Rescuing Cool Math for Older Kids

Do you have math dreams for your children?

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.