Math Concepts: basic facts of addition, multiplication.
Players: one.
Equipment: one deck of math cards (poker- or bridge-style playing cards with the face cards and jokers removed).
The best way to practice the math facts is through the give-and-take of conversation, orally quizzing each other and talking about how you might figure the answers out. But occasionally your child may want a simple, solitaire method for review.
In the land of Fantasia, where people communicate by crystal ball, Wizard Mathys has been placed in charge of keeping the crystal connections clean and clear. He decides to figure out how many different ways people might talk to each other, assuming there’s no such thing as a crystal conference call.
Mathys sketches a diagram of four Fantasian friends and their crystal balls. At the top, you can see all the possible connections, but no one is talking to anyone else because it’s naptime. Fantasians take their siesta very seriously. That’s one possible state of the 4-crystal system.
On the second line of the diagram, Joe (in the middle) wakes up from siesta and calls each of his friends in turn. Then the friends take turns calling each other, bringing the total number of possible connection-states up to seven.
Finally, Wizard Mathys imagines what would happen if one friend calls Joe at the same time as the other two are talking to each other. That’s the last line of the diagram: three more possible states. Therefore, the total number of conceivable communication configurations for a 4-crystal system is 10.
For some reason Mathys can’t figure out, mathematicians call the numbers that describe the connection pattern states in his crystal ball communication system Telephone numbers.
Hint: Don’t forget to count the state of the system when no one is on the phone crystal ball.
Feature photo at top of post by Christian Schnettelker (web designer) and wizard photo by Sean McGrath via Flickr (CC BY 2.0). This puzzle was originally featured in the Math Teachers At Play (MTaP) math education blog carnival: MTaP #76.
Math Concepts: sorting by attribute (card suits), counting up, counting down, standard rank of playing cards (aces low).
Players: two or more, best with four to six.
Equipment: one complete deck of cards (including face cards), or a double deck for more than six players. Provide a card holder for young children.
Deal out all the cards, even if some players get more than others. The player to the dealer’s left begins by playing a seven of any suit. If that player does not have a seven, then the play passes left to the first player who does.
After that, on your turn you may lay down another seven or play on the cards that are already down. If you cannot play, say, “Pass.”
Once a seven is played in any suit, the six and the eight of that suit may be played on either side of it, forming the fan. Then the five through ace can go on the six in counting-down order, and the nine through king can go on the eight, counting up. You can arrange these cards to overlap each other so the cards below are visible, or you can square up the stacks so only the top card is seen.
Students can explore prime and non-prime numbers with these free favorite classroom games:
For $15-20 you can buy a downloadable file of the beautiful, colorful, mathematical board game Prime Climb. Or pick up the full Prime Climb game box at Amazon.
Or you can try the following game by retired Canadian education professor Jerry Ameis:
Math Concepts: multiples, factors, composite numbers, and primes.
Players: only two.
Equipment: pair of 6-sided dice, 10 squares each of two different colors construction paper, and the game board (click the image to print it, or copy by hand).
On your turn, roll the dice and make a 2-digit number. Use one of your colored squares to mark a position on the game board. You can only mark one square per turn.
The first player to get three squares in a row (horizontal, vertical, or diagonal) wins. Or for a harder challenge, try for four in a row.
* * *
This game was featured in the Math Teachers At Play (MTaP) math education blog carnival: MTaP #79. Hat tip: Jimmie Lanley.
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“Math Games with Factors, Multiples, and Prime Numbers” copyright © 2015 by Denise Gaskins. Image at the top of the post copyright © Jimmie via flickr (CC BY 2.0).
Math Concepts: addition to thirty-one, thinking ahead.
Players: best for two.
Equipment: one deck of math cards.
Lay out the ace to six of each suit in a row, face-up and not overlapping, one suit above another. You will have one column of four aces, a column of four twos, and so on—six columns in all.
The first player flips a card upside down and says its number value. Then the second player turns down a card, adds it to the first player’s number, and says the sum.
Players alternate, each time turning down one card, mentally adding its value to the running total, and saying the new sum out loud. The player who exactly reaches thirty-one, or who forces the next player to go over that sum, wins the game.
Math Concepts: counting up to five, thinking ahead.
Players: two or more.
Equipment: none.
Each player starts with both hands as fists, palm down, pointer fingers extended to show one point for each hand. On your turn, use one of your fingers to tap one hand:
The last player with a live hand wins the game.
Six years ago, my homeschool co-op classes had fun creating this April calendar to hand out at our end-of-semester party. Looking at my regular calendar today, I noticed that April this year starts on Wednesday, just like it did back then. I wonder when’s the next time that will happen?
A math calendar is not as easy to read as a traditional calendar — it is more like a puzzle. The expression in each square simplifies to that day’s date, so your family can treat each day like a mini-review quiz: “Do you remember how to calculate this?”
The calendar my students made is appropriate for middle school and beyond, but you can make a math calendar with puzzles for any age or skill level. Better yet, encourage the kids to make puzzles of their own.
At home:
Post the calendar on your refrigerator. Use each math puzzle as a daily review “mini-quiz” for your children (or yourself).
In the classroom:
Post today’s calculation on the board as a warm-up puzzle. Encourage your students to make up “Today is…” puzzles of their own.
As a puzzle:
Cut the calendar squares apart, then challenge your students to arrange them in ascending (or descending) order.
If you like, you may use the following worksheet:
Submission details here: Kids’ Project — More Math Calendars?
Unending digits …
Why not keep it simple, like
Twenty-two sevenths?—Luke Anderson
Encourage your students to make their own Pi Day haiku with these tips from Mr. L’s Math:
And remember, Pi Day is also Albert Einstein’s birthday! Check out this series of short videos about his life and work: Happy Birthday, Einstein.
CREDITS: Today’s quote is from Luke Anderson, via TeachPi.org. Background photo courtesy of Robert Couse-Baker via Flickr, text added (CC BY 2.0).
From Numberphile: “How accurately can we calculate Pi using hundreds of REAL pies? This video features Matt Parker, who believes this is the world’s most accurate pie-based Pi calculation.”
Pi Day is coming soon. Maybe you’d like to try a pi project with your family? Check out my Pi Day Roundup of links.
I found this delightful animation today:
The ball is traveling around a shape that can’t exist in our real world: the Penrose triangle. This illusion is the basis for some cool art, like Escher’s Waterfall. And I’m using it in my Math You Can Play books as a design on the back of my playing cards:
Here’s a few links so you can try it for yourself:
I’ve sent the first two Math You Can Play books to a copy editor (she edits the text part), so my focus this month is on finishing the illustrations and downloadable game boards. And designing the book covers — I think I’ll call this latest iteration done.
If everything stays on schedule, both Counting & Number Bonds and Addition & Subtraction should be available by mid- to late-spring. Fingers crossed…
