Call it a math club or math circle, the name didn’t matter, but the activity was always fun. We did non-schooly games and projects, and the kids enjoyed both the camaraderie and the experience of thinking hard in a stress-free setting.

If you’d like to pull together a math club/circle of your own, here are some tips.

Today’s puzzle involves an unusual teacher trying to collect students to participate in a group activity…

The Original Story

It appears that an ingenious or eccentric teacher, as the case may be, desirous of bringing together a number of older pupils into a class he was forming, offered to give a prize each day to the side of boys or girls whose combined ages would prove to be the greatest.

Well, on the first day there was only one boy and one girl in attendance, and, as the boy’s age was just twice that of the girl’s, the first day’s prize went to the boy.

The next day the girl brought her sister to school. It was found that their combined ages were just twice that of the boy, so the two girls divided by prize.

When school opened the next day, however, the boy had recruited one of his brothers. It was found that the combined ages of the two boys were exactly twice as much as the ages of the two girls, so the boys carried off the honors that day and divided the prize between them.

The battle waxed warm now between the Jones and Brown families, and on the fourth day the two girls appeared accompanied by their elder sister; so it was then the combined ages of the three girls against the two boys. The girls won, of course, once more bringing their ages up to just twice that of the boys.

The struggle went on until the class was filled up, but our problem does not need to go further than this point. Tell me the age of that first boy, provided that the last young lady joined the class on her twenty-first birthday.

[By Sam Loyd, quoted by Martin Gardner in Mathematical Puzzles of Sam Loyd.]

Math for Young Children

It makes me wonder what the teacher intended to do with his students when he first gathered them.

Perhaps he had in mind some of the activities from the Early Family Math website, or Maria Droujkova’s and Yelena McManaman’s book Moebius Noodles?

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

Writing to Learn Math: Problem-solving cares less about whether an answer is right and more about whether a solution makes sense.

Do you want your children to develop the ability to reason creatively and figure out things on their own?

Help kids practice slowing down and taking the time to fully comprehend a math topic or problem-solving situation with these classic tools of learning: Notice. Wonder. Create.

Notice: Look carefully at the details of the numbers, shapes, or patterns you see. What are their attributes? How do they relate to each other? Also notice the details of your own mathematical thinking. How do you respond to a tough problem? Which responses are most helpful? Where did you get confused, or what makes you feel discouraged?

Wonder: Ask the journalist’s questions: who, what, where, when, why, and how? Who might need to know about this topic? Where might we see it in the real world? When would things happen this way? What other way might they happen? Why? What if we changed the situation? How might we change it? What would happen then? How might we figure it out?

Create: Create a description, summary, or explanation of what you learned. Make your own related math puzzle, problem, art, poetry, story, game, etc. Or create something totally unrelated, whatever idea may have sparked in your mind.

Math journaling may seem to focus on this third tool, creation. But even with artistic design prompts, we need the first two tools because they lay a solid groundwork to support the child’s imagination.

How To Use a Problem-Solving Prompt

When children face a tough math problem, their attitude can make all the difference — not so much their “I hate homework!” attitude, but their mathematical worldview. Does your child see math as answer-getting or as problem-solving?

Answer-getting asks “What is the answer?”, decides whether it is right, then forgets it and goes on to the next question. Problem-solving cares less about whether an answer is right and more about whether a solution makes sense.

Students who care about problem-solving want to explore the web of interrelated ideas they discovered along the way: How can they recognize this type of problem? Can this one help them figure out others?

What could they do if they had never seen a problem like this one before? How would they reason it out?

Why does the formula work? Where did it come from, and how is it related to basic principles?

What is the easiest or most efficient way to manipulate the numbers? Does this help the problem-solver see more of the patterns and connections within our number system?

Is there another way to approach the problem? How many ways can they think of? Which do they like best, and why?

Journaling Prompt 89: Candy Puzzle

You are working for a chocolate factory. You need to design a box to hold 48 candies.

 

How will you arrange the box? Can you find more than one way?

 

What would be the hardest number of candies to package? Why?

And puzzles are great for teaching, too!

Here is a puzzle from a master of mathematical ingenuity…

Dudeney’s Cross of Cards

In this case we use only nine cards — the ace to nine of diamonds. The puzzle is to arrange them in the form of a cross, exactly in the way shown in the illustration, so that the pips in the vertical bar and in the horizontal bar add up alike.

In the example given it will be found that both directions add up 23.

What I want to know is, how many different ways are there of rearranging the cards in order to bring about the result ?

It will be seen that, without affecting the solution, we may exchange the 5 with the 6, the 5 with the 7, the 8 with the 3, and so on. Also we may make the horizontal and the vertical bars change places. But such obvious manipulations as these are not to be regarded as different solutions. They are all mere variations of one fundamental solution.

Now, how many of these fundamentally different solutions are there?

The pips need not, of course, always add up 23.

[From Amusements in Mathematics, H. E. Dudeney, Thomas Nelson and Sons, 1917.]

Play with the Puzzle

When you solve a mathematical puzzle, that’s never the end of the story. You can always find more ways to play with the ideas.

For example, Dudeney’s next puzzle asks a couple of new questions:

• How many different ways can you arrange the cards in a solution without making a fundamentally different answer?
• How many total possibilities are there to solve the puzzle, counting every arrangement as different?

And those two questions led me to wonder:

• How many ways could you arrange the cards in this cross pattern, without worrying about their sums?
• If you put cards into the cross pattern at random, what is the chance your arrangement would solve the puzzle?

What questions can you ask?

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.

Writing to Learn Math: Math journal explanations avoid the formality that turns so many students away from geometry proofs.

Do you want your children to develop the ability to reason creatively and figure out things on their own?

Help kids practice slowing down and taking the time to fully comprehend a math topic or problem-solving situation with these classic tools of learning: Notice. Wonder. Create.

Notice: Look carefully at the details of the numbers, shapes, or patterns you see. What are their attributes? How do they relate to each other? Also notice the details of your own mathematical thinking. How do you respond to a tough problem? Which responses are most helpful? Where did you get confused, or what makes you feel discouraged?

Wonder: Ask the journalist’s questions: who, what, where, when, why, and how? Who might need to know about this topic? Where might we see it in the real world? When would things happen this way? What other way might they happen? Why? What if we changed the situation? How might we change it? What would happen then? How might we figure it out?

Create: Create a description, summary, or explanation of what you learned. Make your own related math puzzle, problem, art, poetry, story, game, etc. Or create something totally unrelated, whatever idea may have sparked in your mind.

Math journaling may seem to focus on this third tool, creation. But even with artistic design prompts, we need the first two tools because they lay a solid groundwork to support the child’s imagination.

How To Use an Explanation Prompt

Math journal explanations avoid the formality that turns so many students away from geometry proofs. These informal “reason-poems” drive at the heart of a student’s understanding. How did they figure this out? Why does their method work? Is the pattern they found real or just a temporary coincidence? How do they know?

When you run out of creative journaling ideas, you can always go back to the basic mathematical question: “Why?”

For older students, challenge them to explain a concept so that a kindergarten student or second grader could understand. That’s more difficult than it sounds, but the attempt forces students to clarify their own ideas about the topic.

Journaling Prompt 294: Math Eyes

Imagine you have special glasses that let you see everything through the lens of math. Choose an item from your room or something in your house.

 

Don’t tell what it is, but describe it using as much math as you can. Think about measurements, shape, position, designs or patterns, motion, etc.

 

Extra challenge: Read your description to someone. Can they identify the object?

Back when my children were young, the original Primary Math series from Singapore was one of my favorite math curricula. I tweaked our school program constantly, so none of my kids had the same education, but three of them spent a good part of their elementary years in those books.

And I followed the Math in Singapore 2007 blog for its single season of publication. The blog has gone the way of many others, preserved only in the Internet Archive.

In the post I re-discovered, Patsy Wang-Iverson was reporting on a week-long seminar organized by Celine Koh, who offered the following problems (adapted from school exams and study books) for teacher discussion.

How many can you solve?

The Puzzles

Grade 3

A mechanic fixed 12 wheels to 5 bicycles and tricycles.

How many of them were bicycles and how many were tricycles?

Grade 3/4

Mrs. Tan is 31 years old and her daughter is 13 years old.

How many years ago was Mrs. Tan 3 times as old as her daughter?

Grade 4/5

Jane used 880g of a packet of sugar to bake a cake and 1/10 of the remaining sugar to make jelly.

She then had 3/7 of the packet of sugar left.

How much sugar was in the packet at first?

Grade 5/6

Tim and Sally each have some money.

If Tim spends $80 per day and Sally spends $40 per day, Tim will have $500 left when Sally has spent all her money.

If Tim spends $40 per day and Sally spends $80 per day, Tim will have $1100 left when Sally has spent all her money.

Find the amount of money Sally has.

Grade 5/6

Four toy cars cost as much as 3 dolls.

Five toy cars cost $3.50 more than 2 dolls.

Clare spent $14 on equal number of toy cars and dolls. How many toy cars did she buy?

Grade 5/6

John has a tank of fish.

The number of guppies is 25% of the total number of fish in the tank.

He buys as many guppies as he had.

Find the percentage of the angel fish now in the tank.

Grade 5/6

A jar contained some chocolates and sweets.

At first, the number of chocolates was 60% of the sweets.

After adding in another 10 chocolates and 10 sweets, the number of chocolates becomes 80% of the number of sweets.

How many sweets were there at first?

Grade 5/6

Class A and Class B have the same number of pupils.

The ratio of the number of boys in Class A to the number of boys in Class B is 3:2.

The ratio of the number of girls in Class A to the number of girls in Class B is 3:5.

Find the ratio of the number of boys to the number of girls in Class A.

Grade 6

The number of 20-cent coins to the number of 50-cent coins in a box was 3:2.

Lyn took out four 50-cent coins and replaced them with 20-cent coins of the same value.

After that the ratio of the number of 20-cent coins to the number of 50-cent coins became 7:2.

How much money was there in the box?

Grade 6

There are two bags of stones labelled A and B.

In Bag A, there are 350 black stones and 500 white stones.

In Bag B, there are 400 black stones and 100 white stones.

How many black and how many white stones should be transferred from Bag B to bag A so that 50% of the stones in Bag A and 75% of those in Bag B are black?

The Answers

The cool thing about math is that you really don’t need an answer key. Just put your numbers back into the original problem to check whether they make sense.

I’m a Bit Rusty

I did fine on the first two problems, but I stumbled a bit on the 4/5th-grade “How much sugar…” problem. Got it in the end, but it took some thought.

Tim and Sally threw me for a bit, because I made an arithmetic mistake in checking my first answer. So then I did the problem again with a different approach, only to get the same “wrong” answer. So I went back, found my misstep, and everything checked out.

Then the toy cars were tricky, but manageable. When I checked my answer, I saw a different approach that would been much easier.

After that, the guppies felt like a walk in the park. (Or, maybe, a swim in the kiddie pool?)

I misread the problem with the chocolate and sweets at first — I think of chocolates as a sub-category of sweets, but in this problem they are totally different. (Perhaps “sweets” are what I would call “hard candy”?)

Finally, I resorted to algebra for three of the last four questions.

Since algebra isn’t allowed, I guess that makes me smarter than a 4th grader, but only about mid-way through 5th grade?

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

Writing to Learn Math: When students create their own math, they forge a personal connection to mathematical concepts and relationships. And it’s fun!

Do you want your children to develop the ability to reason creatively and figure out things on their own?

Help kids practice slowing down and taking the time to fully comprehend a math topic or problem-solving situation with these classic tools of learning: Notice. Wonder. Create.

Notice: Look carefully at the details of the numbers, shapes, or patterns you see. What are their attributes? How do they relate to each other? Also notice the details of your own mathematical thinking. How do you respond to a tough problem? Which responses are most helpful? Where did you get confused, or what makes you feel discouraged?

Wonder: Ask the journalist’s questions: who, what, where, when, why, and how? Who might need to know about this topic? Where might we see it in the real world? When would things happen this way? What other way might they happen? Why? What if we changed the situation? How might we change it? What would happen then? How might we figure it out?

Create: Create a description, summary, or explanation of what you learned. Make your own related math puzzle, problem, art, poetry, story, game, etc. Or create something totally unrelated, whatever idea may have sparked in your mind.

Math journaling may seem to focus on this third tool, creation. But even with artistic design prompts, we need the first two tools because they lay a solid groundwork to support the child’s imagination.

How To Use a Create-Your-Own-Math Prompt

When students create their own math, they forge a personal connection to mathematical concepts and relationships. And it’s fun!

Children might make up a math game, write a story or poem, draw a comic, or pose a problem. Create math art, think up a challenging question, or write a puzzle. Since earlier chapters focused on writing and math art, most of these prompts involve creating puzzles or problems.

The “Story Problem Challenge” is one of my favorite math club activities. My students invent their own word problems in any style they like. They don’t have to know how to solve the problems they create. We read the stories aloud, and everyone works together to find the solutions.

For puzzles where the child already knows the answers (for example, “Two Truths and a Lie”), let them trade with a friend. Can they each solve the other’s puzzle? Can they stump each other? Or save the child’s work and let them come back to it another day, after they’ve forgotten the answers.

And when students create something they’re proud of, let them share it with the world. Visit the Student Math Makers Gallery at tabletopacademy.net/math-makers to share your children’s math creations.

Journaling Prompt 97: Bus Puzzles

A bus can hold ___ people. It starts out empty (except for the driver). At the first stop, ___ people get on. At the next stop…

 

Write a story for the bus.

 

What math questions might you ask about your story?

A wooden cube that measures 3 cm along each edge is painted red. The painted cube is then cut into 1-cm cubes as shown below. How many of the 1-cm cubes do not have red paint on any face?

Create Your Own Math

And then he challenges us as teachers:

This is strategically placed at the end of a right-hand page, and I was able to resist turning to read on. I came up with a list of 15 other questions that could have been asked — some of which I used in my Alexandria Jones stories.

Lechner wrote only seven elementary-level problems, and yet his list had at least two questions that I had not considered.

How many can you come up with?

For hints on creating your own list, read Jonathan Halabi’s How to modify problems—an example.

My Favorite Puzzles

Several of the puzzles I created grew from my experience with MathCounts problems about combinatorics and probability — topics that weren’t in the curriculum during my schooldays, but which I now thoroughly enjoy.

• If I choose one of the small cubes at random and toss it in the air, what is the probability that it will land red-painted side up?

• If I tossed all the small cubes in the air, so that they landed randomly on the table, how many cubes should I expect to land with a painted face up?

• If I put all the small cubes in a bag and randomly draw out 3, what is the probability that at least 3 faces on the cubes I choose are painted red?

• If I put the small cubes in a bag and randomly draw out 3, what is the probability that exactly 3 of the faces are painted red?

The amazing thing to me was that I’ve learned enough in my years of math coaching to actually solve the problems I made up. Well, at least, I was able to get answers that seemed reasonable to me. I would love to hear what you come up with, as a “reality check” on my own calculations.

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.

Writing to Learn Math: What did the author mean? Put the thought in your own words. Do you agree or disagree? Why?

Do you want your children to develop the ability to reason creatively and figure out things on their own?

Help kids practice slowing down and taking the time to fully comprehend a math topic or problem-solving situation with these classic tools of learning: Notice. Wonder. Create.

Notice: Look carefully at the details of the numbers, shapes, or patterns you see. What are their attributes? How do they relate to each other? Also notice the details of your own mathematical thinking. How do you respond to a tough problem? Which responses are most helpful? Where did you get confused, or what makes you feel discouraged?

Wonder: Ask the journalist’s questions: who, what, where, when, why, and how? Who might need to know about this topic? Where might we see it in the real world? When would things happen this way? What other way might they happen? Why? What if we changed the situation? How might we change it? What would happen then? How might we figure it out?

Create: Create a description, summary, or explanation of what you learned. Make your own related math puzzle, problem, art, poetry, story, game, etc. Or create something totally unrelated, whatever idea may have sparked in your mind.

Math journaling may seem to focus on this third tool, creation. But even with artistic design prompts, we need the first two tools because they lay a solid groundwork to support the child’s imagination.

How To Use a Quotation Prompt

Let students choose how they want to react to the quotation. Or offer one of the following questions:

• What did the author mean? Put the thought in your own words.
• Do you agree or disagree? If you agree, can you think of someone who would disagree? Why?
• Is this quote a general principle, or only for specific situations? Describe a time when it might apply, or when it might not.
• Tell a time in your life when you lived up to the quotation — or when you wish you had.
• How does the quote relate to math, science, history, or another subject?

Short exercises are great writing practice. But occasionally you’ll want to assign deeper essay topics, such as:

• Look up the author’s name online. Who are/were they, and why do people care what they said?
• Quotes are often misattributed. Did the author really say this?
• What have others said about the same topic? Search out a variety of quotes related to this one. How are they similar? How are they different?
• Does thinking about the quotation make you want to change anything, in yourself or in the world? How could you put that idea into action?

Quotation from Dan Finkel

Somehow, a big part of the experience of math is trouble. Frustration is the status quo. But when you get something—the thrill!

—Dan Finkel

My book business had been on hiatus for nearly 15 years, as I focused on homeschooling five children. I posted on forums and blogged off and on, but the old books fell into (not entirely undeserved) oblivion.

Now my older kids were moving out into their adult lives, and I’d begun to think about publishing again. I dusted off the old manuscripts to see what could be salvaged and began my adventure of indie publishing.

And all the gurus agreed, every author needed an email newsletter.

Share a playful math activity every month? Sure I could do that!

So while I revised and edited the manuscript for Let’s Play Math, to be published in paperback that fall, I launched my first “Playful Math” email, with an idea that’s still fun all these years later: Play math on your calendar.

For Elementary Children

Any internet search can turn up a variety of printable calendars. Choose your favorite.

Young children can use the calendar as a number line to do addition and subtraction beyond what they might normally handle. Look for addition and subtraction patterns:

• 3 + 5 = ? Now go to 13 + 5, and 23 + 5.
• What do you notice?
• What do 11 − 7, 21 − 7, and 31 − 7 have in common?
• Take turns finding and describing patterns.

Older children can practice their times tables:

• Mark the numbers you hit when you count by 2.
• What pattern do they make?
• Make the counting-by-3 pattern, or mark the 7s, etc.
• Which counting-by patterns are your favorites?
• What happens if you start at a weird number, like counting by 6s but starting at 5?

What other patterns can you discover?

Algebra “Magic” Patterns

Try some of Cynthia Lanius’s algebra calendar puzzles…

The Basic Square: Ask a friend to secretly choose four calendar dates that all touch each other and form a square. (For example, 18, 19, 25, and 26.) The friend should add those four numbers together and tell you the sum.

Then you “magically” identify the dates!

(Your secret: Divide the sum by 4, then subtract 4. The answer is the first date of your friend’s square.)

The Advanced Square: For a tougher puzzle, ask your friend to make a square with nine dates, three rows of three. (For example, 11–13, 18–20, and 25–27.) Again, secretly add the numbers and say only the sum.

Again, you can “magically” find their chosen dates.

(This time, divide the sum by 9. That answer is the center date of your friend’s square.)

• Using what you know about calendar patterns, can you explain WHY the calendar magic works?

Don’t peek! But the answers are here:

• Fun with Calendars
  (the Basic Square)
• More Fun with Calendars
  (the Advanced Square)

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.

Writing to Learn Math: Number play doesn’t have to follow school math methods.

Do you want your children to develop the ability to reason creatively and figure out things on their own?

Help kids practice slowing down and taking the time to fully comprehend a math topic or problem-solving situation with these classic tools of learning: Notice. Wonder. Create.

Notice: Look carefully at the details of the numbers, shapes, or patterns you see. What are their attributes? How do they relate to each other? Also notice the details of your own mathematical thinking. How do you respond to a tough problem? Which responses are most helpful? Where did you get confused, or what makes you feel discouraged?

Wonder: Ask the journalist’s questions: who, what, where, when, why, and how? Who might need to know about this topic? Where might we see it in the real world? When would things happen this way? What other way might they happen? Why? What if we changed the situation? How might we change it? What would happen then? How might we figure it out?

Create: Create a description, summary, or explanation of what you learned. Make your own related math puzzle, problem, art, poetry, story, game, etc. Or create something totally unrelated, whatever idea may have sparked in your mind.

Math journaling may seem to focus on this third tool, creation. But even with artistic design prompts, we need the first two tools because they lay a solid groundwork to support the child’s imagination.

How To Use a Number Play Prompt

Number play doesn’t have to follow school math methods. Remember the Math Rebel rule: A student may write anything that is true or that makes sense.

Most number play prompts offer nearly infinite variation. Change the numbers in the description, and wherever there is a blank you may put in any number you like. Each time you revisit the puzzle, it’s new again.

Older students may experiment with fractions, decimals, or exponential notation. Or try numbers in another base — do the patterns they found hold up when they change the way they count? Can they express these patterns with algebra?

Journaling Prompt 8: Triangular Numbers

You’ve heard of square numbers. Triangular numbers are their smaller cousins.

 

Arrange dots in a bowling-pin pattern. Count the dots to find the triangular number: one dot in the first row (T1 = 1), two in the second row (T2 = 1 + 2), three in the third row (T3 = 1 + 2 + 3), etc.

 

Keep adding more dots. Each row is one dot longer than the previous row. How many triangular numbers can you find?

 

Do you see any patterns? Can you think of any questions to ask?