Solving Simultaneous Equations with Common Sense

Simultaneous equations belong in elementary-school mathematics curricula. That's been my mantra for many years, and I want to examine it now in the context of an interactive Web Sketchpad activity. When I say that elementary-age students should encounter simultaneous equations, I don't mean that they should be instructed in the standard algebraic procedure for solving pairs of equations … Continue Reading ››

Moving Beyond Formulas When Investigating Triangle Area

For the past year, my blogging partner Scott and I have worked with the team of Everyday Mathematics to build interactive Web Sketchpad models for their forthcoming new edition. It's been fun for both of us to find ways to insert dynamic mathematics into their K–6 curriculum. Last year, I shared … Continue Reading ››

Exploring Factor Rainbows

This week, I'm going to describe one of my favorite activities for introducing young learners to multiplication and factors. It comes from  Nathalie Sinclair, a professor of mathematics education at Simon Fraser University. In the interactive Web Sketchpad model below, press Jump Along to watch the bunny take 2 jumps of 4 … Continue Reading ››

Isosceles Triangle Puzzles

As readers of this blog can probably tell, I like puzzles. I especially enjoy taking ordinary mathematical topics that might not seem puzzle worthy and finding ways to inject some challenge, excitement, and mystery into them. This week, I set my sights on isosceles triangles. It's common to encounter isosceles triangles as supporting players in geometric proofs, but … Continue Reading ››

Dancing Unknowns: You Haven’t Seen Simultaneous Equations Like These!

When it comes to simultaneous equations, I like to push the bounds of conventional pedagogical wisdom. In an earlier post, I offered a puzzle in which elementary-age students solve for four unknowns given eight equations. Now, I'd like to present a puzzle that might sound even more audacious: Solving for ten unknowns. Oh, … Continue Reading ››

When I was child, I loved to solve the brainteasers in logic puzzle magazines. You probably know the type: Ruth, Phyllis, and Joan each bought a different kind of fruit (orange, apple, pear) and a different vegetable (spinach, kale, carrots) at the supermarket. No one bought both an orange and carrots. Ruth didn't buy an apple or kale.Continue Reading ››

Covering Your Bases: An Interactive Dials Model

There are certain topics in mathematics education not appropriate for polite discussion. Number bases other than 10 fit this category well, perhaps because of their association with the maligned "new math" of the 1960s. That's a shame because there is a lot to learn from them, especially when presented as interactive puzzles. Below are eight dials, each with … Continue Reading ››

The Return of the Odometer

In my prior post, I presented an interactive Web Sketchpad odometer that is a great tool for introducing young learners to place value. Well, technology moves fast these days, and the latest odometers are more powerful than ever. While our prior odometer featured '+' buttons above each digit, our newest innovation in number-tracking technology features  '+' and … Continue Reading ››

Exploring Place Value With an Interactive Odometer

Below is an interactive odometer built with Web Sketchpad. Press each of the '+' keys and observe their effect on the odometer's value. Also notice how your button presses are tracked in the table below the odometer. I built this model as a way to support students' development of … Continue Reading ››