Category Archives: Educational Technology

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 ››

Binomial Multiplication and Concreteness Fading

I was delighted that Daniel recently posted our Binomial Multiplication sketches in Web Sketchpad format. I thought about those sketches when I noticed a fairly new myNCTM thread on "When and How do we phase out the body in math education?" This thread raises a very important question for us as … Continue Reading ››

Binomial Multiplication and Factoring Games

The four Web Sketchpad activities below from our Dynamic Number project  provide a sequenced collection of challenges and games that develop an area model approach to binomial multiplication and factoring. You can click any of the images to open the interactive websketches on a separate page.

Dynamic Algebra Tiles, Part One

In the first websketch, … Continue Reading ››

Algebra Cross Number Puzzles

In my previous post, I wrote about cross number puzzles—puzzles that mix arithmetic and logic to introduce students to place value, commutativity, and the addition and subtraction algorithms. Now, I'd like to present a variant of cross number puzzles that adds some algebra to the mix. Below (and here on its own page) are … Continue Reading ››

Cross Number Puzzles

We live in a golden age of number puzzles. Sudoku is probably the most famous of all modern-day number puzzles, but there are many Japanese puzzles that are also gaining popularity, such as KenKen and Menseki Meiro. In this post, I'd like to introduce a number puzzle for young learners that predates … Continue Reading ››

Exploring Multiples on a Dynamic Number Grid

What would it take to build a better number grid for young learners? A typical number grid contains 10 columns with the numbers progressing from 1-10, 11-20, 21-30 and so on, from row to row. We decided to upend this tradition and make a dynamic number grid with Web Sketchpad that allows students to … Continue Reading ››

Digging Deep Into Varignon’s Theorem

In the interactive Web Sketchpad model below (and here on its own page), ABCD is an arbitrary quadrilateral whose midpoints form quadrilateral EFGH. Drag any vertex of ABCD. What do you notice about EFGH? The midpoint quadrilateral theorem, attributed to the French mathematician Pierre Varignon, is relatively new in the canon of geometry theorems, dating to 1731. Mathematics … Continue Reading ››