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GAMES FOR FLUENCY FOR 4TH & 5TH GRADE
JOHN FELLING
SINGAPORE MATH IN-DEPTH SUMMIT 2017
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STRATEDICE LEVEL: 3 – 6
SKILLS: problem solving, probability
PLAYERS: 2 (1 vs 1)
EQUIPMENT: tray of dice (each player needs 18 of their own color)
GOAL: for each player to build rows or columns of three or more dice of their own color in anydirection (horizontal, vertical or diagonal) and at the same time block or prevent their opponent from doing the same
GETTING STARTED: To determine which player starts, each player rolls 2 dice. The greatest sum begins.
Player One begins by rolling one of their dice and placing that die in any position on the tray. Player Two now takes their turn, rolling one of their dice and placing it in any position in the tray. Play continues until all spaces are filled.
EXAMPLE:
Players add the face value of all rows or columns of three or more dice of their own color and total these sums. The player with the highest score wins.
Player One rolls a 5 and places it on the board.
Player Two rolls a 3 and places it on the board.
Player One rolls a 2 and places it on the board.
Player Two rolls a 6 and places it on the board.
Player One rolls a 4 and places it on the board.
At this point, Player One has three in a row. This will count as 11 points (5+2+4) at the end of the game.
©Box Cars and One-Eyed Jacks 2
STRATEDICE VARIATIONS:
1. Play a golf-like variation where the goal of the game is to avoid getting three in a row of yourown color. Any three or more in a row of your own color score against you. After adding upthe sums, the player with the least total sum wins. Ask students to write about how theirstrategy changed.
2. Have players multiply the numbers when totalling their score. The products from each scoringrow and column are added together. The greatest sum wins.
EXAMPLE:4 x 5 x 2 = 40 6 x 2 x 3 = 36 2 x 4 x 3 = 24
40 + 36 + 24 = 100 points
MATH JOURNAL WORK AND EXTENSIONS: Have the students explore and discover the following:
1. One strategy might be for players to count sixes and fives more than once by building anintersecting row and column with that particular die.
EXAMPLE:
2. Can you improve your score by using high numbers to score, and low numbers to stop youropponent’s strategy
In this example, Player One has used the 5 die both vertically and horizontally and is now able to score twice with it.
4 + 1 + 5 = 10 4 + 2 + 5 = 11
Have students explore the associative property of multiplication which states: "the product stays the same when the grouping of factors is changed."
©Box Cars and One-Eyed Jacks 3
STRATEDICE RECORDING SHEET
PLAYER ONE PLAYER TWO
©Box Cars and One-Eyed Jacks 4
ORDER IN THE COURTLEVEL: Grade 3 - 5
CONCEPTS:ordering fractions, equivalent fractions, fractions less than one and greater than one, analytical thinking Variation: Primary - naming fractions to ¹/⁶, Middle Years - decimal equivalents, mixed numbers
PLAYERS: 1 vs 1
EQUIPMENT: 1 x regular double die per player, 1 recording sheet per player
GOAL: to order a series of 5 fractions from least to greatest
GETTING STARTED:Player One rolls the die and uses the two numbers to create a fraction less than one, then records it on an open space in the Least to Greatest gameboard. Students may use fraction pieces or the Fraction Decimal Percent Chart on page 101 to help them make decisions. Player Two takes their turn rolling the die, creating a fraction less than one and recording it on their gameboard. Players record their fractions as rolled. If they roll a 4 and a 6, they record ⁴/⁶. Teachers may choose to have students convert their fractions to equivalent fractions with smaller denominators (⁴/⁶ rolled, ⅔ recorded). If a player's roll creates a fraction that is equivalent to one already on their gameboard, they have to record it in the "rejects" section of their gameboard. Players continue taking turns. A player wins the round if, at the end of equal turns, they are the first to have recorded, in order from least to greatest, five non equivalent fractions. A player "strikes out" if they roll a third reject. The player who wins the most rounds wins the game.
math talk
math talk
"½ is greater than ²/⁶ and less than ³/⁵"
1. Use 12-sided double dice.2. Allow fractions greater than one to be used by using
the outside (top) number of a regular double die as the numerator and theinside (bottom) number as the denominator.
3. Use a 3-in-a-cube die to create mixed numbers such as 3 ½.
Roll five double regular dice at once and build proper fractions. Players line them up from least to greatest, stacking equivalent fractions on top of each other. Record the rolls on the gameboard, circling equivalent fractions.
"²/⁴ is equivalent to ³/⁶"
primary
rule twis
t
64 = ⁶/⁴
©Box Cars and One-Eyed Jacks 5
98
ORDER IN THE COURTPlayers record the decimal equivalent (to 2 places) on the gameboard just below the fraction. They can use this decimal variation for all versions of the game.
middleyears
math talk"2 and ²/⁵ is equivalent to 2 and 40 hundredths or 2.40"
2 and 2 ÷ 5 is 2 and 40 hundredths or 2.40
math
thinking
2 ²/5
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00
2.40
ROLL 3-in-a-cube
math talk
2 ÷ 3 gives a quotient of 0.666... which rounds to 0.67 or 67 hundredths
"⅔ is equivalent to about 67 hundredths or .666 repeating"
math
thinking2
3
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
⅔
ROLL
math talk
"½ is equivalent to 50 hundredths or 0.50"
1 ÷ 2 = 0.50math
thinking
12
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
½
ROLL
2 2 5
©Box Cars and One-Eyed Jacks 6
99
ORDER IN THE COURT RECORDING SHEET
LEAST GREATEST
REJECTSSTRIKE OUT!
ROUND ONE PLAYER ONE
LEAST GREATEST
REJECTSSTRIKE OUT!
ROUND TWO PLAYER ONE
LEAST GREATEST
REJECTSSTRIKE OUT!
ROUND THREE PLAYER ONE
LEAST GREATEST
REJECTSSTRIKE OUT!
ROUND FOUR PLAYER ONE
LEAST GREATEST
REJECTSSTRIKE OUT!
ROUND ONE PLAYER TWO
LEAST GREATEST
REJECTSSTRIKE OUT!
ROUND TWO PLAYER TWO
LEAST GREATEST
REJECTSSTRIKE OUT!
ROUND THREE PLAYER TWO
LEAST GREATEST
REJECTSSTRIKE OUT!
ROUND FOUR PLAYER TWO
©Box Cars and One-Eyed Jacks 7
SIMPLY FRACTIONSLEVEL: Grade 3 - 5
CONCEPTS: rename fractions to simplest forms
PLAYERS: 2, 1 vs 1 or 4, 2 vs 2
EQUIPMENT: 2 x double regular dice, recording sheet Variation: use x 12-sided double dice
GOAL: to have the greatest number of unique fractions in their simplest forms
GETTING STARTED:For each round, players each roll two double regular dice and use the rolls to create two fractions with values less than or equal to one. Players say and record their fractions as rolled, then re-record their fractions in their simplest form on the recording sheet. Players may want to refer to the Fraction Decimal Percent Chart on page 100. Players score a point for for each new fraction in their simplest form. In subsequent rounds, if a player rolls a fraction in its simplest form that is a duplicate of one created in a previous round, they score a strike (X). Play ends after six rounds. Players final scores are calculated by the total of their points, less strikes.
Example:Outside number Inside number
8
SIMPLY FRACTIONS1. Use 12-sided double dice instead of double regular dice. Rules and scoring remain the
same.
2. The outside number on the die (top) is always the numerator, and the inside number onthe die (bottom) is always the denominator. This twist allows opportunities for fractions withvalues greater than one. Use either double regular or 12-sided dice for this twist.
3. Players determine which number is to be the numerator, and which will be the denominator.This twist also allows opportunities for fractions with values greater than one.
4. Players calculate the decimal equivalents of their fractions, rounded to hundredthsplace if necessary. All other rules and scoring remain the same.
JOURNAL WORK AND EXTENSIONS:1. Explain why 12 is the maximum score possible in six rounds, and why the maximum score would
decrease if a seventh round was required.
2. What would be a perfect score that used 12-sided double dice? How did you figure that out? If youused two 12-sided double dice, how many rounds could you roll before you had to record a strike?How did you figure that out?
middleyears
rule twis
t
FRACTION DECIMAL PERCENT CHART
1/1One Whole1.00 100%
1/2 One Half 0.50 50%
2/2 Two Halves 1.00 100%
1/3 One Third 0.333 33%
1/4 One Fourth
0.25 25%
2/4 Two Fourths
0.50 50%
4/4 Four Fourths
1.00 100%5/5
Five Fifths 1.00 100%
4/5 Four Fifths
0.80 80%
3/5 Three Fifths
0.60 60%
2/5 Two Fifths 0.40 40%
1/5 One Fifth 0.20 20%
1/6 One Sixth 0.166 17%
2/6 Two Sixths 0.333 33%
3/6 Three Sixths
0.50 50%
6/6 Six Sixths 1.00 100%
5/6 Five Sixths 0.833 83%
4/6 Four Sixths 0.666 67%
3/4 Three Fourths
0.75 75%
2/3 Two Thirds 0.666 67%
3/3 Three Thirds
1.00 100%
9
SIMPLY FRACTIONS RECORDING SHEET
Roll Simplify Points Roll Simplify Points
1Record
1Record
Record Record
2Record
2Record
Record Record
3Record
3Record
Record Record
4Record
4Record
Record Record
5Record
5Record
Record Record
6Record
6Record
Record Record
PLAYER ONE PLAYER TWO
Final ScoreStrikesPoints− =
Final ScoreStrikesPoints− =
10
OPERATION MIXED OPS
LEVEL: Grade 4 and up
SKILL: solving multi step problems using + - x ÷ , order of operations
SET UP: horizontal, 1 shaker per student
PLAYERS: 2 (1 vs 1)
GOAL: to use as many dice as possible in solving an equation
GETTING STARTED:
Have students stand or sit side-by-side. Each player shakes their container until STOP is called.
The referee calls out the target answer. Players use dice from their shake to create a math
sentence with the answer equal to the target answer called by the referee. Players earn 1 point
per die, up to a perfect score of 7.
TEACHING NOTE:
Order of operations rules are PEMDAS (Please Excuse My Dear Aunt Sally)
First, do (Operations within Parentheses) and Roots and Expressions in order from left to right.
Second, do Multiplication and Division in order from left to right.
Last, do Addition and Subtraction in order from left to right.
FOLLOW UP ACTIVITIES:
1. Players roll a die before they shake to determine the target answer for the round.
2. Players create multiple equations per shake, which equal the target answer.
3. Players use dice in order from left to right to create an equation equal to the target. A bonus
of 5 is scored for this type of equation.
4. Players substitute 0-9 and 1-12 dice into the shaker.
EXAMPLES
Referee calls "11" as target.
11
Player One's shake
MATH THINK
"6 + 4 = 10. I just need 1 more to make 11. Then, after that, all I have to do is continue to make
combinations that equal 1, and then x or ÷ those combinations by the 11 to still equal 11."
6+4 + 3÷3 x [(1+1)÷2] = 11
MATH THINK
"I could start with 6 + 3÷3 to equal 7. The take 7 + 2 to make 9. I could take 9 + 4 to make 13 and
then - 1 and -1 to make 11. I don't need to put the 3÷3 into brackets because, according to "order
of operations" I would have to ÷ first before doing any + or - ."
6 + 3÷3 + 2 + 4 - 1 - 1 = 11
MATH THINK
"I can use my dice in order from left to right to score 5 more points by 1 + 3 + 6 + 3 to equal 13.
Then 13 - 4 to make 9. 9 x 1 still makes 9. Finally 9 + 2 makes the target 11."
(1 + 3 + 6 + 3 - 4) x 1 + 2 = 11
12
OPERATION MIXED OPS - RECORDING SHEETTarget
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Name: Name:Total Score =
Score# of Dice UsedSolution to Equal TargetSHAKE
13
I'M BALANCED
LEVEL: Grade 8
SKILL: solving linear equations with one variable, solving pairs of simultaneous linear equations
SET UP: horizontal, middle die removed, 1 shaker per student
PLAYERS: 2 (1 vs 1) or teams of 2 (2 vs 2)
GOAL: to create as many balanced equations as possible per round
GETTING STARTED:
Have students stand or sit side-by-side. Players shakes their container until STOP is called. Using
the three dice from each side of the open space, players simultaneously create equations that have
the same answer (balanced equations). They continue to create as many additional balanced
equations that they can before the round is over. The round is over when both players are no
longer able to create new balanced equations or when the teacher calls TIME. The winner is the
player with the most balanced equations after three rounds.
FOLLOW UP ACTIVITIES: 1. Players create 20 balanced equations in the fewest rounds they can.
2. Players use the same numbers from a single shaker and see who can get the most
balanced equations before TIME is called for the round.
EXAMPLES
Player One Player Two 6, 3, 1 5, 5, 2 4, 3, 1 5, 6, 3
6 + 3 - 1 = 8 5 + 5 - 2 = 8 4 + 3 + 1 = 8 5 + 6 - 3 = 8
(3 - 1) x 6 = 12 5 + 5 + 2 = 12 4 - (3 - 1) = 2 5 + 3 - 6 = 2
6 - 3 - 1 = 4 5 - (5 - 2) = 2 3 x 4 + 1 = 13 3 x 6 - 5 = 13
1 x 6 - 3 = 3 5 ÷ 5 + 2 = 3
Player One created four balanced equations while Player Two only created three balanced equations. Player One scored 4 points and won the round.
14
I'M BALANCED - RECORDING SHEET
=
= =
= =
=
= =
= =
=
= =
= =
=
= =
= =
=
= =
= =
=
= =
= =
Name: Date:
15
SHAKE A ROUND - Advanced
LEVEL: Grade 5 and Up SKILL: rounding numbers to specific place values, rounding to decimals (variation) SET UP: horizontal, 1 die in each slot, 1 shaker per student, (optional dice include: place
value systems die, 7 x 0-9 dice, place value dice, decimal dice). PLAYERS: 2 (1 vs 1) GOAL: to have the greatest value for the rounded place value GETTING STARTED:
Have students stand or sit side-by-side. Each player shakes their container until STOP is called.
Players read their numbers. Teacher calls the specific place value to compare. Players re-read
their numbers, rounding at the called place value. The player with the greatest amount for that
place value wins the round.
MATH TALK Player One MATH TALK Player Two
"I have three million, two hundred fifty six "I have five million, five hundred fifty three
thousand, six hundred eleven." thousand, six hundred fifty six."
Teacher calls "ten-thousands place"
MATH THINK Player One MATH THINK Player Two
"I have fifty six thousand which is closer to "I have fifty three thousand which is closer to
sixty thousand" fifty thousand."
MATH TALK Player One MATH TALK Player Two
"Three million, two hundred fifty six thousand, "Five million, five hundred fifty three
six hundred eleven, rounds to three million," thousand, six hundred fifty six, rounds to
two hundred sixty thousand. My sixty thousand five million, five hundred fifty thousand."
is greater than your fifty thousand. I win a point."
FOLLOW UP ACTIVITIES:
16
1. Players fill in recording sheet and circle rounded place value.
2. Players play six rounds, rounding to 10s, then 100s etc finish with rounding to millions.
3. Players use 0-9 dice (or place value dice or decimal dice) inside each slot.
4. A slot is left open to represent the decimal place. Players can then round to closest 1s,
0.1s, 0.01s, etc.
17
SHAKE A ROUND (Advanced)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Name: Name: Total Score =
SHAKE and circle place to round to Rounded Number Score
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