A bit of April Fool’s Day fun from Google Maps:
I’m still working on Let’s Play Algebra, the sequel to my Let’s Play Math book.
Here’s a quick taste of things to come…
In math education, a manipulative is a hands-on object that represents an abstract concept. Many homeschoolers are familiar with Cuisenaire rods, base 10 blocks, fraction circles, and other common elementary math toys. Now we need a hands-on object to represent a variable, an unknown number. Ideally, we want several small items about the same size, so they are easy to work with, in two different colors to represent positive and negative variables.
Teacher supply stores sell algebra manipulatives, and virtual manipulatives are available online, but I like the idea of making my own. In Vision in Elementary Mathematics, W. W. Sawyer uses a bag with stones inside, tied shut so we cannot see how many there are. I could cut out felt circles (in two colors), wrap them around a few pebbles, and tie them shut with rubber bands.
When Henry Borenson invented the Hands-On Equations system, he used board-game-style pawns. I have several old chess sets with missing pieces, and chess pawns come in two colors. If I look at a pawn from the side and squint my eyes a little, I can even imagine it looks something like a small bag. Maybe.
Or I could fold origami boxes for my variables.
But my favorite algebra manipulatives, which I will use for the Keep Your Balance game in this book, are acrylic octagon jewels like these. They come in a variety of colors, so I can choose my favorite color or pick up an assortment. I like the amber or topaz, which look like crystalline gold. For negative variables, I’ll use black gemstones as antimatter. My children love imaginative stories, so solving an equation will mean figuring out what our “pirate treasure” is worth.
Don’t Forget the Constant Numbers
We also need a symbol to represent known numbers: pebbles, coins, dry beans, Cuisenaire rods, or any other countable items will work. In an earlier edition of this book, I used Cheerios (with raisins for the negative numbers) because these are cheap and easy to find in large quantity, and because my children have always liked it when solving a math puzzle involved getting a snack.
But in keeping with the treasure theme, I think gold coins would make wonderful manipulatives, along with black coins for antimatter. I could buy plastic gold coins, but it’s even easier to spray-paint regular pennies. Don’t worry: it’s not illegal to deface pennies for educational use — just don’t try to pass them off as actual gold!