#mathgamemonday — Public Fediverse posts

Math Game Monday: Push the Penny

This game offers young children a chance to practice counting and early addition skills while racing to beat their parents.

Many parents remember struggling to learn math. We hope to provide a better experience for our children.

And one of the best ways for children to enjoy learning is through hands-on play.

Push the Penny

Math Concepts: addition to one hundred, thinking ahead.

Players: two or more.

Equipment: playing cards (remove face cards and jokers), a hundred chart, and a penny or other small token.

Set-Up

Print a hundred chart for players to share. You may choose any style you like: 1–100, 0–99, top-down, or bottoms up.

The 23-page printable (pdf) Number Game Printables Pack file includes hundred charts, graph paper, and game boards from the first two Math You Can Play books.

How to Play

Deal three cards per player and set the rest of the deck face down as a draw pile. Place the chart in the middle of the table, with the penny on the first square.

On your turn, lay one card from your hand face up on the discard pile. Move the penny forward that many squares, and then draw to replenish your hand.

If adding the number on your card would move the penny past one hundred, then you must subtract your number and move backward instead. Whoever pushes the penny to one hundred by exact count wins the game.

Variations

Play two cards from your hand and choose whether you want to add or subtract the numbers to find out how far the penny moves.

Or start at one hundred and push the penny down to number one.

History

My math club students have enjoyed playing a variety of count-to-one-hundred games. This version is a modification of the 99 Game from Julie Reulbach’s collection “Math Games for Classrooms.”

 
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Math Game Monday: The Partitions Game

This game features the Cuisenaire rods, but you may play with any math manipulative based on length: Montessori bead chains, Mortensen or Math-U-See blocks, etc. Or draw pictures on graph paper.

Many parents remember struggling to learn math. We hope to provide a better experience for our children.

And one of the best ways for children to enjoy learning is through hands-on play.

The Partitions Game

Math Concepts: partitions, part/whole, addition, multiplication, algebra.

Players: two or more.

Equipment: Cuisenaire rods (or other math manipulatives) or graph paper, pencil and paper (optional).

Set-Up

Dump the rods on the table, where all players can reach them. Clear a space in the middle for building your game.

Players must agree in advance whether the same rods in a different order will count as a new partition.

How to Play

The first player chooses any rod (yellow or longer) and sets it in the middle of the table. Or if using graph paper, the first player outlines a row of squares (five or longer).

The second player adds a new row of two or more rods that make the same length. Or draws a new same-length row of squares, split into two or more sections.

Players continue to add rows in turn. Each row must be different from all those already played.

Whoever plays the last new partition, leaving the other players stumped, wins that round and gets to choose a new starting rod.

Variation

Depending on the age of your child, you may want to keep “score” by writing an expression to represent each row. You may use numbers, but I like to give children a head-start on understanding algebra by using the color names or initials.

For example, you might write the game above as:

• orange = 2 × yellow = green + black, etc.
• o = 2y = g + k, etc.
  [We use k for black, t for tan (brown), and b for blue.]
• 10 = 2 × 5 = 3 + 7, etc.
  [Assuming you treat the white rod as one unit.]

Writing everything out does not increase the mathematical content of the game. The written symbols are not mathematics, any more than the lines and dots written on a staff are music. Music only happens when we play the notes, just as math only happens when we think the ideas.

Your children will be thinking like a mathematician, even if they write nothing down. But writing helps them grow comfortable with math notation (the way we write math on paper), which will be useful when they want to communicate their own mathematical thoughts.

 
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Math Game Monday: Fraction Product Game

This game helps students master multiplying and dividing fractions.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Fraction Product Game

Math Concepts: multiplying fractions, equivalent fractions.
Players: two, or two teams.
Equipment: printed game board, colored markers or a set of matching tokens for each player, two glass gemstones or other small tokens to mark the factors.

The free 44-page PDF Multiplication & Fraction Printables file includes traditional and spiral forms for each of the Product Games.

How to Play

The first player places a stone on any one of the factors at the bottom of the board. The second player places the other stone on a factor — the same or different — and then marks the product of those two numbers by coloring the square or placing a token.

On each succeeding turn, a player moves just one stone to a new number and then marks the product of those two factors. If both players agree that all possible moves have already been colored in, the player whose turn it is may make a fresh start by moving both stones.

Whichever player marks four (or more) squares in a row — horizontally, vertically, or diagonally — wins the game. The squares must touch each other at edges or corners, with no gaps. If neither player can make four in a row, then the player who has the most sets of three in a row wins.

History

Have you figured out yet how much I love John Golden’s blog? About this game, Golden writes:

“I launched the game by playing me vs. the class. Re-emphasizing that you only get to change one factor at a time, the goal is to get four in a row, and the new idea that there are equivalent fractions. If you multiply and get 6/12, you can cover 1/2, and vice versa.

“Then the students played pair vs. pair. At the end we summarized by discussing what they noticed about the game, and what they thought made for a good strategy.

“I did point out to them that someone would tell them fraction division was hard, but they’ve already done it when they’re figuring what to multiply 3/4 by to get 6/12.”

 
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Math Game Monday: Shut the Box (Cards)

This game builds mental math skills in young students, and is fun for all ages.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Shut the Box (Cards)

Math Concepts: addition, number bonds up to nine.
Players: two to four.
Equipment: one deck of playing cards, two six-sided dice.

How to Play

Each player lays out the ace through ten of one suit, face up.

On your turn, roll the dice and add the numbers together. Turn face down one or more of your cards whose numbers add up to make that sum.

For instance, if you roll a six and a four, you could choose the 8 and 2, or the 6 and 4, or the 7 and 2 and 1, or any other combination that makes a sum of ten. If you cannot turn down the full amount of your roll, you lose that turn.

Pass the dice to the next player.

If all the higher numbers are already covered, a player may choose to roll only one die.

The first player to turn down all their cards wins the game.

Variations

Traditionally, each player takes a single, long turn. You keep playing until you roll a sum you can’t make, and then you add up the uncovered numbers to make your score. Pass the cards and dice to the next player. Whoever gets the lowest score wins the game.

Older students can add the jack (=11) and queen (=12) for a greater challenge.

Children may also enjoy playing Shut the Box as a solitaire game.

Plus or Minus: Players may choose to turn down either the sum or difference of the numbers on their dice. Subtraction offers more options near the end of the game, when there are only a few numbers left.

History

Shut the Box is a traditional English pub game, also known as Canoga, which may have been played as early as the twelfth century in Normandy. The “box” is a wooden tray with a row of numbers one to nine along the top length, each with a cover that can either slide or swing to hide the number. As a gambling game, each player would ante an agreed amount into a pool, which would be awarded to the winner.

 
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Math Game Monday: Power Up

This game gives students a fun reason to think about calculating with exponents.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Power Up

Math Concepts: powers (exponents).
Players: only two.
Equipment: one printed character sheet for each player, two six-sided dice, pencils or markers. Calculator optional.

The FREE 68-page printable (pdf) Prealgebra & Geometry Printables file features hundred charts, coordinate grids, assorted graph paper, and all the game boards for the Math You Can Play: Prealgebra & Geometry book.

Set-Up

Students create their own superheroes or supervillains using character sheets from the printables file or on regular notebook paper. Give your character a name and three superpowers, magical abilities, or technological gadgets. Describe the character’s powers:

• Greater Ability = …
• Lesser Ability = …
• Random Ability = …

Briefly explain your character’s origin story and draw a picture (optional).

How to Play

Each battle consists of three rounds, one for each of the superpowers. In the first round, players may choose which ability they want to use. For the second round, choose either unused power. Finally, the players call upon their remaining abilities.

Each player rolls one or two dice, as needed for their chosen superpower:

• Greater Ability: Roll one die. Use 4 as the base, your roll as the exponent.
• Lesser Ability: Roll one die. Use 3 as the base, your roll as the exponent.
• Random Ability: Roll two dice. Choose which is the base and which is the exponent.

Calculate how much damage your attack inflicts upon your opponent. Whoever does the most damage wins that round.

The player who wins two of the three rounds wins the battle. If there is a tie, fight one more round, with both players using their random ability.

Variations

Players get twelve base points to split between their character’s superpowers. For example, you might give one ability base 6 and both of the others base 3. A random ability (rolling two dice) costs four base points, so you could make all three superpowers random.

Power Team Assemble: Two teams of players battle each other. For each round, teammates multiply their individual scores to calculate the total damage they inflict.

History

Game creator John Golden writes:

“Note that it’s okay for heroes to fight heroes, as those kinds of misunderstandings happen all the time. Villains might fight another villain because they’re just so darn evil. (Or misunderstood.) Also, it’s okay to end in a tie: ‘We may have fought to a standstill, but I’ll get you next time, Snake Lady!’”

Read the delightful origin story for this game — including a cartoon battle between Captain Victory and the Snake Lady — at Golden’s Math Hombre blog.

 
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Math Game Monday: Next-Door Neighbors

This game builds number sense and a playful approach to math.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Next-Door Neighbors

Math Concepts: number properties, numbers within 100.

Players: two players, child and adult.

Equipment: printed hundred chart.

Set-Up

The free 50-page PDF Hundred Charts Galore! file offers many variations of hundred charts. Choose your favorite, or change it up each time you play.

How to Play

Ask your child to choose any two next-door neighbor numbers — that is, two numbers in side-by-side squares — but not to tell you which ones. Then the child should add the numbers and tell you the sum.

Can you show off your magical skills by identifying the original numbers? Just subtract one from the sum, and then divide that new number in half to find the smaller of your child’s two neighbor numbers.

It may take several tries for children to figure out this trick. After they get it, take turns adding neighbor numbers for the other person to guess.

Variations

Do you notice a pattern in the next-door neighbor sums? Will the total always be odd? Why, or why not?

What will happen if you add two apartment-house neighbors (one number above the other) — will the answer still be odd? Can you think of a “magic trick” pattern to identify the original numbers from their sum?

What about two numbers that sit diagonal to each other, touching at a corner?

Answers to the Puzzle

Teacher’s Tip: Don’t peek. Nobody likes a spoiler.
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Next-door neighbor sums are the same as the double of the smaller number, plus one. To find the original numbers, subtract that extra one and then divide the answer in half. That will give you the smaller of the two numbers.

The next-door neighbor sums are always odd because they are doubles-plus-one, which is the definition of an odd number.

Apartment-house neighbors are ten apart, numbers like 32 and 42. If someone tells you the sum, you can subtract that extra ten and then divide the result in half. That will give you the smaller of the two numbers — then add ten to get the larger number.

But numbers that sit diagonal to each other may be either nine or eleven apart. Since you don’t know which way the diagonal slants, there is no way to discover them just from their sum.

 
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Math Game Monday: Grid Fight

This game uses the area model to visualize and build understanding of integer multiplication.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Grid Fight

Math Concepts: integer multiplication, area model for multiplication.

Players: two players or two teams.

Equipment: printed gameboard or square grid paper, playing cards, pencils or colored markers.

The FREE 68-page printable (pdf) Prealgebra & Geometry Printables file features hundred charts, coordinate grids, assorted graph paper, and all the game boards for the Math You Can Play: Prealgebra & Geometry book.

Set-Up

Print a gameboard for the players to share. Or make your own gameboard on square grid paper: two 12 × 12 squares separated by a “zero” line.

Label one square positive (+) and the other negative (−). Choose which player or team will use the positive side of the gameboard grid and who takes the negatives.

Remove the face cards from your deck. Agree on which color represents negative numbers.

How to Play

Deal three cards to each player. Place the rest of the deck face down as a draw pile.

On each turn, both players make their move at the same time. Choose one card to play and hold it face down on the table in front of you. When both players are ready, turn up the chosen cards and multiply the numbers.

If the product is greater than zero, the positive player colors a rectangle of that size on the positive side of the grid. If the product is negative, that player colors a rectangle on the negative side.

Your goal is to fill in as many complete rows as you can, as in the game Tetris. But if you can’t fit your rectangle on the grid, you lose that turn.

Both players discard their used cards and draw to replenish their hands.

Play twelve turns. Whoever fills in the most rows wins the game.

Variations

Do you want a longer game? Play on both halves of the gameboard at once. Players may color their rectangle in either square (on their own side of the zero line) wherever they can fit it in. The game continues until the grids are so full that players lose three turns in a row.

History

I owe this game (and many others!) to the amazing John Golden. Visit his Math Hombre Games webpage for more ideas.

 
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Math Game Monday: Digit Disguises

This game requires students to make logical deductions about number relationships.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Digit Disguises

Math Concepts: addition, subtraction, multiplication, division, algebraic reasoning.

Players: two players or two teams. Best with teams.

Equipment: printed gameboards (optional), pencils and paper, or whiteboard and markers.

Set-Up

The FREE 68-page printable (pdf) Prealgebra & Geometry Printables file features hundred charts, coordinate grids, assorted graph paper, and all the game boards for the Math You Can Play: Prealgebra & Geometry book.

Each player or team needs a separate gameboard.

If you’re not using printed gameboards, each player or team makes a chart with two columns labeled Mine and Theirs. List the letters A–J in each column. Next to each letter in your own column, write one of the whole numbers 0–9 in any mixed-up order. Fold your paper to keep that column hidden from your opponent. Slip a paperclip over the fold for greater security.

How to Play

On your turn, ask for the result of a basic arithmetic calculation involving two different letters. For example, you might ask:

• A + B = ?
• C − D = ?
• E × F = ?
• G ÷ H = ?

But you may not ask for something like “I − I” or “J ÷ J.”

The other player/team figures out the answer to your question, using their values for each letter, but they do not tell you the number. If the answer is on their chart, they tell you the letter for that value. Or they tell you that the result is not one of their letters.

Players never say a number in response to a question. They only say a letter or “Not a letter.”

Write notes to help you remember each clue. You’ll need these to deduce your opponent’s number code.

Then it is their turn to ask you for a clue about your secret code.

When one player/team claims to have broken the opponent’s number code, the game is over. They read aloud the number values they have figured out. If they’re entirely correct, they win the game. But if any of the answers are wrong, the opponent wins.

Variations

Don’t end the game after the first code is guessed. Whether the guessing team won or lost, the other team keeps asking questions until they also break the code. If both teams fail, the game is a tie.

For Beginners: Start with only four unknown numbers, and allow players to give number answers in response to each question.

Keeper of the Code: (Mastermind-style) One player makes the code, and the other players try to crack it. Players take turns asking for clues, but they may discuss the answers and plan a strategy together. This variation is good for younger players, if you let them be the Keeper while older students or adults are guessing.

History

Math lecturer David Butler created this game and writes:

“I was struck by how quickly the logic got complicated, and then how quickly it all cascaded into finding everything when I finally got a few different numbers.”

Butler also shared a printable gameboard that can fold to stand on the table Battleship-style, hiding your secret code.

 
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Math Game Monday: Walter Joris’s Sequencium

This game takes strategic thinking and planning ahead, and it makes a great journaling prompt, too.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Walter Joris’s Sequencium

Math Concepts: strategic thinking.

Players: two players or two teams.

Equipment: blank paper, colored pencils or markers.

How to Play

Draw a 6 × 6 grid of squares as a gameboard for players to share. Each player needs a different color pencil or pen.

Players begin by each writing the number 1 in opposite corner squares. Then take turns writing numbers until the grid is full.

On your turn, choose a square that touches any of your own previously numbered squares at a side or corner. Write the number that is one greater than the square you are touching. Draw a short line to connect those two numbers.

Your number sequence may branch and may cross the opponent’s line. Each branch continues the counting sequence from whichever square it touches.

If your new square is touching more than one of your numbers, continue counting from the higher number. Whoever reaches the greatest number wins the game.

Variations

Use the game as a journaling prompt. Here are some sample questions:

• What is your strategy for winning?

• Do you think this is a fair game, or does one player have an advantage?

• How would you count score, so you could compare your performance from one game to the next?

• How would you modify the game rules? Is your version easier or harder than the original game?

• Do you prefer logical strategy games or games of chance? Or do the best games have a bit of both? Explain.

 
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Math Game Monday: Symmetry Challenge

This game builds visual thinking skills.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Symmetry Challenge

Math Concepts: symmetry, geometry.

Players: only two.

Equipment: graph paper or blank hundred chart, colored pencils or markers.

Set-Up

Each player will need a printed sheet of graph paper or a blank hundred chart. Draw a line that divides the page in half. Your line may be vertical, horizontal, or diagonal.

Or draw two lines that split the chart into fourths. With two lines of symmetry, the pattern will match in both directions: top reflects bottom, and left reflects right.

How to Play

With felt-tip markers or colored pencils, draw lines or fill in squares to make a pattern in one section (half or fourth) of your chart.

Trade papers with a friend. Can you complete each other’s puzzle? Whatever shapes you see on one side of a mirror line, draw their reflections on the other side.

Variation

Advanced Puzzle: Color shapes in different sections of the chart. Your shapes should not match each other symmetrically, but when all of them have been reflected across the line(s) of symmetry, they will create a finished design.

 
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Math Game Monday: Decimal Product Game

This game builds understanding of decimals, and also of the inverse relationship between multiplication and division.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Decimal Product Game

Math Concepts: multiplying decimals, decimal place value.

Players: two players or two teams.

Equipment: printed game board, colored markers or a set of matching tokens for each player, two paperclips or other small tokens to mark the factors.

Set-Up

The free 44-page PDF Multiplication & Fraction Printables file features two decks of mathematical model playing cards, plus hundred charts and all the game boards for the Math You Can Play: Multiplication & Fractions book.

How to Play

The first player places a paperclip on any one of the factors at the bottom of the board. The second player places the other paperclip on a factor — the same or different — and then marks the product of those two numbers by coloring the square or placing a token.

On each succeeding turn, a player moves just one paperclip to a new number and then marks the product of those two factors. If both players agree that all possible moves have already been colored in, the player whose turn it is may make a fresh start by moving both paperclips.

Whichever player marks four (or more) squares in a row — horizontally, vertically, or diagonally — wins the game. The squares must touch each other at edges or corners, with no gaps. If neither player can make four in a row, then the player who has the most sets of three in a row wins.

History

This variation on The Product Game comes from John Golden’s blog. He writes about his conversation with fifth-grade students:

“We discussed how to get hundredths. I think they knew on some level it was tenths times tenths, but had a bit of the ‘we haven’t been taught this yet’ syndrome. I used the analogy of a dime being a tenth of a dollar, so what’s a tenth of a dime?

“‘A penny!’

“And what part of a dollar is a penny? How many does it take to make one dollar? It is terrific that they are used to seeing one cent written as .01.”

 
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Math Game Monday: Bowling

This game builds calculations skills and helps develop fluency.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Bowling

Math Concepts: addition, subtraction, multistep calculation, column addition (for final score).

Players: any number.

Equipment: one deck of math cards, game board, ten tokens for covering numbers, pencil or pen, and (optional) scratch paper for adding up the scores.

Set-Up

You can print the bowling game board and score sheet from the Number Game Printables Pack, or draw your own game board and use the printable score sheets from the Apollo’s Templates website.

The 23-page printable (pdf) Number Game Printables Pack file includes hundred charts, graph paper, and game boards from the first two Math You Can Play books.

How to Play

Place the deck face down where all players can reach. When it’s your turn, roll your bowling ball by flipping up three cards. On your game board, cover the pins you knock down:

• The numbers on your cards.
• Any numbers you can make by adding or subtracting two cards.
• Any numbers you can make by adding and subtracting with all three of the cards. Each card may be used only once in each calculation.

For example, if you roll a two, four, and ace, you can cover those numbers and also:

• 3 = 4 − 1
• 7 = 1 + 2 + 4
• What else can you find?

If you cover all the numbers, you rolled a strike, and that’s the end of your turn. If you don’t cover all the numbers, discard those cards and turn up three more for your next ball. Can you cover the remaining numbers now? If so, that’s a spare.

Your score for each turn is how many numbers you cover, with special rules for strikes and spares as explained below.

After you roll two balls, the next player takes a turn. Keep going until each player has ten turns. If the draw pile runs out of cards, reshuffle the discards to replenish it.

How to Use the Score Sheet

The rules for keeping score in bowling seem confusing until you’ve played a few games. Each larger square box on the score sheet is called a frame and represents your score for one turn. The two (or three) smaller square boxes are for keeping track of each time you roll your ball.

One complete game of bowling consists of ten turns, with a maximum score of 300 points. You might think that with ten numbers to cover in each turn, the most you could score would be 100 points, but strikes and spares get bonuses.

For each turn, write down how many numbers you covered with your first ball in the first small box, or if you got a strike, mark an X there. If you threw a second ball, mark down how many more numbers you covered in the second small box, or if you got a spare, write a slash (/). If you did not get a strike or spare, add the numbers you wrote down and put that total score at the bottom of the frame.

A spare earns one bonus ball, and a strike earns two, which means you can’t finish scoring your frame yet. On your next turn, the balls you throw will count not only for their own frame but also as bonus points on your strike or spare. After you’ve thrown your next ball (or two balls, for a strike), add ten for the strike or spare plus the value of the bonus(es) and write in that total at the bottom of the unfinished frame.

Notice that the bonus balls get counted twice, once as part of the strike or spare and once for their own frame. And if you throw three strikes in a row, the third one will be counted three times:

• As the second bonus throw in the first strike frame.
• As the first bonus throw on the second strike.
• And finally as part of its own frame, along with its own bonus balls.

When you get to the last frame, you will see three small boxes. That’s because any players lucky enough to throw a strike or a spare still get their bonus balls. If you don’t get a strike or spare, ignore that third little box.

Finally, add up all the points from all ten frames to make your total score for the game.

 
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Math Game Monday: Area Battle

This game pushes students to consider area and perimeter beyond the basic shapes.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Area Battle

Math Concepts: area, square units, perimeter, regular and irregular polygons.

Players: two to four.

Equipment: homemade game cards, pencils or markers.

The FREE 68-page printable (pdf) Prealgebra & Geometry Printables file includes Area Battle card templates, along with all the game boards for the Math You Can Play: Prealgebra & Geometry book.

Set-Up

Students cut square grid paper into 5 × 5 squares. Each student creates a personal deck of eleven cards, as follows:

• Regular or irregular polygons, one with each shaded-in area: 1, 2, 3, …, 8, and 9 square units. The area must be easy to count, so build each polygon from a combination of squares and half-squares.
• Two additional polygon cards with areas of the player’s choice.

Claim your deck: Mark the back of each card with your insignia (initials, emoticon, math symbol, etc. — your choice). Decorate as desired, so long as it doesn’t bleed through the paper and obscure your polygons.

How to Play

Stack your card deck face down in front of you. Draw the top two cards for your hand.

On your turn, call “high” or “low” for whether the greatest or least area wins the trick. Then each player chooses a card from their hand and holds it face down. When all players are ready, turn the cards up, and the winner captures them all. Each player keeps a pile of prisoner cards.

In case of a tie, those players reveal their other card, and the longest perimeter takes the trick. If it’s still a tie, leave the cards on the table for the winner of the next trick.

Players draw one or two new cards to replenish their hands before the next turn.

The game ends when at least one player runs out of cards. Whoever has captured the most prisoners wins the game. Give the prisoner cards back to their owner, unless you are playing the Spoils of War variation.

Variations

In between games, players can make new cards. But they must always play with a deck that fits the rules: nine cards with the areas 1–9, plus two extras.

Perimeter Battle: On each turn, the low or high perimeter takes the trick. In case of a tie, the greatest area wins the second fight.

Spoils of War: If you win the game, you may claim one card from your prisoner pile to replace the matching card from your deck. Erase the identification and add your own symbol on the back. You may offer your old card to the losing player as a consolation prize, or keep it as a backup card.

History

When John Golden created and tested this game, the students gave it “universal thumbs up as to whether they would recommend it to other teachers. They were requesting time to play in class later, which is surely a good sign.”

 
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Math Game Monday: Codebreaker

This game challenges players to make logical deductions about number permutations.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Codebreaker

Math Concepts: permutations, logical deduction.

Players: two or more.

Equipment: paper and pencil, or whiteboard and marker.

How to Play

One player (the codemaker) thinks of a three-digit number between 000 and 999, writes this number on a piece of paper, and folds the paper to hide it. The other players (codebreakers) draw a two-column chart labeled Guesses and Clues. Players can each keep separate written records, or all may share a single chart on a whiteboard.

The codebreakers take turns guessing a three-digit number, which they record in the guess column. The codemaker responds with the appropriate clues:

• If one of the digits is the right number in the right place, say “There’s one number correct,” and draw a smiley face in the clues column. Do not tell which digit won the smiley.

• If one of the digits is a correct number but in the wrong place, say “There’s one number right, but it’s not where it belongs,” and draw an empty circle in the clues column.

• If more than one digit matches the secret code, tell the total number of correct and almost-right digits—and draw that many smiley faces and plain circles—but never reveal which digit matches which clue.

With two players, a round of play is two numbers, so each player has a chance to be the codemaker. Whoever breaks the code with the fewest guesses wins. For group play, whoever guesses the number gets to be codemaker for the next round.

Variations

For beginners, don’t allow repeating digits, and make it easier by using only the numbers 1–5. A secret number like 142 would be fine, but not 223. Advanced players can use four- to six-digit numbers and allow repetition.

Or try playing without paper, keeping track of guesses and clues in your head. This is a mind-bending challenge, but it can be done.

History

In the wee morning hours on a cross-country road trip, I made up the paperless version of Codebreaker to keep the driver awake. In my mind, it was a modification of the commercial board game Mastermind, but according to Wikipedia, similar guessing games with numbers or words date back at least a century.

 
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Math Game Monday: Math Model Rummy

This game builds conceptual understanding of multiplication or fraction models.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Math Model Rummy

Math Concepts: multiplication or fraction models.

Players: two or more.

Equipment: one deck of math model cards, or a double deck for four or more players.

Set-Up

You can work with your children to create a deck of math model cards, sketching the pictures on index cards or on a stack of old business cards with blank backs. Each deck should include 10–15 sets, or books. Take your time, making just two or three books each day while talking about real-life situations the models might symbolize. When you think the deck is finished, lay the cards out on the table in sets, to make sure each book has all its members.

Or take the quick route: download my free Multiplication & Fraction Printables file, which includes two decks of premade math model cards. Print the pages on card stock, and laminate for durability if desired.

Your card deck need not include every possible fraction or every math fact in the times tables. But it should offer enough variety to cement the most common multiplication models in your children’s minds. For example, my multiplication card deck includes products from 2×2 to 6×6. Each book consists of four cards — the multiplication equation or fraction, plus three pictures.

How to Play

Deal seven cards per player, and place the remaining cards face down as a draw pile. Turn up the top card of the deck to start the discard pile.

On your turn, you may either draw the top card from the deck or pick up the discard pile as far back as desired. But if you pick up more than the top discard, you have to meld the farthest-back card you take.

After drawing, you may meld — that is, place three or more matching cards face up on the table in front of you. If you have the fourth card in a set that has already been played (by any player), you may also lay that down in front of you.

Finally, put one card on the discard pile to end your turn. But if you discard a card that could have been played, any other player can call “Rummy!” and meld your discard.

If the deck runs out, take all the discards except the top one. Shuffle these cards and place them face down so the next player has a stack to draw from. Play continues until one player runs out of cards (either by laying them all down or by discarding the last one).

Scoring

Count each player’s score as follows:

• Each card played on the table is worth 5 points.
• For every card remaining in the hand, subtract 2 points.
• The player who went out gets a bonus of 15 points.

You may play a single hand, just for fun. Or play several hands, and the first player to reach 300 points wins the game. Or set a different point goal based on how long you want the game to last.

Variations

Floater: You must have a discard to end the game, and this must be a card that could not be melded. If you lay down all your cards without a discard, you become a floater. Continue to play your turn — drawing or picking from the discard pile and melding cards — until you can go out with a proper discard. (But it is illegal to pick up just the top discard and immediately discard it again.)

History

According to the Pagat website, Rummy-style games first appeared in the early twentieth century. Like many card games, Rummy picked up different flavors as it traveled from one player to another over the years. Feel free to modify the rules above to fit your family’s favorite way to play.

 
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Math Game Monday: Tax Collector

This game makes children think about multiplication and notice how prime numbers are special.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Tax Collector

Math Concepts: multiplication, prime numbers, factors and multiples.

Players: two or more players or two teams.

Equipment: blank paper or a printed hundred chart, pencils or markers. Calculator optional.

Set-Up

Choose a set of numbers (the more numbers, the longer the game) such as 1–30 or 1–100. Write the numbers at the top of your paper, so you can mark them out as they are used. Or use a printed hundred chart to mark numbers, keeping score in the margins or on scratch paper.

How to Play

One player is the tax collector, and all the others work together as a team of shop owners. Or the players on one team are tax collectors, and the other team entrepreneurs.

First, a shop owner marks any available number by crossing it out or coloring that square on the chart. Add this number to the running total of shop owner profits.

Once a number is marked by any player, it cannot be used again.

After each shop-owner turn, the tax collector marks all the factors of that number that have not been previously scored. Add these numbers to the running total of taxes.

Continue turns with shop owners claiming a profit amount and the tax collector looking for factors to tax. The game ends when the shop owners have no legal play — that is, there are no numbers with factors left. The tax collector claims all remaining numbers.

Whoever collects the most money (profit or tax) wins.

Warning: You must always pay the tax collector! No shop owner may mark a number that doesn’t have any factors remaining. If you try to claim a number with no factors, the tax collector takes that whole amount as a penalty.

Variations

The Factor Game: Alternate roles on each turn. The first player chooses a number, and the second collects the tax. Then the second player chooses a number, and the first one collects the tax. At the end of the game, neither player gets the unclaimed numbers.

Factor Blaster: Players alternate roles, as in the Factor Game, and they may choose any unmarked number — including numbers without factors for the other player to claim. In Tax Collector or the Factor Game, you may choose only one prime number (you’ll find out why as you play), but the lack of penalties in Factor Blaster makes the prime numbers into prime targets.

History

In Simply Great Math Activities: Number and Operations, authors Bill Lombard and Brad Fulton write:

“The tax collector usually wins the first game so handily that the students are left believing there is no way for them to win this game. However, assure them there are many ways for the taxpayer to win, and ask them to play another game.”

Teacher coach Terry Kawas created the Factor Blaster variation that emphasizes the importance of prime numbers, to prepare for teaching prime factoring.

 
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Math Game Monday: Greater Than

This game helps students make sense of those confusing rules about multiplication with inequalities.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Greater Than

Math Concepts: integer addition, integer multiplication, working with inequalities.

Players: two players or two teams.

Equipment: printed gameboard or sheet of paper, one deck of playing cards, pencils or markers.

The FREE 68-page printable (pdf) Prealgebra & Geometry Printables file features hundred charts, coordinate grids, assorted graph paper, and all the game boards for the Math You Can Play: Prealgebra & Geometry book.

Set-Up

Agree on which color represents negative numbers. Face cards count as ten, aces as eleven.

The suits also represent operations:

• Spades and hearts = add the number.
• Clubs and diamonds = multiply by the number.

Print a gameboard for players to share. Or prepare a scoresheet with three columns: one for each player’s running score, and a column in the middle for the inequality sign. Choose a player to deal the first hand.

How to Play

Deal four cards to each player or team. Players each choose one card as their initial value, holding the card face down in front of them. At the dealer’s signal, both players reveal their cards.

If the two cards played have the same value, players return them to their hands and choose a different starter card.

Write the players’ initial numbers in their columns. In the middle column, draw an inequality symbol (> or <) with its open end toward the greater value.

The non-dealer plays first. Choose one card from your hand and lay it on the table. Write the operation represented by that card in the first box of the next line on the gameboard (or beside the next line of the scoresheet). Then do the indicated calculation:

• If your card is a spade or heart, add the value to each player’s current score.
• If your card is a club or diamond, multiply each player’s score by that number.

Write the new sum or product in each player’s column on the scoresheet. Finally, draw the correct inequality symbol in the middle column.

A hand consists of two turns for each player, beginning with the non-dealer. So the dealer takes the next turn, playing a card, writing it at the start of the third line, and doing the calculations based on the values in the previous line. The non-dealer fills the next line, and the dealer plays the final line of that hand. Players do not draw new cards after each turn, so plan ahead how best to use the cards you have.

After the dealer’s second turn, whoever has the greater value wins that hand. Circle the winning score. Mix all cards back into the deck and pass it to the other player to deal the next hand.

The first player to win three hands wins the game.

Sample Game

Tony challenges Steve to a game of Greater Than. Tony deals the first hand, and the players reveal their initial cards. Tony plays the queen of hearts, for a value of −10. Steve has the eight of spades, for a value of +8.

As the non-dealer, Steve goes first. He plays the three of clubs and writes “×3” on the next row. Then he multiplies both scores by three and writes each product in that player’s column. He writes the less-than sign “<” to show that he’s in the lead.

Tony lays down the ten of spades, adding 10 to each score. Steve chooses the five of hearts, adding −5 to the scores. Steve still has the greater value, but Tony gets one more turn.

Tony plays the two of diamonds, which multiplies both scores by −2. Multiplying by a negative number changes the sign of the scores, and Tony wins the hand with 50 points.

Variations

House Rule: Does having the last play offer too great an advantage? Give the dealer one less card at the start of each hand.

Or add a level of risk to the game by having both players reveal their operation cards at the same time, as they did with their initial numbers. On each turn, choose a card and hold it face down until both players are ready. The card with the lesser value does its operation first. (And remember that −9 is less than +2.) This means the dealer may play before the non-dealer, depending on which cards they choose.

History

John Golden, who created this game, writes:

“I think this is a good educational game, but only close to a good strategy game. I can’t quite figure out what’s missing, so if you have a variation or adaptation to try, please let me know.”

If you think of a variation to share, post it in the comments on his original Math Hombre blog post:

• mathhombre.blogspot.com/2012/09/greater-than.html

 
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Math Game Monday: Dominoes

This classic family game is a great way to play with numbers and logical strategy.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Dominoes

Math Concepts: subitizing dot patterns, thinking ahead.

Players: two or more.

Equipment: one set of double-six or double-nine dominoes, or two sets for five or more players.

Set-Up

Turn all domino tiles (also called bones) face down on the table and mix them around. Each player draws several tiles, as follows:

• Two players draw seven tiles each.
• Three or four players draw five tiles each.
• Five or more players use a double set of dominoes and draw five each.

Set your tiles upright on their sides, so the other players cannot see them. These tiles are your hand, and the ones left on the table are called the wood pile (also known as the bone yard).

How to Play

Whoever has the highest double goes first, placing that tile face up on the table. If no doubles are available, turn everything face down, reshuffle, and draw again.

Play proceeds to the left around the table. Domino tiles are played end-to-end in a long row (the train), with only the outer ends available for adding new tiles. On your turn, you may play one of the tiles in your hand to either open end of the train if the dots (called pips) on one side of your tile match the tile on that end.

Doubles are placed crosswise to the direction of the train, with the middle of the domino touching its neighboring tiles. Players may not match tiles to the ends of the doubles, however, only to the middle of the other side, continuing the train in whichever direction it was growing.

If you have no tile that will play, draw one tile from the wood pile. If you can play that one, do so. Otherwise, add it to your hand. This marks the end of your turn. If you cannot play from your hand and there are no tiles left to draw, you must pass.

The first player to run out of tiles wins the game (or in Muggins, wins that round). If no player is able to go out, then all players add up the pips on their remaining tiles. The player with the smallest sum wins.

Variations

Domino games vary tremendously around the world, and even from one family to another within the same town. Whenever you play with friends, be sure to agree on the rules before you draw the first tile.

Cross Dominoes: Make a double train. After the first double tile is played, the next four tiles must match it. Two of these are placed normally, at the middle of each side of the first tile, and the other two connect to the ends. If players do not have a matching tile, they must pass. After the four matching tiles have made a cross shape, play continues normally, except in four directions instead of two.

Muggins: Play as for Cross Dominoes, but keep score as you go along. At the end of each turn, the player adds up the pips showing on the live tiles at all four ends of the train, including both halves of any exposed doubles. If these make a multiple of five, the player adds that number to his or her score. At the end of each round, players add up the pips remaining in their hands, round to the nearest five, and subtract those points from their total so far. The first player to reach 200 points (or some other agreed-upon total) wins the game.

Fives and Threes: Play as for Muggins, but score all multiples of three or five.

History (and a Puzzle)

Domino-like tile games seem to have originated in China, and they came to Europe through the great trading cities of Venice and Naples. Some game historians claim the European game was invented independently, because European domino sets are different from Chinese sets in several ways. (For instance, Chinese tiles come in suits, like a set of playing cards.) Dominoes spread across France and reached England in the late eighteenth century, where the game became a favorite pastime in British pubs.

Puzzle: Encourage your children to examine a set of domino tiles and describe what they notice. For example, every possible combination (double-0, 0|1, 0|2, etc.) is a single tile, but there are no duplicates: 0|1 is the same tile as 1|0.

Ask them, “If you bought a set of dominoes at a garage sale, how could you tell whether any of the tiles were missing? Can you figure out how many tiles there should be?”

Spoiler: To find the answer, make a systematic list, and be careful not to count any of the combinations twice. A double-six set should have twenty-eight tiles, and a double-nine set will have fifty-five. A new set from the store may contain extra blank tiles, which can be decorated with paint or white nail polish to replace lost pieces.

 
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Math Game Monday: Double Digit

This game pushes students to think more deeply about the meaning of place value.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Double Digit

Math Concepts: place value, addition.

Players: any number.

Equipment: six-sided die, pencil and paper for keeping score.

How to Play

Take turns rolling a die. Add that number to your score as either “ones” or “tens.” For example, if you roll 3, you can choose to add 3 or 30.

After everyone has seven turns, the player whose score is closest to 100 wins.

Optional challenge: Anyone who goes past 100 loses.

Variations

Use the game as a journaling prompt. Here are some sample questions:

• What is your strategy for winning?

• Do you think this is a fair game, or does one player have an advantage?

• How would you count score, so you could compare your performance from one game to the next?

• How would you modify the game rules? Is your version easier or harder than the original game?

• Do you prefer logical strategy games or games of chance? Or do the best games have a bit of both? Explain.

 
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Math Game Monday: Farkle

A great classic game for groups or family play.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Farkle

Math Concepts: addition to ten thousand, probability with dice.

Players: any number.

Equipment: six six-sided dice, pencil and paper for keeping score.

Set-Up

Optional: The Number Game Printables Pack includes a Farkle scoring guide. Cut the page in half and give one sheet to each player.

The 23-page printable (pdf) Number Game Printables Pack file includes hundred charts, graph paper, and game boards from the first two Math You Can Play books.

How to Play

On your turn, throw all six dice. If you like your score (see below for scoring), write it down and pass the dice to the player on your left. Or keep going. But beware: every time you roll the dice, you must set aside at least one scoring die. If none of the dice score, you have farkled, and you lose all the points you have accumulated that turn.

If you get all six dice to score, you have hot dice, and you may roll them all again to continue building up points. If you don’t farkle, then whenever you decide to stop rolling, add the points you have collected to your running total for the game. Writing down this score marks the end of your turn.

The first player to reach 10,000 points might win the game. But all the other players get one last chance to try and pass that score without farkling. Highest final score wins.

Scoring the Dice

There is often more than one way to score your dice, and you do not have to set aside every die that could score. Try to keep the highest score you can, while still leaving yourself as many dice as possible to throw again, thus decreasing your risk of a farkle.

Every roll is scored separately. If you set aside two ones and then get another one on your next throw, that does not count for 1,000 points.

Each 1 = 100 points
Each 5 = 50
Three 1s = 1,000
Three 2s = 200
Three 3s = 300
Three 4s = 400
Three 5s = 500
Three 6s = 600
Four of a kind = Double the score for three of them
Five of a kind = Double the score for four of them
Six of a kind = Double the score for five of them
Three pairs = 500
Straight (1-2-3-4-5-6) = 1,000
Two triples = 2,500

History

Farkle-style games have been played around the world for centuries, probably since dice were invented. Because of this, rule variants are common, so be sure that all players agree on which version you’re playing before the game begins.

 
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Math Game Monday: Decimal Point Pickle

This game challenges students to think strategically about the meaning of decimal numbers and place value.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Decimal Point Pickle

Math Concepts: decimals, place value, numerical order.

Players: any number.

Equipment: one deck of math cards, whiteboard and markers for each player, or pencils and blank paper.

Set-Up

Each player draws a path with ten spaces big enough to write in three-digit numbers. Decimal Pickle paths can be utilitarian or creative: a simple row of boxes, a curvy chain of circles, a series of stair steps, a caterpillar of ovals with legs, or a string of flowers with open centers for writing in. But every path needs to have ten spaces with a clear beginning and end.

If you draw the Pickle paths on paper, you can laminate these drawings or slip them into sheet protectors for repeated play. But if you make a new drawing each time, then the game can express the children’s personalities as their artistic skills develop.

How to Play

Remove the tens from the deck, but add the queens to represent zeros (or leave in the tens and count them as zeros). Shuffle the deck and place it face down where all players can reach.

On your turn, flip over the top card. If the card is black, stop flipping: that is your number. If the card is red, keep it and flip up an additional card. Again, if it’s black, you stop, but if it’s red, flip over one last card. You never flip more than three cards.

Now, arrange your card(s) to make a decimal number less than one. If you’ve drawn a single (black) card, you have no choice — for instance, if you draw a black seven, you must make .7. If you draw a red card and then a black card, you have two options — for instance, a red two and a black six lets you make either .26 or .62. Queens are zeros, so the smallest number you can make is a queen = .0, and the largest is three nines = .999.

Say your number, and write it into one of the spaces on your path. Always make sure the numbers increase from the beginning of your path to the end. If there’s no place to fit in your number and keep the least-to-greatest pattern, then you miss that turn.

Discard face up next to the draw pile. If you run out of cards in the draw pile, shuffle the discards to replenish it. The first person to fill a path, with all the numbers in order from least to greatest, wins the game.

Variations

Play that you always flip over two or three cards (color doesn’t matter). Or play without the three-card limit, so you might hit a 10-digit or longer decimal.

Or leave the 10s in the deck, letting them take two decimal digit places — so if you turn up a 7 and a 10, you could make the numbers .710 or .107. If you draw more than one 10 card, you may end up with a four-digit (or longer) decimal.

House Rule: Decide how strict you will be about the “increasing order” rule and repeated numbers. Can a player use both .6 and .60 as part of a valid train? Or will the player have to keep trying for new cards to replace one of the equivalents?

History

Blogger John Golden invented this version of the Number Train game.

• mathhombre.blogspot.com/2010/05/decimal-point-pickle.html

He writes:

“The fifth-grade came up with two names, Destination Elimination (which I like because it rhymes), and Decimal Pickle. This was suggested by a student whose answer for everything is ‘pickle.’ But here, it reminded me of a childhood game that none of the kids knew but kind of fits: the baseball game Pickle.

“As often with a new game, I played me vs. the class first. It was clear that the blackjack-esque possibility of extra cards was exciting, and they quickly got the idea that it was a big advantage. I didn’t castigate anyone for saying ‘point two three’ but often asked, ‘So how do you say that number?’”

 
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Math Game Monday: Scrambled Times Tables

If want to drill multiplication math facts, this game is one of my favorite ways to practice.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Scrambled Times Tables

Math Concepts: multiplication facts, times tables.

Players: any number.

Equipment: pencil and paper, optional printed blank hundred chart.

Set-Up

A scrambled times table is just like a regular times table, except the numbers at the top and along the side are all mixed up.

Print a blank hundred chart or draw a 10×10 grid. Draw the multiplication symbol in the top left corner.

The free 50-page PDF Hundred Charts Galore! file features printable 1–100 charts, 0–99 charts, bottom’s-up versions, multiple-chart pages, blank charts, game boards, and more.

How to Play

Write the numbers two to ten in the squares along the top and down the left-hand side, as above. But don’t write the numbers in counting order. Mix them up.

Can your child fill in the products on the scrambled chart? Each square should be the product of the numbers in the top and left-hand squares.

Be sure to let your child scramble a chart for you to solve, too.

Variations

For a more advanced puzzle, instead of writing numbers at the top and side of your chart, just write in several of the products. To solve this puzzle, your child must use those clues to decide where the scrambled factors go before he or she can fill in the rest of the chart.

For Further Play: In addition to making your own scrambled times tables for each other to solve, you may enjoy Iva Sallay’s blog Find the Factors. She offers a wide variety of puzzles rated from easy (level one) to challenging (level six), many with fun themes to encourage play.

• findthefactors.com

 
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Math Game Monday: Greedy Pig

This game tests each player’s risk tolerance as they roll dice to rack up points.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

This game tests each player’s risk tolerance as they roll dice to rack up points.

Greedy Pig

Math Concepts: addition, probability of dice rolls, strategic thinking.

Players: two or more.

Equipment: two 6-sided dice, pen and paper for keeping score.

How to Play

Players agree on a target score, such as 100. The first player to reach or pass the target wins the game.

Roll two dice as many times as you want, adding the numbers to your score. Stop when you wish, and pass the dice to the next player.

Beware: If you roll a 1 before you stop, you lose all the points you added during that turn. If you roll double-1, your score resets to zero.

Optional House Rule: If you roll doubles other than double-1, you have to roll again. You can’t end your turn on doubles.

Variation

Use the game as a journaling prompt. Here are some sample questions:

• What is your strategy for winning?

• Do you think this is a fair game, or does one player have an advantage?

• How would you count score, so you could compare your performance from one game to the next?

• How would you modify the game rules? Is your version easier or harder than the original game?

• Do you prefer logical strategy games or games of chance? Or do the best games have a bit of both? Explain.

History

Pig is a folk-game cousin to Farkle and was first described in print by American magician and author John Scarne in his 1945 book Scarne on Dice.

 
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Math Game Monday: The Number That Must Not Be Named

This challenging game stretches everyone’s working memory and offers children the delightful possibility of stumping an adult.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

The Number That Must Not Be Named

Math Concepts: addition, subtraction, multiplication, division, integers, fractions, factoring, powers and roots, prime numbers, and other number properties.

Players: two or more (a cooperative game).

Equipment: none.

Set-Up

Because all calculations are done mentally, players must agree on what types of numbers are allowed. For example, beginners may want to start with the positive whole numbers 1–100. As players gain experience, you can expand the range of possibilities.

How to Play

The first player names any number within the permissible range. Players take turns naming mathematical operations, performing each calculation mentally but never saying their answer aloud.

For example, suppose the first player names “15.” Turns may then proceed as follows, with the number changing as shown in parentheses:

• “Times two.” (30)
• “Divided by five.” (6)
• “Squared.” (36)
• “Subtract it from one hundred.” (64)
• “Square root.” (8)
• “Cube root.” (2)
• “To the fifth power.” (32)
• “Plus one.” (33)
• “Nearest prime number.” (31)
• etc.

Players try to show style by naming operations that haven’t been used, especially something particular to the current number. Since the last calculation left the number at thirty-one, you might say “plus sixty-nine.” This proves you’ve been paying attention and gives everyone’s brain a brief rest on the nice, round number 100.

If a player names a calculation that makes no sense or that takes the number outside the agreed-upon range, that player is out of the game.

At any time, one player may challenge another to name the current number. If the challenged player says the wrong number, that player drops out of the game. But if the answer is correct, then the challenger is out.

The game continues until only one player remains, or until the players decide to stop.

History

When I was a kid, our teachers used to make students keep up with a long chain of mental calculations. This game offers students a chance to fight back and see if they can stump the teacher.

I found the game on Joel David Hamkins’s blog. Your children may also enjoy his Rule-Making Game:

• jdh.hamkins.org/the-rule-making-game

 
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Math Game Monday: Countdown

This game helps students develop strategic thinking while practicing their subtraction skills.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Countdown

Math Concepts: subtraction within one hundred, thinking ahead.

Players: best for two.

Equipment: a hundred chart, penny or other token to mark your place.

Set-Up

The 23-page printable (pdf) Number Game Printables Pack file includes hundred charts, graph paper, and game boards from the first two Math You Can Play books.

Print your choice of hundred chart for players to share.

How to Play

Start with the penny on one hundred (or ninety-nine, if you prefer the 0–99 chart). The first player subtracts any amount from one to ninety-nine (ninety-eight on the alternate chart) and moves the penny to the new number.

On each succeeding turn, players subtract any amount from one up to twice as much as the previous move — but keep in mind that your opponent will then be able to subtract up to twice as much as you do.

The player who gets to zero wins the game.

Variations

The Calendar Game: The first player says any date in January. Then each player in turn increases either the month or the day (but never both at once) and says a new date later in the year. Whoever says December 31 loses the game.

History

Countdown can also be called Fibonacci Nim. It was originally described by M. J. Whinihan and is included in the book Winning Ways for Your Mathematical Plays, Volume 4, by Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy. I discovered it in an online lesson by Geoff Patterson.

Jim Pardun shared the Calendar Game in a comment on Dan Meyer’s Tiny Math Games blog post.

 
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Math Game Monday: Pattern Blocks Challenge

This cooperative game fosters vocabulary and geometric visualization skills.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Pattern Blocks Challenge

Math Concepts: geometric vocabulary, visualization.

Players: two or more (a cooperative game).

Equipment: pattern blocks.

How to Play

Players each take an assortment of pattern blocks and sit back-to-back on the floor. Or sit at a table with something tall between them to block their view of each other’s designs.

One player, the builder, creates a design with the blocks and tries to describe the design in words so the other players can duplicate it.

The player who comes closest to the exact design becomes the next builder.

Variation

Pattern Block Symmetry: Place a pencil, chopstick, or other straight object to act as a line of symmetry on the table or floor. One player places any block on the right-hand side of the line. The other matches it with a symmetric block on the left, and then places a new block for the first player to match. Continue building until both players agree the design is finished.

 
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Math Game Monday: Coordinate Gomoku

This is a fun and challenging logic/strategy game for upper-elementary and middle school. One of my favorites!

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Coordinate Gomoku

Math Concepts: ordered pairs, coordinate graphing (four quadrants).

Players: two players or two teams.

Equipment: dotty or lined square grid paper, different colored pencils or markers.

Set-Up

Players share one sheet of dotty or lined grid paper. Each player needs a different colored pencil or marker, and they may want to choose a symbol like X, O, star, or small triangle to make their marks perfectly distinct.

How to Play

The first player claims any dot on the grid by marking it with his or her symbol. If you are using lined graph paper, choose any place where two lines intersect.

This is the origin (0,0) for your game. Draw the horizontal and vertical lines (the x and y axes) that meet at that point.

On succeeding turns, you must name the coordinates of a point before you mark it. If you make a mistake naming the point, your opponent can give the correct (x,y) coordinates and mark it with their own symbol — and they still get to take their own turn.

The first player or team to mark five points in a horizontal, vertical, or diagonal row with no gaps wins the game.

Variations

House Rule: How do you want to handle overlines that have six or more points in a row? In traditional Gomoku, only an exact five-in-a-row line can win.

Swap2: Does the first player win too often? What you need is a variation on the “pie rule” — one person slices the pie, and the other gets first choice of piece. Reduce the first-player advantage with these starting moves, which are often used in tournament play. The first player marks two Xs and one O. The second player selects one of three options:

• Accept these moves and mark an O. Turns continue with the first player marking X.
• Take over the Xs, so the first player goes next with O.
• Or mark one additional X and O, then let the first player choose which letter to claim. Whoever plays O takes the next turn.

Words to Know

On a coordinate graph, the horizontal x-axis number line and the vertical y-axis number line meet at the point (0,0), called the origin. The origin is the point from which we measure all other coordinates.

Like zero on a number line, the origin is an arbitrary point. It can go anywhere on your paper.

The horizontal and vertical axes divide the coordinate plane into four areas called quadrants. In the first quadrant, both x and y coordinates are positive numbers.

If we draw the axes in the traditional position, so that the first quadrant is in the top right-hand section of the page, the other quadrants are numbered in order counterclockwise. What types of (x,y) numbers do you find in each quadrant?

History

Gomoku is a Japanese game played with stones on the Go board. Math teachers have played coordinate-graph Gomoku games with students for decades. The Nrich Maths website added the idea of letting the origin float to wherever the first point is marked.

 
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Math Game Monday: Sim

This game challenges students to plan ahead and think strategically.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Sim

Math Concepts: geometry, strategy.

Players: only two.

Equipment: colored pencils or markers, paper.

How to Play

Draw a circle. Add 6 dots spaced out around the circumference.

Each player needs a different colored pencil or marker.

Take turns drawing straight lines across the circle to connect two of the dots. The first person to complete a triangle in their own color with all three corners on the circle loses the game.

Variations

Use the game as a journaling prompt. Here are some sample questions:

• What is your strategy for winning?

• Do you think this is a fair game, or does one player have an advantage?

• How would you count score, so you could compare your performance from one game to the next?

• How would you modify the game rules? Is your version easier or harder than the original game?

• Do you prefer logical strategy games or games of chance? Or do the best games have a bit of both? Explain.

 
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Math Game Monday: Concentration with Math Model Cards

This game lays a great foundation for your child’s understanding of multiplication and fractions.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Concentration with Math Model Cards

Math Concepts: multiplication or fraction models, visual/spatial memory.

Players: any number.

Equipment: one deck of math model cards.

Set-Up

You can work with your children to create a deck of math model cards, sketching the pictures on index cards or on a stack of old business cards with blank backs. Each deck should include 10–15 sets (also called books). Each book consists of four cards — the multiplication equation or fraction, plus three pictures.

Your card deck need not include every possible fraction or every math fact in the times tables. But it should offer enough variety to cement the most common multiplication models in your children’s minds. For example, my multiplication card deck only includes products from 2×2 to 6×6, but students who master these models can extend the concepts to think about any calculation.

Take your time, making just two or three books each day while talking about real-life situations the models might symbolize. When you think the deck is finished, lay the cards out on the table in sets, to make sure each book has all its members.

The free 44-page PDF Multiplication & Fraction Printables file features two decks of mathematical model playing cards, plus hundred charts and all the game boards for the Math You Can Play: Multiplication & Fractions book.

Get Your Printables File ❱

Print either the Multiplication Models or Fraction Models card deck for this game.

How to Play

Shuffle the cards and lay them all face down on the table, spread out in a single layer. The cards may be placed in an array or arranged in a haphazard cloud, as long as no card covers any other card.

On your turn, flip two cards face up. If the cards match, representing the same product or fraction, then you get to take the pair. If they do not match, leave the cards showing for a few seconds so all players can see what they are. Then turn them face down and let the next player take a turn.

Keep the cards you capture in a personal score pile. When all the cards are claimed, whichever player has collected the most is the winner.

Variations

House Rule: How will you handle the frustrating cycle where a player turns up new cards and sees that one of them would match a previously exposed card, but the other player grabs that pair, leaving the first player to try unknown cards again next turn? At our house, if you find a pair, you get a free turn and can flip over two more cards — which means every player exposes new cards that the next player can use. Free turns expire when there are ten or fewer cards left on the table, to keep one lucky player from claiming all the last pairs.

Mixed Groups: When playing with a wide range of ages, let the younger players flip three cards per turn and keep any two that match.

Equivalent Fractions: Instead of matching the fraction and pictures exactly, players may take any two cards that name the same amount of stuff. A card labeled 3/6 can match with a picture of 2/4, since both of them are worth half of one whole thing.

History

Concentration is my favorite ice-breaker game for math club meetings because the game is quick to learn and easy to play in large groups. It is also a game that older children and adults can enjoy as much as the beginning students do. More than once, when my teenage daughter walked through the room where the younger children were playing, she asked to join in the game.

 
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Math Game Monday: Dinosaur Race

This game helps preschool children develop counting and number sense.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Dinosaur Race

Math Concepts: number symbols, counting beyond ten, number line.

Players: any number.

Equipment: subitizing cards, number line racetrack, small plastic dinosaur or other toy for each player.

Set-Up

Draw a straight path on paper or a manila file folder, either horizontal or slanted uphill (so the larger numbers will be higher). Divide the racetrack into twelve to twenty spaces large enough for small toys to rest in. Or glue squares of colored construction paper in a long line on poster board. Number the spaces in order, beginning with one.

Create subitizing cards by drawing 1, 2, or 3 dots on several index cards or cut-up squares of cardboard. Better yet, let your kids make them with dot markers (but make sure the dots don’t show through the back).

Turn the subitizing cards face down and spread them out to form a fishing pond. Do not use dice or regular playing cards. The number of squares moved each turn must be low enough to recognize at a glance, or else counting will distract the player from saying the track numbers in order.

How to Play

Each player should choose a small dinosaur or other toy and place it near the beginning of the racetrack. On your turn, draw a card and move your dinosaur that many spaces, saying each number as you land on it. Cards should be mixed back into the pond after each turn.

This is the most important rule: when moving their toys, players must say the number in each space. Repeating the numbers in order focuses the child’s attention and helps build number sense, a gut feeling for how numbers work, which is important to future learning.

The first player to reach the end of the path wins the race.

Variations

After children have played the game normally many times, try starting at the end of the path and counting down the number line.

Or use the game board for counting practice. Count pennies or dried beans onto the racetrack spaces, or write numbers on small plastic lids so children can match them to the board.

Whole-Body Counting: Draw a Dinosaur Race path outdoors with sidewalk chalk, or use colored painter’s tape along a hallway floor. Children can walk or jump along the line, saying the numbers as they go.

History

Counting up and down a number line forms a strong foundation for children’s understanding of arithmetic. Dinosaur Race is based on the research of Robert S. Siegler and Geetha B. Ramani, who studied how preschool children responded to a variety of games. Playing a number line game like Dinosaur Race for as little as an hour (in fifteen-minute segments spread out over a couple of weeks) made a dramatic difference in the children’s ability to learn and retain arithmetic facts, while similar games played on a round track or on a linear track without numbers produced no measurable change.

 
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