Middle school – Denise Gaskins' Let's Play Math

Homeschool Memories: Bill Gates Proportions II

Posted on January 21, 2026January 3, 2026 by Denise Gaskins

Once upon a time, when my kids and I were young…

Later the same year, not too long after our discussion of the Bill Gates proportions, I stumbled on some more data. I discovered that the median American family’s net worth was $93,100 in 2004, most of that being home equity.

This gave me another chance to play around with proportions. And since I was preparing a workshop for our regional homeschooling conference, I wrote a sample problem:

The median American family has a net worth of about $100 thousand. Bill Gates has a net worth of $56 billion. If Average Jane Homeschooler spends $100 in the vendor hall, what would be the equivalent expense for Gates?

In the last post, I explained that a proportion sets two ratios equal to each other, like equivalent fractions. Each ratio must compare similar thing to similar thing in the same order.

In this case, we are interested in the ratio “Expense compared to Net Worth.”

Continue reading Homeschool Memories: Bill Gates Proportions II

Math Game Monday: Odd–Even–Prime Race

Posted on January 19, 2026January 7, 2026 by Denise Gaskins

$Learn a new math game every week, for free$

This game challenges upper-elementary and middle school students to practice strategy and mental math as they race across a number chart.

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.

Odd–Even–Prime Race

Math Concepts: addition, subtraction, multiplication, odd and even, prime and composite numbers, strategic thinking.

Players: two or more.

Equipment: printed hundred chart of your choice, 2 six-sided dice, small toy or token for each player.

Continue reading Math Game Monday: Odd–Even–Prime Race

Homeschool Memories: Putting Bill Gates in Proportion

Posted on January 14, 2026January 3, 2026 by Denise Gaskins

Money Bag, dollar banknotes and stacked coins on wooden table

Once upon a time…

We were getting ready for the annual homeschool co-op speech contest, and a friend emailed me for help.

“Can you help us figure out how to figure out this problem?

“This is related to C’s speech. I think we have all the information we need, but I’m not sure:

“The average household income in the United States is $60,000/year. And a man’s annual income is $56 billion.

“Is there a way to figure out what this man’s value of a million dollars would be, compared to the person who earns $60,000/year? In other words, I would like to say—$1,000,000 to us is like 10 cents to Bill Gates.”

We found out later that her son’s numbers weren’t exactly right. He hadn’t understood the difference between income and net worth, so he made Gates sound richer than reality.

But the basic math principles never change, and it’s fun to play with big numbers.

Continue reading Homeschool Memories: Putting Bill Gates in Proportion

Math Game Monday: Domino Fraction War

Posted on December 15, 2025November 26, 2025 by Denise Gaskins

$Learn a new math game every week, for free$

This game offers upper-elementary and middle school students plenty of practice doing estimation and mental math with fractions.

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.

Domino Fraction War

Math Concepts: proper fractions, comparing fractions.

Players: two or more.

Equipment: one set of double-six or double-nine dominoes.

Continue reading Math Game Monday: Domino Fraction War

Math Game Monday: Hidden Hexagon

Posted on December 1, 2025October 12, 2025 by Denise Gaskins

$Learn a new math game every week, for free$

This game offers a fun twist on the old classic Battleship. Can you discover your opponent’s secret shape before they find yours?

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.

Hidden Hexagon

Math Concepts: coordinate graphing (first quadrant), simple linear equations, irregular polygons.

Players: two players or two teams.

Equipment: printed gameboard or square grid paper for each player, pencils, ruler or other straightedge.

Continue reading Math Game Monday: Hidden Hexagon

How to Think like a School Math Genius

Posted on October 22, 2025September 4, 2025 by Denise Gaskins

$Teen student thinking$

“The true joy in mathematics, the true hook that compels mathematicians to devote their careers to the subject, comes from a sense of boundless wonder induced by the subject.

“There is transcendental beauty, there are deep and intriguing connections, there are surprises and rewards, and there is play and creativity.

“Mathematics has very little to do with crunching numbers. Mathematics is a landscape of ideas and wonders.”

—James Tanton

James Tanton has a new website. It looks cool, and it’s a great place to discover the things he’s working on these days.

But his wonderful, old-fashioned site full of great insights and interesting problems is gone.

😞 I hate it when some part of the internet that I love disappears. So here’s my attempt to recover one tiny bit of the old site, five tips for creative problem solving through intellectual play.

Continue reading How to Think like a School Math Genius

Puzzle: Patty Paper Trisection

Posted on August 20, 2025August 20, 2025 by Denise Gaskins

One of the great unsolved problems of antiquity was to trisect any angle, to cut it into thirds with only the basic tools of Euclidean geometry: an unmarked straight-edge and a compass.

Like the alchemist’s dream of turning lead into gold, this proved to be an impossible task. If you want to trisect an angle, you have to “cheat.” A straight-edge and compass can’t do it. You have to use some sort of crutch, just as an alchemist would have to use a particle accelerator.

One “cheat” that works is to fold your paper.

I will show you how it works, and your job is to show why.

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Happy Pythagorean Triple Day!

Posted on July 22, 2025July 28, 2025 by Denise Gaskins

Pythagorean Theorem demonstrated with tangrams

Thursday is Pythagorean Triple Day, one of the rarest math holidays.

The numbers of Thursday’s date: 7/24/25 or 24/7/25, fit the pattern of the Pythagorean Theorem: 7 squared + 24 squared = 25 squared.

Any three numbers that fit the a² + b² = c² pattern form a Pythagorean Triple.

Continue reading Happy Pythagorean Triple Day!

Skit: The Handshake Problem

Posted on April 23, 2025July 12, 2025 by Denise Gaskins

If seven people meet at a party, and each person shakes the hand of everyone else exactly once, how many handshakes are there in all?

Our homeschool co-op held an end-of-semester assembly. Each class was supposed to demonstrate something they had learned.

I threatened to hand out a ten question pop quiz on integer arithmetic, but instead my pre-algebra students presented this skit.

Download a Printable Script

Cast

1-3 narrators (or more, if you have a large group)
7 friends (non-speaking parts, adjust to fit your group)

Props

Each friend will need a sheet of paper with a number written on it big and bold enough to be read by the audience. The numbers needed are 0, 1, 2, 3, … up to one less than the number of friends. Each friend keeps his paper in a pocket until needed.

Continue reading Skit: The Handshake Problem

Middle School Math Proof

Posted on January 17, 2024May 5, 2024 by Denise Gaskins

Homeschool Memories…

Kitten (my daughter) and I sat on the couch sharing a whiteboard, passing it back and forth as we took turns working through our prealgebra book together.

The chapter on number theory began with some puzzles about multiples and divisibility rules.

Continue reading Middle School Math Proof