#prealgebra — Public Fediverse posts

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: 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: 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: 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: 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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I have a file of note on conics... I called it "Conics (Prealgebra)"

WTF prealgebra??????????????????????

Conics are not seen in prealgebra.

I probably meant precalculus and my brain farted.

:holdthepain:

#BrainFart #prealgebra #precalculus #math

Game: Target Number (or 24)

[Photo by stevendepolo via Flickr (CC BY 2.0).]

Math concepts: addition, subtraction, multiplication, division, powers and roots, factorial, mental math, multi-step thinking
Number of players: any number
Equipment: one deck of playing cards (face cards and jokers removed), pencils and scratch paper, timer (optional)

Set Up

All players must agree on a Target Number for the game. Try to choose a number that has several factors, which means there will be a variety of ways to make it. Traditionally, I start my math club students with a target of 24.

Shuffle the deck, and deal four cards face down to each player. (For larger target numbers, such as 48 or 100, deal five or six cards to each player.) The players must leave the cards face down until everyone is ready. Set the remainder of the deck to one side.

How to Play

• At a signal, all players pick up their hands and look at the cards. Each player tries to combine all four numbers in his hand to make the target number.
• Players may add, subtract, multiply, or divide the numbers in any order, but they may not put two cards together to make a two-digit number. With older students, allow using one card as an exponent on another. Factorials and the square root function may also help to spice up the game.
• Each card may be used only once in the calculation.

For example, if the target number was 24, and you were dealt a 4, 3, 7, and 9, you might try:
(9 × 3) – 7 + 4 = 24
or
(9 – 7) × 3 × 4 = 24
but not
(9 ÷ 3) × 4 = 24,
which ignores the 7 card.

• There is an element of chance to the deal. Some hands will not make the target number, no matter how you combine them.
• If after a few minutes, all players seem stumped, the dealer should give each player one more card. Then the players may use all five cards in their hands or choose any combination of four cards.
• On rare occasions, the dealer may have to deal another round of extra cards before any player can hit the target.

Endgame

When you figure out a way to make the target number, lay your cards face up on the table. Explain your calculation so the other players can check it.

The first player to make the target number, using at least four cards in legal arithmetic calculations, is the winner of that hand. Play several hands, scoring one point per hand, and the first player to score six point wins the game.

Variations

Target Race: To eliminate the element of chance, deal four cards face up in the middle of the table. All players use these cards, and whoever is the first to figure out how to calculate the target number wins that hand.

Target Number with Variables: For a faster-paced game, include the face cards in your deck, and let them work as variables. A face card in your hand may take any value that a number card might have, from 1 to 10.

Target Dice: Instead of cards, throw five dice on the table. All players try to combine the numbers showing on the dice to make the target number.

Timed Target Number: Give each player a piece of paper and a pencil or pen. Set the timer for an agreed-upon time, perhaps 10 or 15 minutes. Deal 8 cards face up on the table, and start the timer. Each player writes on a piece of paper all the ways he can combine any of these numbers to make the target number. Each card may be used only once in each calculation, but it may be reused in as many different calculations as you can think of. For example, if the target is 24, and a player wants to use the equation 3 × (4 + 4) = 24, there must be a 3 and two 4s on the table. Whoever comes up with the most (valid) ways to calculate the target number wins.

Target Solitaire: Play a solitaire game by dealing 8 cards face up and challenging yourself to find all the ways they can be combined to make your target number.

Comments

Peggy Kaye (Games for Math) suggests a game like my Timed Target Number variation, but for younger students. She deals out only 5 cards and sets the target number as 10.

I have also enjoyed the commercial version of Target Number, called the 24 Game, which uses special playing cards invented by Robert Sun. The game comes in a wide range of levels, allowing students to practice topics from simple addition and subtraction to fractions, decimals, and even algebra.

 
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