= 58
= 59
= 60
= 61
= 62
= 63
= 64
= 65
= 66
= 67
= 68
= 69
= 70
= 71
= 72
= 73
= 74
= 75
= 76
= 77
= 78
= 79
= 80
= 81
= 82
= 83
= 84
= 85
= 86
= 87
= 88
= 89
= 90
= 91
= 92
= 93
= 94
= 95
= 96
= 97
= 98
= 99
= 100
16
ROUND ONE
PLAYER
ONE
ROUND TWO
PLAYER
ONE
ROUND THREE
ROLL ON PLACE VALUE
PLAYER
ONE
PLAYER
TWO
PLAYER
TWO
PLAYER
TWO
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 by the player with the highest value in that place. A third "upside down" bonus point is
awarded to the player with the biggest number when the tray is turned upside down and the numbers are
compared.
17
ROCK & ROLL
ROLL REGULAR DICE TO BUILD PLACE VALUE AS FOLLOWS
2 DICE:
TENS /
ONES
HUNDREDS /
TENS /
ONES
THOUSANDS /
HUNDREDS /
TENS /
ONES
TEN THOUSANDS /
THOUSANDS /
HUNDREDS /
TENS /
ONES
TEN THOUSANDS /
THOUSANDS /
HUNDREDS /
TENS /
ONES
3 DICE:
4 DICE:
5 DICE:
6 DICE:
HUNDRED THOUSANDS /
Roll dice, arrange for greatest possible number
First to call ROCK & ROLL scores 5 POINTS
All other players must freeze their dice when ROCK & ROLL is called.
If a player's number is greater than the player who called ROCK & ROLL, they also get 5 POINTS
ROLL
NUMBER
EXPANDED NUMBER
1
2
3
4
5
6
7
8
9
10
18
Batters Up!
Skills:
Place Value to 100 000s, Addition with Expanded Notation
Equipment: Cards 0-9. Place Value System die, paper/pencil
Goal:
Greatest total sum after ten rounds wins
Getting 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 the 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.
19
20
•
•
•
•
Ten
Millions
Millions
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
Ones
My Number
Use 0-9 Dice
Roll and then record on sheet to build number. Compare numbers with opponent at end of round. Largest number wins.
For 3 players, the between number wins (ie not largest or smallest)
Randomly choose specific place value, compare with opponent. Largest number wins.
Hundred
Millions
What's My Number
Fraction Horse 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 dice in the racetrack at the end
Each player has their own 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 equivalent
fraction, both players put their dice into the
black tray. 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.
Concepts: Comparing & Ordering Fractions
Equipment: Stratedice Tray / Player
Goal/Object: to be the between fraction, have
the most dice in the 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 NOT
WIN. Player with the LARGETS fraction DOES
NOT WIN. Player with the IN-BETWEEN
FRACTION WINS THE ROUND. Winner 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 lids
(they all lose because no one is "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 Fractions
Order In The Court
Box Cars "Piece It Together With Fractions" page 49
Box Cars "Double Dare You" page 15 (Adapted)
Concepts: Fraction Number Sense,
Equivalent Fractions
Equipment: Fraction Pieces (circles)
Goal/Object: Find as many ways as possible
of creating the whole (1) using at least two
different kinds of fraction piece sizes.
Players create a circle
using at least two different colored fraction
pieces. They then color 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.
Concepts: Comparing and Ordering Fractions
Equipment: 1 double regular die & gameboard
per player
Goal/Object: To place all 5 fractions in order 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 gameboard. Player two rolls 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 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 smaller than 2/5)
21
BASIC FRACTION HORSE RACE
BASIC FRACTIONS WORK AND SCORE SHEET
RECORD AND CIRCLE WHICH
GAME
NUMBER
MY ROLLED
FRACTION
MY REDUCED
FRACTION
(if necessary)
MY
MY
PLAYER HAS THE
PARTNER'S
FRACTION
PARTNER'S
REDUCED
FRACTION
LEAST FRACTION
ME
MY PARTNER
(if necessary)
1
2
3
4
5
6
7
8
9
10
POINT TOTAL
22
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: 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.
 Use Fraction Circles or Fraction Bars to check accuracy.
Copyright Box Cars and One Eyed Jacks Inc.
23
24
One Twelfth
1/12 0.083 8%
One Eleventh
1/11 0.091 9%
One Tenth
1/10 0.10 10%
Two Elevenths
2/11 0.182 18%
Seven Twelfths
7/12 0.583 58%
Ten Twelfths
10/12 0.83 83%
Eleven Twelfths
11/12 0.92 92%
Twelve Twelfths
12/12 1.00 100%
Eleven Elevenths
11/11 1.00 100%
Ten Tenths
10/10 1.00 100%
Nine Ninths
9/9 1.00 100%
Eight Eighths
8/8 1.00 100%
Ten Elevenths
10/11 0.909 91%
Nine Tenths
9/10 0.90 90%
Eight Ninths
8/9 0.888 89%
Nine Elevenths
9/11 0.818 82%
Nine Twelfths
9/12 0.75 75%
Eight Elevenths
8/11 0.727 73%
Eight Twelfths
8/12 0.667 67%
Seven Elevenths
7/11 0.636 64%
Eight Tenths
8/10 0.80 80%
Seven Ninths
7/9 0.777 78%
Seven Tenths
7/10 0.70 70%
Six Ninths
6/9 0.666 67%
Six Tenths
6/10 0.60 60%
Six Elevenths
6/11 0.545 55%
Six Twelfths
6/12 0.50 50%
Five Elevenths
5/11 0.454 45%
Five Twelfths
5/12 0.417 42%
Four Elevenths
4/11 0.364 36%
Five Tenths
5/10 0.50 50%
Five Ninths
5/9 0.555 56%
Seven Eighths
7/8 0.875 87.5%
Seven Sevenths
7/7 1.00 100%
Six Sixths
6/6 1.00 100%
Five Fifths
5/5 1.00 100%
Four Fourths
4/4 1.00 100%
Three Thirds
3/3 1.00 100
Six Sevenths
6/7 0.857 86%
Five Sixths
5/6 0.833 83%
Six Eighths
6/8 0.75 75%
Five Sevenths
5/7 0.714 71%
Four Sixths
4/6 0.666 67%
Two Halves
2/2 1.00 100%
Four Fifths
4/5 0.80 80%
Three Fourths
3/4 0.75 75%
Five Eighths
5/8 0.625 62.5%
Four Sevenths
4/7 0.571 57%
Three Fifths
3/5 0.60 60%
Two Thirds
2/3 0.666 67%
Four Eighths
4/8 0.50 50%
Four Ninths
4/9 0.444 44%
Four Tenths
4/10 0.40 40%
Four Twelfths
4/12 0.33 33%
Three Elevenths
3/11 0.273 27%
Three Tenths
3/10 0.30 30%
Three Twelfths
3/12 0.25 25%
Two Tenths
2/10 0.20 20%
Two Ninths
2/9 0.222 22%
Three Eighths
3/8 0.375 37.5%
Three Sevenths
3/7 0.429 43%
Three Ninths
3/9 0.333 33%
Two Sevenths
2/7 0.286 29%
Three Sixths
3/6 0.50 50%
Two Fourths
2/4 0.50 50%
Two Fifths
2/5 0.40 40%
Two Sixths
2/6 0.333 33%
Two Eighths
2/8 0.25 25%
Two Twelfths
2/12 0.166 17%
One Ninth
1/9 0.111 11%
One Eighth
1/8 0.125 12.5%
One Seventh
1/7 0.143 14%
One Sixth
1/6 0.166 17%
One Fifth
1/5 0.20 20%
One Fourth
1/4 0.25 25%
One Third
1/3 0.333 33%
One Half
1/2 0.50 50%
One Whole
1/1 1.00 100%
Copyright Box Cars And One-Eyed Jacks Inc.
Fractions Decimals Percents
Fractions “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 their deck at the same time. Players count out loud “1, 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 a 5 and Player Two turned over an 8. When they
said “point” Player One pointed to 63 and said “five eighths of 100 is 63”. Player Two
pointed to 65 and said “five eighths of 100 is 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 line is considered “1”. Players say the decimal equivalent when they
voice their answer. In the example, Player One would have pointed to 63 and said
“Five eighths of one is 0.63”. Player 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 line is considered 100%. Players say the percent equivalent when they
Voice their 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
25
Balanced Equations
© Box Cars And One-Eyed Jacks Inc.
Concepts: Problem Solving, Linear Equations
Equipment: Two 3-in-a-Cube Dice / Game
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
"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 (Traditional)
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
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 all other players' answers 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) 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)
26
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 discard into 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.
27
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
28
COMMIT AND CAPTURE
1.
X
2.
+
(
-
)
-
÷
X
=
=
2
3.
-
4.
+
5.
X
X
-
=
÷
X
=
(
+
)
(
-
3
=
-
)] =
6.
[
7.
÷
+
X
=
8.
÷
X
-
=
X
Quick 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 is complete for
both teams, the team with the greatest value as an answer wins the round.
Quicker Version: Played the same as above but the roll 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 who wins when the outcome is -34 for one team and +19 for the other team (-34 has
a greater absolute value compared to +19)?
2. What about playing for the smallest possible value?
3. What about playing for the middle value in a game of 3 teams?
29
What's My Number
Salute
Box Cars "All Hands On Deck" Mystery Number (adapted)
Concepts: Place Value to 100,000.000s
Equipment: One 0-9 die and gameboard
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 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) 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
Concepts: Missing Addend, Factor
Equipment: Cards 0-12 (J=11 Q=12 K=0)
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 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 Solving, Linear Equations
Equipment: Two 3-in-a-Cube Dice / Game
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
"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
Concepts: Solving Linear Equations
Equipment: Solve for X dice, Exponent Dice
and various other dice.
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. 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)
30
Rolling 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.
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. 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 build a graph each round by lining the dice up (similar to a bar graph). The graph builds as each round is
completed.
Thought Provokers:
1. How did you figure out your prediction before each roll?
2. Do you think it matters if you rolled each die individually for a round as opposed to "mixing" using a super mush? Why
do you think that?
Players: ____________________ ____________________ ____________________
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
31
Salute
Sweet 16
Box Cars "All Hands On Deck" Mystery Number (adapted)
Concepts: Missing Addend, Factor
Equipment: Cards 0-12 (J=11 Q=12 K=0)
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 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
Concepts: Mixed Operations,
Order of Operations
Equipment:
1x1-30 die, Cards 0-12
(J=11 Q=12 K=0)
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. First 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, 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. 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?
32