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.

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 299: Farmer’s Market

Mr. Tam had 480 more pears than apples at his fruit stand. Then he sold half of each type of fruit. Now he has four times as many pears as apples.

 

How many apples did he start with?

 

Make up a farmer’s market puzzle of your own.

Today I’m sharing a few treats from The Moscow Puzzles by Boris Kordemsky, which mixes classic brainteasers and original stumpers.

Recreational math expert Martin Gardner called Kordemsky’s book “the outstanding puzzle collection in the history of Russian mathematics.”

Have fun playing logic with your kids!

A Weather Forecast

It is raining at midnight—will we have sunny weather in 72 hours?

Shoes and Socks

I went to the closet while my sister was asleep, so I left the light off.

I found my shoes and socks, but I must confess they were in no kind of order—just a jumbled pile of 6 shoes of three brands, and a heap of 24 socks, black and brown.

How many shoes and socks did I have to take with me to be sure I had a pair of matching shoes and a pair of matching socks?

Apples

Three kinds of apples are mixed in a box. How many apples must you take to be sure of at least 2 apples of one kind? At least 3 apples of one kind?

Arbor Day

On Arbor Day the Young Pioneers of the fourth grade started early and planted 5 trees before the sixth-graders came. But they planted them on the side assigned to the sixth grade.

The fourth-graders had to cross the street and start over, so the sixth-graders finished first. To pay their debt, they crossed the street and planted 5 trees. They planted 5 more trees, and all the work was finished.

Were the sixth-graders ahead by 5 or 10 trees?

[Both rows of trees were the same length.]

A Purchase

“Your pencils, notebooks, and colored paper cost $1.70.”

“I bought 2 pencils at 2 cents each and 5 pencils at 4 cents each—and 8 notebooks and 12 sheets of colored paper, I don’t remember the prices. But the bill can’t be $1.70.”

Why not?

A Crime Story

An elementary school teacher in New York State had her purse stolen. The thief had to be Lillian, Judy, David, Theo, or Margaret.

When questioned, each child made three statements:

Lillian:

(1) I didn’t take the purse.

(2) I have never in my life stolen anything.

(3) Theo did it.

Judy:

(4) I didn’t take the purse.

(5) My daddy is rich enough, and I have a purse of my own.

(6) Margaret knows who did it.

David:

(7) I didn’t take the purse.

(8) I didn’t know Margaret before I enrolled in this school.

(9) Theo did it.

Theo:

(10) I am not guilty.

(11) Margaret did it.

(12) Lillian is lying when she says I stole the purse.

Margaret:

(13) I didn’t take the teacher’s purse.

(14) Judy is guilty.

(15) David can vouch for me because he knows me since I was born.

Later, each child admitted that two of his statements were true and one was false. Assuming this is true, who stole the purse?

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.

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 Lao-Tzu

Knowing others is intelligence; knowing yourself is true wisdom. Mastering others is strength, mastering yourself is true power.

—Lao-Tzu

Here are some dreams shared the authors of Avoid Hard Work!

For our children, we dream that mathematics…

• … makes sense.
• … is more than just arithmetic.
• … is joyous.
• … makes them strong.
• … is meaningful.
• … is creative.
• … is full of fascinating questions.
• … opens up many paths to solutions.
• … is friendly.
• … solves big problems and makes the world better.
• … is a powerful tool they can master.
• … is beautiful.
• … lets them learn in their own ways.
• … is connected to their lives.
• … asks “why” and not just “how.”
• … opens the world.

Cool Math for Older Kids

James Tanton (one of the above-mentioned authors) used to have a website full of cool math puzzles. Unfortunately, that’s gone the way of too many sites I used to love. But I was doing research on something else and stumbled upon the Internet Archive’s web backup of his “MAA AMC Curriculum Inspirations” puzzles, so I decided to rescue a few of them.

I’ve got two puzzles for upper-elementary to middle school, and two for middle-to-high school.

These are challenges taken from the AMC competitions, along with Tanton’s wonderfully encouraging, common-sense tips for figuring them out—Including how to get started when you have absolutely no idea what to do.

Have fun playing math with your older kids!

But First…

Tanton also wrote a short-lived blog on the Medium website. This was one of my favorite articles, “Two Key — but ignored— Steps to Solving Any Math Problem.”

Great tips to help you tackle the challenge problems below!

“Every challenge or problem we encounter in mathematics (or life!) elicits a human response. The dryness of textbooks and worksheets in the school world might suggest otherwise, but connecting with one’s emotions is fundamental and vital for success — and of course, joy — in doing mathematics.

“So… Experience mathematics as a human! Help your students do so too!”

—James Tanton

Now, let’s play some math…

Two Trees

The top of one tree is 16 feet higher than the top of another tree.

The heights of the two trees are in the ratio 3 : 4.

In feet, how tall is the taller tree?

Puzzle over the problem for yourself.

For tips or to check your answer download the worked-out solution here.

Angles in a Star

The degree measure of angle A is…?

No peeking!

For tips or to check your answer download the worked-out solution here.

Areas in Triangles

The area of ∆EBD is one third of the area of 3–4–5 ∆ABC.

Segment DE is perpendicular to segment AB.

What is BD?

What fun is a puzzle if someone just gives it away?

For tips or to check your answer download the worked-out solution here.

Differences of Four Numbers

Brian writes down four integers whose sum is 44:

w > x > y > z

The pairwise positive differences of these numbers are 1, 3, 4, 5, 6, and 9.

What is the sum of the possible values for w?

Thinking hard is a challenge—but that’s what makes it fun!

For tips or to check your answer download the worked-out solution here.

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?’”

Writing to Learn Math: Research prompts help students view math as a human endeavor.

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 Research Prompt

Where did math come from? Who thought up the rules? How are the ideas and methods we study used in actual life?

Research prompts help students view math as a human endeavor, something that grew bit by bit as people in many countries across many centuries struggled to understand their world.

While most research journaling is informal, older students may wish to venture into writing more formal reports. Here they can practice essay skills like formulating a thesis statement (a concise summary of the student’s main idea) and organizing facts and information to prove their point.

Be sure to allow plenty of time for students to respond to research-based journaling prompts.

Journaling Prompt 238: Mini-Biography 5

Write about a mathematician whom you think most people have never heard of.

 

Look at mathigon.org/timeline or arbitrarilyclose.com/mathematician-project or mathshistory.st-andrews.ac.uk/biographies for ideas.

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?