Even a Math Workbook Can Be a Game

Homeschooling Memories…

My youngest daughter wanted to do Singapore math. Miquon Red was her main math text at the time, but we added a bit of Singapore Primary Math 1B whenever she was in the mood.

We turned to the lesson on subtracting with numbers in the 30-somethings.

The first problem was pretty easy for her:

30 − 7 = _____

I reminded her that she already knew 10 − 7.

She agreed, “Ten take away seven is three.”

Then her eyes lit up. “So it’s 23! Because there are two tens left.”

Wow, I thought. She’s catching on quickly.

Mom Always Talks Too Much

We went to the next problem:

34 − 8 = _____

“Now, this one is harder,” I said. “But you know what ten minus eight is, right? So we could take one of these tens and—”

She waved at me to be quiet.

I was just getting started on my standard speech about how to turn a tough subtraction like 34 − 8 into the easy addition of “2 + 4 + two tens left.” But her mind was still on the last problem, specifically on the two tens and the seven.

“If you have 27,” she said, “and you add three more, you get 30. And four more is 34.”

“Um, yes, but…” I interrupted.

She shushed me again.

“And then you can take away the four. And then you can take away the three. And then you can take away one more…It’s 26!”

Mom Learns a Lesson

She continued through the next page that way. For every problem, she started with whatever number struck her fancy, usually containing at least one digit from the problem before. She added enough to get up to the 30-something number in the book.

Only then would she deign to subtract the number in question.

I don’t think she ever saw the point of the mental math technique the book and I were trying to teach, but she did have a lot of fun playing around with the numbers.

In the long run, that’s much more important.

Feature photo: “Laughing Girl” by ND Strupler via Flickr (CC BY 2.0).

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Playful Math Carnival #106

Do you enjoy math? I hope so! If not, browsing this post just may change your mind.

Welcome to the 106th edition of the Math Teachers At Play math education blog carnival — a smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college. Let the mathematical fun begin!

By tradition, we start the carnival with a puzzle in honor of our 106th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

Try This Puzzle

If you slice a pizza with a lightsaber, you’ll make straight cuts all the way across. Slice it once, and you get two pieces.

If you slice it five times, you’ll get a maximum of sixteen pieces. (And if you’re lucky you might get a star!)

  • How many times would you have to slice the pizza to get 106 pieces?

Click here for all the mathy goodness!

2017 Mathematics Game

Two of the most popular New Year’s Resolutions are to spend more time with family and friends, and to get more exercise. The 2017 Mathematics Game is a prime opportunity to do both at once.

So grab a partner, slip into your workout clothes, and pump up those mental muscles!

For many years mathematicians, scientists, engineers and others interested in mathematics have played “year games” via e-mail and in newsgroups. We don’t always know whether it is possible to write expressions for all the numbers from 1 to 100 using only the digits in the current year, but it is fun to try to see how many you can find. This year may prove to be a challenge.

Math Forum Year Game Site

Rules of the Game

Use the digits in the year 2017 to write mathematical expressions for the counting numbers 1 through 100. The goal is adjustable: Young children can start with looking for 1-10, middle grades with 1-25.

  • You must use all four digits. You may not use any other numbers.
  • Solutions that keep the year digits in 2-0-1-7 order are preferred, but not required.
  • You may use +, -, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), and parentheses, brackets, or other grouping symbols.
  • You may use a decimal point to create numbers such as .2, .02, etc., but you cannot write 0.02 because we only have one zero in this year’s number.
  • You may create multi-digit numbers such as 10 or 201 or .01, but we prefer solutions that avoid them.

My Special Variations on the Rules

  • You MAY use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal. But students and teachers beware: you can’t submit answers with repeating decimals to Math Forum.
  • You MAY use a double factorial, n!! = the product of all integers from 1 to n that have the same parity (odd or even) as n. I’m including these because Math Forum allows them, but I personally try to avoid the beasts. I feel much more creative when I can wrangle a solution without invoking them.

Click here to continue reading.

New Book: Multiplication & Fraction Games

It’s here! My long-awaited upper-elementary Math You Can Play games book has finally hit the online bookstores.

Multiplication & Fractions features 25 kid-tested games, offering a variety of challenges for school-age students. Children master several math models that provide a sturdy foundation for understanding multiplication and fractions. The games feature times table facts and more advanced concepts such as division, fractions, decimals, and multistep mental math.

Free Online Preview

Click here to find Multiplication & Fractions at your favorite bookstore.
170 pages, ebook: $5.99, paperback: $17.99.

Multiplication & Fraction Games

multfrac-300Maybe you never really understood what multiplication means or what fractions are? As long as you start with an open mind and are willing to engage playfully, the activities in the book can help you as you help your kids.
Anecdotally, these two areas are the first major stumbling point for students in their math studies. The sequencing in the book will help kids develop a strong foundation.
Kids (and parents!) find these games fun. I’ve been field testing math games for the last 18 months and keep seeing how engaged kids get when playing math games.

— Joshua Greene
Multiplication & Fractions Math Games from Denise Gaskins (a review)

Chapters include:

  • Mathematical Models: Learn the basic pictures that help support your child’s comprehension.
  • Conquer the Times Tables: Enjoy practicing the math facts until correct answers become automatic.
  • Mixed Operations: Give mental muscles a workout with games that require number skills and logical thinking.
  • Fractions and Decimals: Master equivalent fractions, work with decimal place value, and multiply fractions and decimal numbers.

If you are a parent, these games provide opportunities to enjoy quality time with your children. If you are a classroom teacher, use the games as warm-ups and learning center activities or for a relaxing review day at the end of a term. If you are a tutor or homeschooler, make games a regular feature in your lesson plans to build your students’ mental math skills.

So what are you waiting for? Clear off a table, grab a deck of cards, and let’s play some math!

Check It Out

It starts with models that are visual explanations of the concepts. Gaskins also breaks learning these concepts into comfortable steps that emphasize patterns and relationships, the real ideas that are behind properly understanding multiplication and fractions (indeed, math generally).
The sequence of games in each section starts by building familiarity and then fluency (speed) to solidify all of that work.

— Joshua Greene
Multiplication & Fractions Math Games from Denise Gaskins (a review)

Multiplication & Fraction Printables

Multiplication & Fraction Printables

Most of the Math You Can Play games use materials you already have around the house, such as playing cards or dice. But this book introduces multiplication and fractions with several games using two special mathematical model card decks.

Click here to download the Multiplication & Fraction Printables, featuring all the math model cards, hundred charts, and game boards you will need for any game in the book.

Number Game Printables

One step closer to getting my long-awaited Multiplication & Fraction Games book out — I finished the printables file! At least, I hope I’ve finished. Sometimes it seems like whack-a-typo never ends…

Multiplication & Fraction Printables

Multiplication & Fraction Printables

Click here to download the Multiplication & Fraction Printables, featuring mathematical model cards, hundred charts, and game boards to accompany the upcoming Math You Can Play: Multiplication & Fractions book.

The Multiplication & Fractions ebook will come out sometime in November, and the paperback should follow in time for Christmas. If you’re interested, my newsletter subscribers will get a special introductory sale price whenever the book is published. Join now!

You may also want to check out:

Number Game Printables Pack

Number Game Printables Pack

Click here to download the Number Game Printables Pack, featuring hundred charts, graph paper, and game boards from the first two Math You Can Play books.

Also, 0–99 charts, and bottoms-up versions, too. (See my blog post Math Debates with a Hundred Chart.) And a fun cut-and-fold game board for playing Shut the Box.

Permission to Use These Files

You have permission to copy and use these game boards and worksheets in your own local classroom, home school, math circle, co-op class, etc. But you may not post them on your own website (though you can link to this post, if you like) or sell them. If you’re not sure how copyright works on the Internet, check out Daniel Scocco’s Copyright Law: 12 Dos and Don’ts.

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KenKen Classroom Puzzles Start Next Week


KenKen arithmetic puzzles build mental math skills, logical reasoning, persistence, and mathematical confidence. Puzzle sets are sent via email every Friday during the school year — absolutely free of charge.

What a great way to prepare your kids for success in math!

Sign up anytime:

How to Play

For easy printing, right-click to open the image above in a new tab.

Place the numbers from 1 to 6 into each row and column. None of the numbers may repeat in any row or column. Within the black “cages,” the numbers must add, subtract, multiply, or divide to give the answer shown.

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FAQ: Trouble with Worksheets

“Worksheet problems make my daughter’s brain freeze. Even simple things such as “2 + ___ = 2″ confuse her. What can I do?”

Can your daughter do math if you put away the worksheet and ask her a real-life problem: “I have a lunch sack. I put two cookies into the sack, and then I give it to you. When you look into the sack, you see two cookies there. Can you tell me what was in the sack at the beginning, before I put my cookies in?”

Or can she solve problems when the answer isn’t zero? Could she figure out how many you started with if she saw four cookies when she looked in the sack?

The idea of having a number for “nothing” can seem strange to young children.

Worksheet Calculations Are Not Math

Can your daughter think mathematically, without calculations?

The symbols on the worksheet are not math. They are just one way of recording how we think about number relationships, and not a very natural way for children. Mathematics is a way of thinking — paying attention to the relationship between ideas and reasoning out connections between them. Encourage your daughter to notice these relationships and wonder about them.

Try watching Christopher Danielson’s video “One is one … or is it?” together, and then see how many different examples of “one” she can find around the house.

The Power of Story

Many kids at this age have a hard time with abstract number math — then their brains will grow up, and they’ll be able to do it. Development varies from one child to another.

When I do worksheets with young children, I turn each equation into a little story. Like the “cookies in a lunch sack” story above.

Sometimes we use blocks or other manipulatives to count on, but often the mental picture of a story is enough. Having something solid to imagine helps the child reason out the relationships between the numbers and symbols.


Quote photo: Carl Vilhelm Holsøe ‘Interior with a mother reading aloud to her daughter’ 19th Century. Image from Plum Leaves via Flickr. (CC BY 2.0)

Click for details about Let's Play Math bookThis post is an excerpt from my book Let’s Play Math: How Families Can Learn Math Together—and Enjoy It, as are many of the articles in my Let’s Play Math FAQ series.

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