Geometry tends not to receive much love in elementary curricula, and that's a shame. In this post, I'll describe some of my new ideas for using Web Sketchpad to introduce young learners to fundamental properties of circles.

On page 1 of the websketch below (and here), begin by asking students to drag point … Continue Reading ››# Category Archives: Math Software

# What’s New with Web Sketchpad in 2019

For the past five years, Scott and I have featured interactive Web Sketchpad models in nearly all our Sine of the Times blog posts. As much fun as it's been to build "websketches" to share with you, we've really wanted to put the creative power of Web Sketchpad into your hands.
And now, finally, that's possible. Today … Continue Reading ››

# Multiplication Is Not Repeated Addition

On the NCTM discussion site myNCTM, there's currently an extended discussion about "Division and multiplication of fractions." As the discussion has continued, I've grown concerned with what I see as a fundamental problem with the way we often introduce multiplication as repeated addition: "Multiplying 4 by 5 means we're combining five groups of four items. … Continue Reading ››

# Find the Secret Number

We created the Web Sketchpad game below (and here) as part of our Dynamic Number project. It challenges elementary-age students to uncover the value of a secret number by collecting and analyzing clues that narrow its range of possible values. The game familiarizes students with inequality signs, introduces the use of

*x*to … Continue Reading ››# The Scaled Maps Problem

Below are two maps of the United Sates, with the smaller map a 50 percent scaled copy of the original. The edges of the two maps are parallel. Imagine that the maps are printed out, with one resting on top of the other.
Believe it or not, you can stick a pin straight through both maps … Continue Reading ››

# Adding and Subtracting Integers

A recent post on the my NCTM discussion group asked about tools to help students visualize and understand addition and subtraction of integers.
I always found this confusing for some of my Algebra 1 students, mainly because they had been told to memorize some rules about whether to add or subtract the two integers and … Continue Reading ››

# Interactive Array Explorations

Arrays can be enormously helpful tools for helping young learners to visualize multiplication. Early work with arrays also sets the stage for more advanced mathematics, like binomial multiplication. In this blog post, I present several interactive arrays built with Web Sketchpad as part of the Dynamic Number project.
The interactive array model below (and … Continue Reading ››

# Fifth Graders Investigate a Mathematical Code

How much tolerance do you have for puzzlement? When faced with a mathematical conundrum, do you embrace the challenge, or do you feel some trepidation at confronting the unknown?
For many of us, an unfamiliar mathematical task is sure to raise our heart rate a beat or two. As teachers, it’s easy to translate these fears … Continue Reading ››

# Dissecting Rectangles Into Squares

The picture below on the left shows a right triangle

*JML*with altitude*KM*. This altitude is defined as the*geometric mean*of*JK*and*KL*. Using similar triangles, you can prove that*JK*×*KL*=*KM*². Another way to think about this construction is shown below on the right. Start with segments*JK*and … Continue Reading ››# A Geometry Gem from Twitter

Twitter is a great place to find geometry problems. The July 22, 2017 post of xylem presented the image below with two squares,

*ABCD*and*BFGE,*sharing a vertex. Given that*AE*= 5, what is the length of*DG?*My first thought was that surely the problem was … Continue Reading ››