Math Prompt: True-False-True

Posted on by Denise Gaskins
girl writing in a notebook, sitting on couch with her corgi

Book, Charlotte Mason's Living MathOne of the stretch goals for my Charlotte Mason’s Living Math Kickstarter campaign is to add a math journaling prompt to the end of each chapter. So, I’ve been playing around with ideas to get readers writing.

Since the book’s all about how to build mathematical reasoning, I’m looking for ways to prompt creative thinking and flexibility in math calculations.

Check Out the Kickstarter

I found some fun ideas in Guy Gattegno and Martin Hoffman’s Handbook of Activities for the Teaching of Mathematics (which you can download here), including the following riff off a puzzle created by Lewis Carroll.

Continue reading Math Prompt: True-False-True

Homeschool Memories: Bill Gates Proportions II

Posted on by Denise Gaskins
Woman on a shopping spree to buy books

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

Homeschool Memories: Putting Bill Gates in Proportion

Posted on 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

        Hints for the Patty Paper Trisection

        Posted on by Denise Gaskins
        drafting tools

        No peeking! This post is for those of you who have given the trisection proof a good workout on your own.

        If you have a question about the proof or a solution you would like to share, please post a comment here.

        But if you haven’t yet worked at the puzzle, go back and give it a try.

        When someone just tells you the answer, you miss out on the fun. Figure it out for yourself — and then check the answer just to prove that you got it right.

        Continue reading Hints for the Patty Paper Trisection

        Puzzle: Patty Paper Trisection

        Posted on by Denise Gaskins
        student using drafting tools

        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.

        Continue reading Puzzle: Patty Paper Trisection

        Skit: The Handshake Problem

        Posted on by Denise Gaskins
        The handshake problem

        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

        Math Journal: The 1-2-3 Puzzle

        Posted on by Denise Gaskins
        colorful numbers 1, 2, 3

        Math Journaling Adventures series by Denise GaskinsThere’s still time to check out my Math Journaling Adventures project and discover how playful writing activities will help your students learn mathematics. Preorder your books today!

        Meanwhile, here’s a math puzzle to share with your kids…

        Write down any whole number. It can be a single-digit number, or as big as you like. For example:

        64,861,287,124,425,928

        Now, count up the number of even digits (including zeros), the number of odd digits, and the total number of digits your number contains. Write those counted numbers down in order, like this:

        64,861,287,124,425,928
        even 12, odd 5, total 17

        Continue reading Math Journal: The 1-2-3 Puzzle

        Memories: The Oral Story Problem Game

        Posted on by Denise Gaskins
        photo of sheep in a field

        Homeschool Memories…

        Perhaps you’ve heard me mention the oral story problem game. It was one of my favorite ways to get my children thinking about math, back in our early days of homeschooling. We played in the car on the way to soccer practice, or while we washed dishes, or sitting in the lobby waiting for a doctor’s appointment.

        The rules are simple: I’ll make up a math problem for you to solve. And then you make up one for me.

        The kids always loved trying to stump me.

        This problem from Henry Ernest Dudeney’s Amusements in Mathematics reminded me of those days. This is exactly the way my eldest loved to torture me…

        Continue reading Memories: The Oral Story Problem Game

        Puzzle: Henry Dudeney’s Pebble Game

        Posted on by Denise Gaskins
        photo of girl playing with pebbles on the beach

        English mathematician and puzzle-meister Henry Ernest Dudeney once wrote:

        “It may be said generally that a game is a contest of skill for two or more persons, into which we enter either for amusement or to win a prize. A puzzle is something to be done or solved by the individual.

          “The example that I give here is apparently a game, but, as in every case one player may win if he only play correctly, it is in reality a puzzle. The interest, therefore, lies in attempting to discover the leading method of play.”

          Below is the puzzle game as Dudeney explained it.

          Play it for fun at first, then see if you can solve the puzzle.

          Continue reading Puzzle: Henry Dudeney’s Pebble Game