COUNT TO 20 - Math Inspirations

Hands on Math
A collection of incredibly awesome math games
Edited by
Emily Dyke and Joe Dyke
“A mind is not a vessel to be filled but
a fire to be kindled.” - Plutarch
Hands-On Math
“Knowing mathematics means being able to use it in purposeful
ways. To learn mathematics, students must be engaged in
exploring, conjecturing, discovering and thinking rather than only
in rote learning of rules and procedures. Mathematics learning is
not a spectator sport. When students construct personal
knowledge derived from meaningful experiences, they are much
more likely to retain and use what they have learned. This fact
underlies teachers’ new role in providing experiences that help
students make sense of mathematics, to view and use it as a tool
for reasoning and problem solving.”
- Standards for School Mathematics: Executive Summary
National Council of Teachers of Mathematics
Copyright © 2014 by J&E Dyke Enterprises, LLC
All rights reserved. Limited reproduction permission. The publisher grants permission to
individuals, including teachers and parents, who have purchased this book or whom have
received it directly from Math Inspirations or one of its approved affiliate partners as a
promotional product to reproduce the pages as needed for use with their own students and
families. Reproduction for an entire school or school district or for any commercial use is
prohibited.
Questions can be mailed to:
Math Inspirations
37914 N. Kyle St.
Queen Creek, AZ 85140
Or emailed to:
[email protected]
Visit our website at www.mathinspirations.com
Printed in the United States of America. First printing August 2013.
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Hands-On Math
A Note to Parents and Teachers
Dear Parents and Teachers,
You are about to see an incredible transformation in your students! The foundation
for all learning and success in education is laid by establishing a love of and passion for
learning. Math is no different. It all starts with fun!
There are so many games and activities available to teachers and parents to
supplement their student’s math experiences. However, not all of those games and
activities encourage deep, intense logical thinking and rarely are able to be easily adapted
and enjoyed and explored by every ability level of math student. We have searched far and
wide to collect games that meet the above criteria. We use all of these games on a
frequent basis with our very own students and children.
In playing these games please adapt and create new variations and rules that help
meet the specific needs of your students. We have had incredible experiences by simply
letting our students create nuanced versions of the games, and with our older students we
often ask “What rules can we change to make this more challenging?” and they love it!
These games have been specifically included in this book to do three things:
1. Help you identify when your young ones are ready to begin engaging higher
level math and move into operations. Look for your student’s ability to
strategize and to recognize that the outcome of the games is based on
superior strategy rather than simple chance. Strategic thinking is the sign
of readiness for critically analyzing, problem solving and formal math. Until
then, it’s all for fun and exposure and to develop a love and passion for math!
2. Develop powerful and unique thinkers. The purpose of mathematics is not to
memorize endless rules, procedures or concepts, rather it is to aid us in
developing our abilities to logically reason, problem solve and think critically.
These are the skills that our students need to be successful in our world,
not computation and calculation. These games provide incredible
opportunities for our students to think deeply, identify difficult patterns
and create brilliant strategies.
3. Supplement your curriculum by providing students with fun, engaging
opportunities to practice in place of mundane worksheets. Your students will
actually enjoy mastering their math facts with these games rather than by
simply memorizing them with flash cards, especially if you couple their
practice with using manipulatives to demonstrate the operations and thinking
in a visual and physical manner.
The key to maximizing the success of these games is allowing your student to think
independently and strategize on their own- YES THIS MEANS DON’T TELL THEM WHAT
TO DO OR WHAT THE BEST STRATEGY IS! They will figure it out!!! They will, through
repetition and observation, create incredibly unique and brilliant strategies that will blow
your mind and often outwit your best strategies. Our students all have brilliant, unique and
powerful minds, our role as their mentors and teachers is not to create their fire; rather it
is to provide the kindling and elements to grow their flames into wildfires!
Enjoy!
Joe and Emily
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Hands-On Math
In loving memory of
Candace Ralphs
(1947-2009)
Thank you for always inspiring us with your passion for learning and life.
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Hands-On Math
Table of Contents
*Personal Favorites
100 and Out…………………………………………………………………………………………………………………..7
*All Aboard!......................................................................................................................8
Alquerque.........................................................................................................................10
Awithlaknannai................................................................................................................12
*Casino..............................................................................................................................14
*Contig 60........................................................................................................................16
Contig Jr. ........................................................................................................................18
*Count to 20...................................................................................................................20
Cover Up...........................................................................................................................21
*Dice War.......................................................................................................................23
Digit Place Game............................................................................................................24
*Double Digit..................................................................................................................25
Even and Odd..................................................................................................................26
Fan Tan............................................................................................................................27
Four in a Row..................................................................................................................28
How Close Can You Get?..............................................................................................30
How Long? How Many?.................................................................................................31
*Krypto............................................................................................................................33
*Krypto Bingo.................................................................................................................34
*Leftovers!......................................................................................................................36
Mastermind…………………………………………………………………………………………………………………37
Nimbi................................................................................................................................38
*Number Smack!............................................................................................................39
Pattern Creation............................................................................................................40
*Pig....................................................................................................................................41
Pigtails!.............................................................................................................................42
Place Value Game...........................................................................................................43
*Poison..............................................................................................................................44
*Producto........................................................................................................................45
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Hands-On Math
*Save Twenty.................................................................................................................47
Say No To Triangles!....................................................................................................48
Shape Dominoes.............................................................................................................49
*Target Addition...........................................................................................................52
*The Coyote and the Hares........................................................................................54
The Factor Game...........................................................................................................56
The Perimeter Stays the Same.................................................................................58
The Subtraction Game.................................................................................................60
Thirty-One Game...........................................................................................................61
Three Corners................................................................................................................62
*Uno Memory..................................................................................................................64
*War!................................................................................................................................65
Other Recommendations……………………………………………………………………………………….…66
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Hands-On Math
100 and Out
Focus: Operations, Number Sense
Prerequisites: Basic Addition
Materials: Partner(s), cards (4 sets of 1-9: Uno, Rook, playing cards, 3x5
index cards all work great), paper, pencil
Objective: To have a final total score as close to 100 without going over.
100 is the highest possible score.
How To Play:
1.) Shuffle the cards and put them in a stack, face down.
2.) Each player draws a score sheet. The score sheet should appear as:
3.) Take turns taking a card from the stack. One card at a time.
4.) Players place the cards they draw in either the ten’s or the one’s place.
Cards cannot be changed once placed.
5.) Players take turns drawing cards from the deck for six turns and then
find the sum of the numbers. For example, a player having a 1, 5, 3 in the
ten’s place and a 5, 2, 2 in the one’s place, would have a sum of 99.
6.) The player who comes the closest to a final sum after 6 cards of 100
without going over wins. A score of 100 is the highest possible score.
Follow-Up: After several games, begin a discussion with your student as to
which cards they put in the tens column and why. Students can also grow
their data collection skills by keeping track of and identifying patterns in
winning scores, tens-column values of winners, and so on. Change things up
by adding a hundreds column and setting the target score as 500.
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Hands-On Math
All Aboard!
Focus: Number Sense, Operations, Probability
Prerequisites: Basic Addition
Materials: Partner(s), two dice for each player, game board (attached at
the end) for each player, markers (candy like Smarties makes this a lot of
fun) to cover numbers
Objective: Be the first to remove all of the markers from the game board.
How To Play:
1.) Each player plays by themselves, at the same time as the other players, in
a race format.
2.) Each player places markers on each of the numbers 2-12 on their game
board so that every number has one and only one marker.
3.) Each player rolls their two dice, they add up the sum and remove the
marker from the corresponding number on the game board. For example, if
they roll a “3” and a “6” they would remove the “9” marker from the board.
4.) Players roll and remove as fast as they can. If a rolled sum has a marker
that has already been removed, the player cannot remove a new marker and
must roll again.
5.) The player who removes all of the markers the fastest wins!
Follow-up: Discuss with other players the numbers that were rolled the
most often. Ask “Why are some totals rolled more than others?” Some
younger children may need assistance recognizing sums using dice (aka
connecting the dot pictures with numbers). An effective way to help is to
ask “Ok (student), you have an “11” left on the board, what will that look like
when you roll it?” Once they show you the dice as a “5” and “6” have them
continue rolling looking for the dice with those two dot pictures.
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Hands-On Math
All Aboard! Game Board
Player 1:
2 3 4 5 6 7 8 9 10 11 12
Player 2:
2 3 4 5 6 7 8 9 10 11 12
Player 3:
2 3 4 5 6 7 8 9 10 11 12
Player 4:
2 3 4 5 6 7 8 9 10 11 12
Player 5:
2 3 4 5 6 7 8 9 10 11 12
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Hands-On Math
Alquerque
History: Alquerque is played on one of the oldest game boards known to
man. The game board was carved on roofing slabs of the Temple of Qurna in
Egypt. This board is a basic pattern for battle games which have been
played in Spain, North Africa, Egypt, Madagascar, Malaysia and the U.S.
Focus: Logical Reasoning, Geometry
Prerequisites: None
Materials: A partner, game board (attached at the end), two differentcolored sets of 12 markers for covering spots on the board
Objective: Capture all of your opponent’s markers (like checkers)
How To Play:
1.) Arrange the markers as seen in the picture above, the center is left open
(each player has 12 pieces each)
2.) Take turns. On each turn, players can move one of their markers to an
empty circle. They can jump the other player’s maker if it is next to one of
theirs and the space beyond it, along a line, is empty. A player must jump if
there is a jump to be made.
3.) Players can only jump one of their opponent’s marker’s per turn
4.) The player who captures all of his partner’s markers wins. There can be a
tie game if neither player is able to get all their partner’s markers.
Follow-up: Discuss your strategies. To vary the game, allow jumping of
multiple markers.
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Hands-On Math
Alquerque Game Board
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Hands-On Math
Awithlaknannai
Focus: Logical Reasoning
Prerequisites: None
Materials: Partner, game board, two different-colored sets of 12 markers (24 total)
Objective: Capture all of the other player’s markers
How To Play:
1.) Arrange your markers on the board as shown below.
2.) Take turns. Players move their pieces to empty spots.
3.) There are two types of moves, capturing and non-capturing. In a non-capturing
move (i.e. no jump), a player may move one marker to any adjacent space. In a
capturing move, a player jumps over the other player’s piece only if they are adjacent
and there is an empty space on the other side of their piece.
4.) Jumping over an opponent’s piece allows a player to capture the other player’s
piece. Only one piece can be captured in a single jump, however, if possible, multiple
jumps are allowed on a single turn.
5.) Only one piece can be moved per turn.
6.) Play continues until one player captures all of the other’s markers or one player
cannot make a move (this would happen if their markers were all blocked from moving
or jumping).
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Hands-On Math
Awithlaknannai Game Board
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Hands-On Math
Casino
Focus: Number Sense, Logical Reasoning, Probability
Prerequisites: Basic addition
Materials: Partner(s), two dice, game board (attached at the end) for each person,
markers to cover numbers
Objective: Players try to cover as many of the numbers on the game board as
possible. The score for a round is the sum of the uncovered numbers. Player with the
lowest total wins.
How To Play:
1.) Take turns throwing the dice. Players add the total of the dice throw and decide
which numbers they will cover. For example, if they threw a 9, they could either
cover the 9 or the 8&1 or the 7&2 or the 6&3 or the 5&4.
2.) Players may only put one marker on each number.
3.) If a player cannot place the sum or BOTH addends, they cannot play. For example,
if they roll a 3&1, but the 1, and 4 are covered, they cannot place a marker on just the
3.
3.) Players continue taking turns until they cannot find any more combinations that
match the numbers they have left.
4.) Add up the total of numbers left uncovered, this is each player’s final score. The
player with the lowest score wins.
Follow-up: Discuss with other players the strategies you can use to help you win. For
a slight variation, roll the dice and cover either the difference or two numbers that
have the same difference.
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Hands-On Math
Casino Game Board
Player 1:
1 2 3 4 5 6 7 8 9 10 11 12
Player 2:
1 2 3 4 5 6 7 8 9 10 11 12
Player 3:
1 2 3 4 5 6 7 8 9 10 11 12
Player 4:
1 2 3 4 5 6 7 8 9 10 11 12
Player 5:
1 2 3 4 5 6 7 8 9 10 11 12
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Hands-On Math
Contig 60
Focus: Logical Reasoning, Probability, Operations
Prerequisites: Basic Operations (add/subtract/multiply/divide)
Materials: A partner, three dice, markers, Contig 60 game board
Objective: Be the first player to connect four (horizontally, vertically, or diagonally)
How To Play:
1.) Take turns. A player rolls 3 dice. The player then uses any combination of
addition, subtraction, multiplication, or division to find a value. For example, the
player may add all three dice values, or add two and multiply by the third, or multiply
two and subtract the third, etc.
2.) All three dice must be used once and only once each turn.
3.) The player marks their final value on the game board.
4.) The second player takes their turn and follows steps 1-3.
5.) If a player’s roll does not have any available combination available on the board,
they lose their turn.
6.) Play continues until one player connects four markers horizontally, vertically, or
diagonally.
Variations:
 Play can be modified to accommodate three players. Use three kinds of markers
and instead of connecting four to win, a connection of three wins.
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Hands-On Math
Contig 60 Game Board
1
2
3
4
5
6
7
8
28
29
30
31
32
33
34
9
27
55
60
64
66
72
35
10
26
54
125
144
150
75
36
11
25
50
120
216
180
80
37
12
24
48
108
100
96
90
38
13
23
45
44
42
41
40
39
14
22
21
20
19
18
17
16
15
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Hands-On Math
Contig Jr.
Focus: Logical Reasoning, Number Sense, Operations
Prerequisites: Basic Understanding of Addition and Subtraction
Materials: Three dice, markers game board, a partner
Objective: The first player to gain 15 points wins.
How To Play:
1.) Take turns. A player rolls 3 dice. The player then uses any combination of addition
and/or subtraction to find a total value. For example, the player may add all three
dice values, add two and subtract one or subtract two values from the third.
2.) All three dice must be used once and only once.
3.) The player marks their value on the game board and scores one point for the round.
4.) The second player takes their turn and repeats the same process.
5.) If player two places their marker on a number adjacent to one of player one’s
markers, then player two scores an additional point.
6.) Play continues until one player reaches 15 points.
Follow Up:
 Have the student add/subtract aloud, using counters to model their addition and
subtraction. Use positive reinforcement and excitement as they think in new ways.
Assist them in seeing new combinations by finding a final value that could be useful on
the board and saying “looks like a ___ could really help you. Is there any way for you
to create a ___?” To mix things up, a fourth die may be added, remember, however,
the game board only contains values 0-18 so some totals might not work. For students
working with other values (integers, products, etc…) the game board can easily be
adapted.
 Play can be adjusted to follow “Connect 4,” i.e. to win you must get four markers in
a row. No points are scored in this version.
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Hands-On Math
Contig Jr. Game Board
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
0
1
2
3
4
5
6
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Hands-On Math
COUNT TO 20
Focus: Logical Reasoning, Problem Solving
Prerequisite: Counting
Materials: None
Objective: Be the person who says “20”
How to Play:
1.) Take turns counting. Start with the number 1.
2.) On a player’s turn, they may say one or two numbers. For example, to start the
game, the first player could say 1 or 1, 2. Let’s assume they say 1,2. Then, the next
player can either say 3 or 3,4.
3.) Play continues back and forth in like manner. The person who says the number
“20” wins.
Follow-up: Discuss your strategies. Is there a way to predict the outcome every
time? Change it up and count by one, two or three or more numbers. You can also
change the target number to begin creating a strategy that works no matter what
number you have as a target.
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Hands-On Math
Cover Up
Focus: Logical Reasoning
Prerequisites: None
Materials: Partner(s), game board, markers
Objective: Place your marker on the last available square.
How To Play:
1.) Take turns. On a player’s turn, they place 1 or 2 markers on the board (one marker
for each square). If they are placing 2 markers they must be side by side either
horizontally or vertically, but not diagonally.
2.) Players continue placing markers on the game board until the last square is
covered.
3.) The player who covers the last available square wins.
Follow Up: After several rounds and after playing on several different sized and
shaped game boards, discuss the different strategies or approaches you might use for
each of the different game boards. To create/facilitate this discussion, try playing
on a board with only 3 squares and discuss the strategies. Then move up to a board
with 4 squares and discuss, growing the board until they recognize patterns and more
complex stratagem.
Variations:

Create your own game boards using different sizes and shapes.
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Hands-On Math
Cover Up Game Board (a)
Cover Up Game Board (b)
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Hands-On Math
Dice War!
Focus: Operations
Prerequisites: Counting
Materials: Partner(s), five dice per person
Objective: Possess all the dice
How To Play:
1.) All players roll all five dice. Each player totals the sum of all of their five dice.
2.) The player with largest sum steals one die from the player with the lowest sum.
3.) Players roll again. This time, the player with the 6 dice only totals their four
highest dice and compares them with the sum of the other player’s four remaining
dice. If the player with the six dice had a higher sum, they would steal another die
from the player with four, leaving them with only 3 dice. In the next round, the
player with the more dice would then only compare the sum of their three highest
against the three of the other player.
4.) In the case of a tie, the player with fewer dice wins the round and steals a die
from the player with the most dice.
4.) Play continues in this manner until one player possesses all of the dice. They are
declared the winner.
Variations:
 In a game of more four or more players, the players with the two largest sums
steal one dice from the two players with the lowest sums.
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Hands-On Math
Digit Place Game
Focus: Number Sense, Logical Reasoning
Prerequisites: None
Materials: A partner, paper, pencil
Objective: Guess the number in as few guesses as possible.
How To Play:
1.) One of the two players picks a two digit number and secretly writes it down on a
piece of paper. (The digits should be different).
2.) The other player then says a two digit number, trying to guess the original number.
3.) For each guess, the first player tells how many digits in the guess are the same as
in the number he picked and how many of the digits are in the same place as the digits
in their number.
- Do not tell which digit is correct…just how many!
4.) Use a chart to record the results, if for example the original number were 43:
Guess
Digit Place
27
0
0
13
1
1
14
1
0
Variations:
 Increase the difficulty by starting with a three or four digit number. You can also
allow repetition of numbers to increase difficulty.
 Change it up entirely by playing Letter Place by using three or four letter words
instead of numbers.
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Hands-On Math
Double Digit
Focus: Number Sense, Logical Reasoning
Prerequisites: Place Value Basics
Materials: Partner(s), pencil, paper, Uno cards (1-9 only)
Objective: Have a final sum closer to 100 than your partner without going over.
How To Play:
1.) Each player draws their own score sheet. The score sheet looks like this:
2.) Take turns. The first player picks a card from the top of the deck, which is face
down. They write their number in either the ones or the tens column of the score
sheet. Once a card is placed in a column it cannot be changed. If they put the number
in the tens column make sure to also put a place holder 0 in the ones column. If they
put the number in the ones column make sure to also put a place holder 0 in the tens
column.
3.) Draw a card and record the number in either the tens or the ones column 7 times
(aka there are seven rounds)
4.) After seven rounds, add up each player’s score. The player whose sum is the
closest to 100 without going over wins!
Follow-up: Choose a different number such as 1000 in order to utilize the larger
place values. For a student familiar with decimals, you can play to get as close to 1 as
possible by counting by tenths, hundredths or thousandths.
25
Hands-On Math
Even and Odd
Focus: Number Sense
Prerequisites: Counting
Materials: Partner(s), one die, paper, pencil
Objective: Reach at least 20 first to win.
How To Play:
1.) Take turns. All players start with 0 points.
2.) The first player rolls the die. If the die is even they add the die value to their
score. For example, if they role a 4, because it is even they add +4 to their score.
However, if the die value is odd, they subtract that amount from their score. For
example, if a player has 15 points and rolls a 1, they subtract one from their score to
get 14 because one is odd.
3.) A player’s score cannot go below 0 points.
4.) The first player to reach or surpass 20 points wins.
Variations:
 If a student has experience with negatives, allow them to go below 0 and allow
surpassing positive 20 to win and negative 20 to win as well.
 To really mix things up with the previous variation, if a player’s score is positive
allow the player to accept or reject even rolls, odds are still mandatory. If the
player’s score is negative, allow the player to accept or reject odds, evens are still
mandatory. In doing this, require an exact score of -20 or +20 to win.
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Hands-On Math
Fan Tan
Focus: Number Sense, Operations
Prerequisites: Counting, Basic Addition and Subtraction
Materials: One to three players, paper, beans (or other small counters), a stick (a
pencil will do but the Chinese use a chopstick)
Objective: At the end of the round, have the number of remaining beans equal your
corner number.
How To Play:
1.) Number each corner of a piece of paper 0 through 3
2.) Each player picks a number from 0 to 3 and writes their initials next to that
number on the paper
3.) Players take turns grabbing a handful of bean counters and put them in a pile in the
center of the paper. The first player uses their stick and counts the beans into four
piles. Each pile needs to be equal. Leftovers (remainders) are put in the center.
4.) The player whose number is the same as the number of beans leftover wins that
round. Put a tally mark by that number on the paper.
5.) After 10 rounds, whichever player has the most tally marks wins.
Follow-up: Since this is a great division game, you could have your students write the
number sentence for each round. (For example, if you had 27 beans in your handful,
you could write 27 ÷ 4 = 6 and 3/4 or 6 r. 3, the former is will be better for them
conceptually). Also, at the end of a round with the beans in equal amounts in the four
corners and with either 1, 2 or 3 beans in the center, have the student find out how
many total counters there are on the paper.
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Hands-On Math
Four in a Row
Focus: Logical Reasoning, Probability
Prerequisites: None
Materials: Partner(s), inch squared paper, markers/counters for each player (one
color for each player)
Objective: Get four of your markers in a row horizontally, vertically, or diagonally.
How To Play:
1.) Take turns.
2.) The first player places a marker on the game board inside a square.
3.) Player two follows, along with any other players.
4.) Play continues until a player is able to place four in a row horizontally, vertically, or
diagonally. As soon as a player has four in a row, they win!
Variations:
 You can increase the level of difficulty by requiring five in a row or by using a
bigger game board.
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Hands-On Math
Four In a Row Game Board
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Hands-On Math
How Close Can You Get?
Focus: Logical Reasoning, Operations
Prerequisites: Two-Digit Subtraction
Materials: Partner(s), Deck of cards (1-9’s only), paper, pencil
Objective: Choose two pairs of cards whose difference is closest to the target
number
How To Play:
1.) Deal four cards to each player face down. Turn the next two cards in the deck up.
These two cards form the target number. The first card goes in the tens’ place and
the second in the ones’ place. For example, if a player turns up a 3 and then a 6, the
target number for the round is 36.
2.) All players turn their cards up and form two two-digit numbers so that their
difference (subtraction) is as close to the target number as possible. For example, if
I was dealt the cards “4, 8, 2, and 1” and my target number was 36, the difference of
81 and 42 has a difference of 39, which is three away from the target number.
3.) Players then share their expressions and compare their differences. The player
with the difference closest to the target number wins.
Variations:
 Play five rounds, adding up the differences between each rounds’ target number
and your expressions’ differences. For example, if the target number for round one
was 36 and my expression has a difference of 39, my score for the round would be 3,
because I was three off the target number. Add up each players scores over five
rounds and the lowest total score wins.
 For younger players, modify the game to dealing three cards to each player and
only turning over one card for the target number, creating a single digit target
number. You can choose to allow only using two of the three cards dealt to you to get
the closest to the target number or you can have them create a one-digit and a twodigit number.
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Hands-On Math
How Long? How Many?
Focus: Number Sense, Logical Reasoning
Prerequisites: None
Materials: Partner(s), one die, set of Cuisenaire rods, game sheets
Objective: Have as few open squares as possible when the game ends.
How To Play:
1.) Each player uses a different 10 by 10 grid on the record sheet. Ideally, these are
10 cm x 10 cm.
2.) Take turns. The first player rolls the die once. This number tells them what
length of Cuisenaire rod (how long) to use. Roll the die again. This second roll
determines “how many” rods of the previous length to take.
3.) The first player then arranges the rods into a rectangle on their grid. They then
trace the shape (or leave the rods in place if you have sufficient supply).
4.) The second player repeats steps 1-3, and the game continues in this manner until
each player is unable to place their new rectangle on the board. Their game is now
over. However, if one player runs out of options, the other can keep going as long they
can place their rectangles on the board.
5.) When players have failed to place a rectangle on the board, they total the
remaining uncovered squares. Players compare totals and the lowest total wins.
Follow-up: After a few games, discuss placement of their initial rectangles on their
grids and where they believe the most effective places are (corners, middle, etc…).
Also, help them make the connection to multiplication by having them write the
multiplication sentence for each rod rectangle inside the shape. For example, a group
of 3 rods of length 4 laid out in a rectangle is 3x4. Help students make the
connection to finding area as well.
31
Hands-On Math
How Long? How Many? Game Board
Covered_________
Uncovered_______
Covered_________
Uncovered_______
32
Hands-On Math
KRYPTO
Focus: Logical Reasoning, Number Sense, Algebra
Prerequisite: Basic Operations (+ - x ÷)
Materials: Deck of UNO cards (or any cards 0-10), paper, pencil
Objective: To use all 5 number cards dealt to you to create the target number
turned up from the deck.
How To Play:
1.) Deal 5 cards to each player, and then turn one card from the deck face up. The
number on that card is the number each player is trying to “target.” (In UNO cards,
skips are 10’s)
2.) Each player, using any combination of addition, subtraction, multiplication or
division, manipulates the five numbers to reach a “target” number on their game
board. Each of the five cards must be used once and only once. For example, if the
cards read “3, 4, 1, 6, 8” in no particular order, I could reach the target number of 11
by 3 x 4 + 1 – (8 - 6) = 11. There is a way, usually more than one, to reach the target
number with any set of five numbers.
3.) The first player to reach the target number yells “Krypto!” and shows their cards
and explains the process they took to reach that number.
Follow-up: Discuss your processes, even if you lost. We allow all players to find a
krypto before each player reveals how they solved the problem. To decrease
difficulty, allow students to use at least 2 but not require all of the cards to be used
to reach the target number. For example, if the cards are 2, 4, 8, 8, and 9 and the
target number is 4, a young student could use 8-8+4 to reach the target number. To
increase difficulty, increase the range of numbers to 1-25. You can, as students
become familiar with, include other operations such as squares and square roots or try
to be super-human by not moving your 5 cards around but by keeping them in the
order they are laid out.
33
Hands-On Math
Krypto Bingo
Focus: Logical Reasoning, Operations
Prerequisites: Basic Operations (+ - x ÷)
Materials: Partner(s), pencil, 5 x 5 bingo sheet, Uno cards
Objective: Mark five bingo spaces in a row horizontally, vertically, or diagonally
How To Play:
1.) Every player is given their own blank bingo game board. Each player writes their
own choice of numbers from 1-25 in each of the 24 squares, excluding the center
square. Numbers can be used only once. The center square is marked as a free space.
2.) Five Uno cards are drawn from the deck and placed face up.
3.) Each player, using any combination of addition, subtraction, multiplication or
division, manipulates the five numbers to reach a “target” number on their game
board. Each of the five cards must be used once and only once. For example, if the
cards read “3, 4, 1, 6, 8” in no particular order, on my bingo game board I could mark
the number 11 because 3 x 4 + 1 – (8 - 6) = 11.
4.) Each player should use the five cards to reach whatever “target” number they
need to complete a bingo. Thus, every player will likely be trying to reach different
numbers. Once a player has created an expression that reaches their “target”
number, they should write that expression down in the box of the “target” number.
5.) Allow enough time for every player to mark a square (this will vary depending on
ability) and then draw 5 new Uno cards from the deck and repeat steps 2-5 until a
player marks 5 “target” numbers or spaces in a row horizontally, vertically, or
diagonally.
Variations:
 For some younger players, drawing 5 new cards for each round can be
overwhelming. In these cases, allow players to mark up to 3 “target” number squares
per each set of 5 Uno cards.
 To decrease difficulty, allow students to use at least 2 but not require all of the
cards to be used to reach the target number.
34
Hands-On Math
Krypto Bingo Game Board
Free
Space
35
Hands-On Math
Leftovers!
Focus: Logical Reasoning, Operations
Prerequisites: None
Materials: Partner(s), one die, 20 counters/beans/markers, 6 cups or 6 index cards
or 6 separate pieces of paper
Objective: Have the most counters/beans at the end of the game.
How To Play:
1.) Place the 20 counters in a pile on the table.
2.) The first player rolls the die and then lays out that many cups or pieces of paper.
3.) Then, the player divides the counters/markers evenly among the cups or pieces of
paper. For example, if I roll a 3 then I lay out three cups and divide the 20 markers
evenly into the three cups. Each cup would have 6 markers and there would be 2
leftover.
4.) The player then verbally states the division expression that describes what just
took place. For example, I would say 20 divided by 3 equals 6 with 2 leftover.
5.) The player keeps the leftovers from their round.
6.) The second player now begins their turn with all of the counters that were
previously placed in the cups. For example, remember the first player took the 2 that
were leftover, so the second player will begin their round with only 18 counters.
7.) Play continues until there are no beans left. Players total their beans and the
player with the most wins!
Variations:
 For players familiar with fractions, instead of keeping leftover whole beans, write
down the fraction remainder. In the example above, player one would have 2 beans
out of the 20 so their fraction would be 2/20 or 1/10. At the end of the second
player’s turn, if there were leftovers, they would write a fraction with 18 as their
denominator. When there are no beans left, each player sums their fractions and the
person with the largest value wins!
36
Hands-On Math
Mastermind
Focus: Logic, Problem Solving
Prerequisites: None
Materials: Partner(s), Cuisenaire rods (other colored counters may work)
Objective: Deduce the hidden selection of rods in as few guesses as possible.
How To Play:
1.) Place the entire set of Cuisenaire rods on the table. A player is chosen as the
pattern maker. The rest of the players close their eyes. The pattern maker chooses
three Cuisenaire rods (no repeating colors) and hides them from the other players.
2.) The other players open their eyes and present possible solutions to the pattern
maker. In this version, each player will present a set of three rods as their guess to
the pattern maker.
3.) The pattern maker then tells that player how many rods in the guess match the
rods that are hidden. For example, if the pattern maker chose blue, red and yellow
rods and the player presents a guess of red, green and brown rods, then the pattern
maker would say “You have one correct color.”
4.) The player then presents a new guess, using the information gathered in the
previous guess and the pattern maker states how many rods in the new guess match
the hidden rods.
5.) Play continues until the player correctly identifies all three rods that were hidden,
in other words, the pattern maker would say “All three colors are correct.” Count how
many guesses it takes to find the pattern and this is the player’s score.
Variations:
 To increase difficulty increase the number of hidden rods to 4 or 5. For even a
higher difficulty, allow repetition of colors. Finally, for super advanced
Masterminders require the correct order of the rods. In this final version, the
pattern maker would divulge two pieces of information for each guess: 1.) How many
colors are correct, and 2.) How many colors are in the right location.
 With multiple players, the players present guesses back and forth, racing to be the
first to identify the hidden pattern.
37
Hands-On Math
Nimbi
History: A Danish mathematician found that he could figure out how to solve the
ancient Chinese game of Nim with a mathematical formula. He worked to create a
game that could not be solved with a formula, but with sound logical thinking: a new
game experience each time.
Focus: Logical Reasoning
Prerequisites: None
Materials: Partner, 16 markers (toothpicks, beans, rocks, sticks, candy…)
Objective: Force the other partner to take the last marker
How To Play:
1.) Place the markers in four straight rows and four straight columns in this manner:
2.) Take turns. The first player may take any number of markers (from 1-4) from any
row or column. The only rule is that the markers need to be adjacent (horizontally or
vertically - NOT diagonally adjacent).
3.) The person who takes the last marker loses.
Follow Up: Monitor the number of moves it takes to win the game. After several
games, discuss with your student methods/strategies to make the game shorter or
longer. What is the least amount of moves needed to win? The most? If needed,
start with a 2 x 2 board and discuss these patterns and then build up to a 3 x3 and a 4
x 4. Are there strategies that can be applied across the different sizes? What
changes in strategy are there as you change the size of the board?
38
Hands-On Math
Number Smack!
Focus: Number Sense
Prerequisites: None
Materials: Deck of cards (Uno or face cards will do), a partner, a moderator (parent)
Objective: Collect the largest number of cards as possible
How To Play:
1.) The moderator does not play but is important to keep everyone on track, it can get
a little crazy!
2.) The moderator holds the deck face down and flips a card face up, laying on the
table.
3.) The two (or more) players, as fast as they can, say the name of the number shown
on the card and slap the card on the table. The player who slaps first and says the
correct number keeps the card.
4.) Play continues in this format until the deck is used up. At the end, whomever has
the most cards wins!
Variations: There are several variations for this game, however, the core purpose is
to help the student(s) develop their number recognition and operations.
 Instead of using cards that display the cardinal number (1, 2, 3…) use cards that
show pictures of objects. For example, instead of an Uno card that displays a two,
show the student a 2 of hearts and white-out the 2 so all they see is the two hearts.
 For students who are studying basic operations, flip two cards and have them add
or multiply or find the difference as fast as they can.
 For more advanced students, add or multiply 2, 3 or 4 cards at a time. Students
can also simplify fractions with the top card being the numerator and the bottom card
being the denominator
39
Hands-On Math
Pattern Creation
Focus: Logical Reasoning, Patterns
Prerequisites: None
Materials: Partner(s), colored blocks/markers (5-10 different colors)
Objective: Identify the pattern and place the next five blocks/markers
How To Play:
1.) Take turns. The first player uses as many blocks as they’d like to create a pattern.
They lay out the first 10 blocks/markers for the other player to see.
2.) The other player then adds 5 more blocks/markers to the end of the line of blocks
to continue the pattern.
3.) If they follow the pattern correctly, they receive one point. If they make a
mistake they receive no points.
4.) Players then switch and the other player creates a new pattern. First one to 10
points wins.
Variations:
 Utilize fewer colors for younger mathematicians, and more colors for older
mathematicians.
 Encourage more complicated patterns for older mathematicians, such as every
third color in the pattern is the color mix of the previous two. For example, Red,
White, and Pink, then Yellow, Blue, and Green. Other complicated patterns could
include every fifth being blue and the ones in-between are lined up warmest to
coolest. Obviously, with patterns like this it will be difficult to predict the next
iterations; however, the challenge with more complicated patterns is to deduce the
rules and logic that govern the existing pattern.
40
Hands-On Math
Pig
Focus: Number Sense, Statistics and Probability
Prerequisites: Basic Addition
Materials: Partner(s), two dice, paper and pencil
Objective: Be the first person to reach 100 (or a smaller number for little
mathematicians)
How To Play:
1.) Take turns. The first player rolls the pair of dice as many times as they want,
adding what comes up in their head (or on paper or using counters or using a
calculator).
2.) If the player rolls and a 1 comes up on one of the dice, they do not get any points
and it is the next player’s turn.
3.) If the player rolls and a 1 comes up on both dice, all of their points for this and
previous rounds are lost, their total goes back to 0 and it is the next players turn.
4.) If a player chooses to stop rolling before a 1 comes up, they write their score down
and add it to their total. The first player to pass a total score of 100 wins.
Follow-up: Play at least 5 games and discuss strategies with your partner(s). Talk
about the likelihood of rolling a 1 on one die and two 1’s as well. Talk about short term
vs. long term probabilities of getting a 1. To increase difficult or to deepen your
discussion, roll three dice and discuss strategies. How is rolling three dice different
from rolling two.
41
Hands-On Math
Pigtails!
Focus: Number Sense, Statistics and Probability
Prerequisites: Basic Addition
Materials: Partner(s), coin, paper and pencil
Objective: Be the first person to reach 10 points.
How To Play:
1.) Take turns. The first player takes their turn and flips a coin.
2.) If the coin is heads, they get a point and they can choose to keep flipping or stop.
If it is tails they lose all of their points for the round and their turn ends.
3.) As long as they keep flipping heads, they can continue to flip as much as they’d like
but when they flip a tails they automatically end their turn and lose all of this round’s
points.
4.) If they choose to stop and keep their points, their points are now protected and
can’t be lost, even if they flip a tails later on.
5.) The player who reaches 10 points first wins!
Follow-up: Play at least 5 games and discuss strategies with your partner(s). Talk
about the likelihood of flipping a heads/tails. Talk about short term vs. long term
probabilities of getting a heads. To increase difficult or to deepen your discussion,
talk about flipping two coins instead of one. How will this change the game and your
strategy?
42
Hands-On Math
Place Value Game
Focus: Logical Reasoning
Prerequisites: Place value
Materials: Partner(s), 1 die, paper and a pencil
Objective: Create the largest number.
How To Play:
1.) Each player needs their own record sheet, it should look like this:
______
, ________ ________ ________
________
Reject
2.) Take turns rolling the die. Each player will write the number rolled in one of the
five spaces, before the next player rolls the die. (Once you write the number, you are
not allowed to change it)
3.) The goal is to try to place the digits so that you will end up with the largest
number possible.
4.) Players may place the result of one of their die rolls in the reject space, therefore
not counting it as part of their number.
5.) Players then compare their number with the other players’ numbers. Decide which
player has the bigger number. They win!
Follow-up:
Discuss strategies with your student, specifically discuss what to do
with small die rolls vs. large die rolls to create the largest number.
Variations:
 For beginners start with two spaces and work up to larger numbers.
 You can also play a simpler version of rolling 5 dice and creating the largest or
smallest number possible with the dice values
 Instead of creating the largest number, you can also aim to create the smallest
number possible
43
Hands-On Math
Poison
Focus: Number Sense, Logical Reasoning, Problem Solving
Prerequisites: Counting
Materials: A partner, counters or beans
Objective: Get your partner to take the last counter/bean
How To Play:
1.) Set out 13 counters/beans.
2.) Take turns.
3.) On their turn, players may take one or two counters/beans. They cannot take zero
or more than two per turn.
4.) The player who “gets stuck” taking the last counter/bean loses.
Follow-up: Play several times but don’t share any strategies with your students.
Allow them to struggle through and hypothesize and test their ideas on their own.
Once you see them start to repeat a process, like always leaving the same amount of
beans near the end or always taking just one bean, talk to them about it and ask them
why they are following that strategy. Then, test it out with them. Try to beat their
strategy and encourage them to develop a new one until they find one that works no
matter what you throw at them!
Variations:
 Vary the number of counters/beans that are laid out. Use different values of even
and odd numbers.
 If you’d really like to go crazy, take more than two beans. For example, allow
players to take up to 4 or 5 beans per turn.
44
Hands-On Math
Producto
Focus: Number Sense, Logical Reasoning, Problem Solving
Prerequisites: Basic Multiplication
Materials: A partner, two dice, counters or beans, game board for each player
Objective: Get five in a row horizontally, vertically or diagonally
How To Play:
1.) Take turns. Roll the two dice and find their product.
2.) Mark their product value on the game board. Some numbers occur more than once,
however, players can choose only one space to mark per turn.
3.) Play continues until one player marks five in a row (like BINGO), at which point
they win!
Variations:
 Create a ten by ten board and use 10 sided dice or Uno cards instead, flipping two
cards over and multiplying them.
 Play “black-out” Producto in which all players play on one game board, using
different markers, taking turns rolling the dice and marking their number. If the
number is unavailable they lose their turn (or roll again) Play continues until all spaces
are filled in and then players add their individual totals – the player with the largest
total wins.
45
Hands-On Math
Producto Game Board
Dice
Values
1
2
3
4
5
6
1
1
2
3
4
5
6
2
2
4
6
8
10
12
3
3
6
9
12
15
18
4
4
8
12
16
20
24
5
5
10
15
20
25
30
6
6
12
18
24
30
36
46
Hands-On Math
Save Twenty
Focus: Probability, Number Sense, Operations, Logical Reasoning
Prerequisites: Addition
Materials: Partner(s), 5 dice, paper, pencil
Objective: Have the highest score after five rounds
How To Play:
1.) Each player rolls five dice to get a score as close to 20 as possible without going
over.
2.) The players can roll up to four times each round.
3.) On each of the four rolls, the player may save as many of the dice as they would
like and, on the next roll, they role only the dice they have not set aside and saved.
4.) After the four dice rolls, the player adds the total of the five dice
5.) If the total is 20 or less, they record that score on the paper. This is the total
score for round one. However, if the total is more than 20, they record a 0 for the
round.
6.) The other player(s) takes their turn repeating steps 1-4. This is the end of round
one.
7.) Play five rounds. Add the total of each of the five rounds. The player with the
highest total wins. The maximum score for the game is 100.
Follow Up: After several games, begin to discuss strategies with your student(s).
Strategies could include always keeping the two highest dice after the first roll, or
keeping four dice that add up to fifteen and then rolling the fifth die and so on.
Encourage your student to explore their strategy, and to try other strategies and
compare the overall point totals of each game.
Variations:
 For a similar experience with younger mathematicians, roll three dice instead of
five. Use the target number of 12. You can also adjust the number of allowable rolls
based on how many dice you use.
47
Hands-On Math
Say No to Triangles!
Focus: Geometry, Logical Reasoning
Prerequisites: None
Materials: A partner, two colored pencils/pens, paper
Objective: Force your opponent into creating a triangle.
How To Play:
1.) Each player needs a different colored pencil/pen. On the paper, draw the 6 dots
that make up the game board below.
2.) Take turns. Each player has a different colored pen/pencil. Player one draws a line
that connects any two dots. Player two then does the same with another pair of dots.
3.) During play, players should avoid drawing three lines in their color that connect to
make a triangle. If a player makes a triangle in their color, they lose. If a player
makes a triangle but not all three sides are the same color, it doesn’t count as a loss.
4.) The game ends when one player connects three of the same colored lines to form a
triangle. They lose!
Follow Up: After several rounds, begin to track relationships between the numbers
of lines drawn and how fast the game is won. Talk with your student about creating
predictions based on this data and strategies based on these patterns. For example,
if your games are consistently ending after each player has drawn 7 lines, then try to
formulate strategies that will decrease this number or help your student recognize
about how many moves they have before the game should be ending.
Variations:
 Create your own game boards using different numbers of dots. Try placing a dot in
the center of the shape.
48
Hands-On Math
Shape Dominoes
Focus: Geometry, Logical Reasoning
Prerequisites: None
Materials: A partner, cut outs of each of the shape dominoes
Objective: Play all of the dominoes in your hand.
How To Play:
1.) Place all of the dominoes face down on the table and mix them up.
2.) Each player takes 6 dominoes (For games of more than 3 players, take less
dominoes or use two full sets of shape dominoes)
3.) The remaining dominoes are left on the table, these are “sleeping dominoes.”
4.) The first player places one of their dominoes face up on the table.
5.) The second player tries to place one of their own dominoes on the table that
matches one side of the previously played domino.
6.) If a player cannot play (i.e. they have no matches available) they must draw from
the “sleeping dominoes” pile. If the domino they draw is playable, they can play it.
7.) Play continues with each player placing a domino or drawing an extra domino from
the “sleeping dominoes.”
8.) The first player to play all of their dominoes wins.
Follow Up: If a player matches non-exact dominoes, take the time to discuss the
similarities and differences between the shapes and the characteristics that make
the shape unique. If a player matches a square to a rectangle, remember that squares
belong to the rectangle family so this could be a valid play. Allow the player to
“prove/defend” their logic. This game is easily modified for more advanced students
by creating new tiles with new shapes.
49
Hands-On Math
Shape Dominoes
50
Hands-On Math
51
Hands-On Math
Target Addition
Focus: Number Sense, Logical Reasoning
Prerequisites: Addition
Materials: A partner, one game board (attached at the end), markers to cover up
numbers on the game board
Objective: Outsmart your opponent to reach the target
How To Play:
1.) Players choose a target number between 25 and 55
2.) Players take turns placing a marker on one of the numbers on the board. They
state the total of the covered numbers each time they place a new marker. For
example, if the first person covered a 5, they would say 5. If the other player then
covered a 3, they would then say 8 because the 5 and the 3 are covered.
3.) Each square may be used only once.
4.) The person who reaches the target number exactly wins. If players are unable to
exactly reach the target number, the result of the game is a tie.
Follow-up: Play several times and then discuss strategy with your partner. To
increase difficulty pick a target number between 0 and 10 and start subtracting your
numbers from 50. If you are comfortable with integers (positive and negative whole
numbers) change the numbers on the game board to negatives and choose a target
number between -25 and -55.
52
Hands-On Math
Target Addition Game Board
5
5
5
5
5
4
4
4
4
4
3
3
3
3
3
2
2
2
2
2
1
1
1
1
1
53
Hands-On Math
The Coyote and The Hares
Focus: Logical Reasoning, Problem Solving
Prerequisites: None
Materials: A partner, 12 “hare” markers and 1 “coyote” marker, game board
How To Play:
1.) Arrange the markers as seen in the picture below. One partner is the 12 “hares”
and the other player is the single “coyote.”
2.) Take turns. Both the coyote and the hares can move one circle at a time, along a
line, in any direction, as long as there is an empty circle adjacent to it.
3.) The coyote can capture a hare by jumping over it (along a line to the next circle
which must be empty). Multiple jumps during a turn are allowed. Captured hares are
removed from the board.
4.) A hare cannot jump over a coyote, but can win if the hares corner the coyote so
that he cannot move.
5.) The coyote wins if he captures enough hares so that they cannot corner him.
Follow-up: As you play, perhaps after several games, discuss with your student how
many hares is “enough hares so that they cannot corner him?” In other words, what is
the minimum number of hares needed for the hares to win? Discuss other observed
patterns and thoughts as the game proceeds, such as the coyote having to wait and
rely on the hares to make an offensive move in order to make a capture. Who has the
advantage in this game? Why? Is there a way for the hares to always win? Or will the
coyote inevitably win every game?
54
Hands-On Math
The Coyote and The Hares Game Board
55
Hands-On Math
The Factor Game
Focus: Number Sense, Logical Reasoning, Problem Solving
Prerequisites: Basic Multiplication, Factorizing
Materials: A partner, colored pencils or crayons, a sheet of paper with the numbers
from 1 – 30.
Objective: Have the largest score at the end of the game.
How To Play:
1.) Each player uses a different color pencil or crayon.
2.) One player selects a number and circles it with their crayon. The other player
then finds all the factors of that number, circling each factor with their crayon.
3.) The process continues, alternating between the two players until there are no
factors left for the remaining numbers.
4.) Players total the numbers they circled. The winner is the player with the larger
score.
**Caution**: Selecting a number with no factors left is an illegal move. If you
make an illegal move, you get to add the number to your score, however, you lose your
next turn to select a number.
Follow-up: You can increase or decrease the range of values available to increase
exposure to the factors of larger numbers. For example, instead of using 1-30, use 150. Discuss strategies with your student, especially any patterns in the numbers that
are consistently still remaining at the end of the game.
56
Hands-On Math
The Perimeter Stays the Same
Focus: Geometry, Logical Reasoning
Prerequisites: Area, Perimeter of Rectangles
Materials: Centimeter squared paper (attached at the end), scissors
Objective: Find three different shapes that have the same characteristics
How To Play:
Draw three different shapes on the centimeter squared paper following three rules:
1.) Stay on the lines when you draw.
2.) You must be able to cut out each shape and have it remain all in one piece.
3.) Each shape must have a perimeter of 30 centimeters.
Write the area on each shape. Cut out the shape that has the greatest area and the
shape that has the least.
Follow-up: Discuss with each other how the perimeter can be constant yet the area
can change. Have the student find the 30-centimeter perimeter shape with the
largest possible area and the smallest possible area. For a variation, change the
required perimeter or start by giving the area instead and find the perimeters of a
few of those shapes.
57
Hands-On Math
The Perimeter Stays the Same Centimeter Board
58
Hands-On Math
The Subtraction Game
Focus: Logic, Operations, Number
Prerequisites: Basic subtraction
Materials: Partner(s), One die or a 0-9 spinner, paper, pencil
Objective: Have the lowest sum after 5 rounds
How To Play:
1.) On the piece of paper, draw the boxes as seen below, one set for each player:
__
___________
REJECT
2.) Take turns rolling the die (or rolling the spinner). After each roll write the number
rolled/spun in one of the boxes. Once it has been written, it cannot be moved and only
one number can go in each box.
3.) Players are able to place one of the rolls/spins into the reject box, which removes
it from being subtracted.
4.) After four rolls/spins, players subtract the one digit number from the two digit
number and record the difference.
5.) Play 5 rounds and add all of the differences from each round together to create a
final sum. The player with the lowest sum wins.
Variations:
 Add a hundreds or thousands place to the top number, make sure to always have at
least one less digit in the bottom number so as to avoid negatives.
 For more advanced students, have them average the 5 rounds together and
compare averages to determine the winner
 Allow more or less rejections to decrease/increase difficulty
59
Hands-On Math
Thirty-One Game
Focus: Logical Reasoning, Addition
Prerequisites: None
Materials: Partner(s), 24 cards (playing, Uno or Rook or home-made) 1-6 of each of 4
suits or colors.
Objective: Be the player who reaches the sum of exactly 31.
How To Play:
1.) Lay out the 24 cards, face up.
2.) Take turns. The first player turns any card face down and says that number out
loud.
3.) The second player turns over any other card, adding that number to the first one.
4.) Continue taking turns turning a card face down and keeping a running total.
5.) Whoever reaches the sum of exactly 31 wins. If neither player hits 31, or if some
one goes over 31 then no one wins that round.
Variations:
Version 2: Designed for beginning adders.
- Use a number grid (attached) to help your student keep the running total. It can
also be helpful to use base 10 blocks, or counters such as beans or cubes.
Version 3: Designed for beginning subtractors.
- Place 31 counters in a pile in the center of the table. As you choose a card and
turn it face down, subtract that amount from the pile of counters. This method
emphasizes the concept of subtraction being the removal or taking away a group from
an initial group.
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Three Corners
Focus: Number Sense
Prerequisites: Counting
Materials: Partner (3 players is ideal), four dice for each player (two of one color
and two of another), poster board/paper
Objective: Choose the corner with the largest sum.
How To Play:
1.) This game is most effective with at least 3 players. Post a sheet of paper/poster
board in three corners of the room. For this example, we will assume your dice are
white and red. Label one corner “White White,” another “White Red,” and the last
“Red Red.”
2.) Sit down at a table in the center of the room together with all players. Each
player chooses which corner they think will have the largest sum at the end of the
game. (At this point it’s a total guess, just for fun)
3.) Each player is given 2 white dice and 2 red dice. All players roll their dice and
identify the two largest values. For example, if I roll a red 2, white 4, red 5, white 6
I would set aside the red 5 and white 6. If there is a tie for one of the two largest,
for example if a 5, 3, 3, and 2 were rolled, then roll again.
4.) Every player then stands up and goes to the poster that matches their roll. For my
red 2, white 4, red 5, white 6 roll above I would go to the “White Red” corner because
of my high red 5 and white 6. If my largest were two white dice, I would have gone to
the “White White” corner and so on.
5.) On the paper, each player writes the sum of their two largest dice.
6.) Players return to the table and repeat the process 10 times.
7.) After 10 rounds, players find the sum of each corner and the player who, in the
beginning, chose the corner with the highest sum wins!
Follow-up: After a few games, discuss with your student any strategies they see in
choosing a corner. Is there one corner that always wins? Always loses?
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Variations:
 Write the sum of all of the dice on the paper instead of only the largest two.
 Set a timer and play for 3 minutes, rolling, running, adding and writing as fast as
possible. Play stops after 3 minutes and each corner is summed.
 Choose the two smallest dice instead, having the lowest final sum win and follow
this up by comparing patterns between this game and the original.
 This game can be adapted for nearly any operation, even division. Have the
students write the largest fraction they can with the two largest dice and then sum
the fractions at the end.
 For different ability groups, have an addition corner, multiplication corner and so
on, assigning each student to an operation of their ability. They only go to that corner
after each roll.
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Hands-On Math
UNO Memory
Focus: Number Sense, Logical Reasoning, Problem Solving
Prerequisites: Counting
Materials: Partner(s), a deck of UNO cards (or face cards or Phase 10 or Rook
cards)
Objective: Find as many matches as you can that have a sum of 10
How To Play:
1.) Take out 2 sets of 0-9 UNO cards and 2 skips (these will be used as 10’s). There
should be 22 cards. Shuffle.
2.) Spread out the cards face down.
3.) Take turns finding matches that add up to 10.
4.) If you find a match your turn continues. If your two cards do not add up to ten,
your turn ends and it is the other player’s turn.
Variations:
 To mix things up, try finding pairs that have a difference of 5.
 You can also choose a different target sum or difference, however, in this
variation, not all the cards will be able to have matches.
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Hands-On Math
War!
Focus: Operations, Number Sense
Prerequisites: Counting
Materials: A partner, Deck of UNO cards (or other numbered cards)
Objective: Possess all of the cards in the deck.
How To Play:
1.) Deal each player half of the deck, face down. Players are not allowed to view the
cards. Play begins with each player flipping over one card. The player with the highest
value wins both cards and sets them aside into their “winning pile.”
2.) If the cards are the same value, each player then places the next 3 cards face
down on the table and flips the fourth. Whichever player has the highest value
between the fourth cards then takes the original two, the 6 face down and the two
fourth cards for a total of 10 cards. If the fourth cards are ties again, the process is
repeated until one player wins that group of cards.
3.) When a player uses their whole original deck, they take the “winning pile” and
shuffle and then use those cards to draw from.
4.) Play ends when one player possesses all of the cards, meaning the other player has
no more cards left to play in their hand or in their “winning pile.”
Variations:
 War is extremely adaptable for all ages and abilities and math concepts. For
example, instead of flipping one card, flip two or three or more! Instead of the
largest value winning, have the smallest, or let the winner of the previous flip decide
what will win the next. The possibilities are endless. Some other variations include:
 Flip over two cards and add, subtract, multiply, or divide them
 Flip over two cards, one for the numerator and the other for the
denominator, then compare the two fractions
 Flip over two pairs of cards, each pair making a different fraction and then
adding, subtracting, multiplying or dividing them and comparing
 Flip over two cards to make a fraction and one other for a whole number and
multiply or divide
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Other Great Games and Activities That Every Home Should Have
Board Games:
Yahtzee
Master Mind
Chess
Mancala
Checkers
Uno
Set
Risk
Stratego
Parchisi
Open Source:
(All of these resources can be found for free by doing a search online)
Tangrams
Tic-Tac-Toe
Logic Puzzles
Sodoku
Number Grids
Rosetta Puzzles
Cryptograms
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