Elementary Mathematics, Math Software

Deducing the “Mystery” Fraction

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Estimation is an important mathematical skill, yet we rarely ask students to make estimates that relate to fractions. As part of the Dynamic Number project, we created a "mystery" fraction challenge  that presents a green point somewhere between 0 and 1 on the number line. The point's location can be represented as a fraction with … Continue Reading ››
Common Core, Educational Technology, Math Software, Professional Development, Real-World Math

Binomial Multiplication and Concreteness Fading

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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 ››
Educational Technology, Math Software

Binomial Multiplication and Factoring Games

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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, students … Continue Reading ››
Educational Technology, Elementary Mathematics, Math Software

Multiplication Arrays

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I've lost track of how many  parents have quizzed me as to why the mathematics their children are learning is so different from what they remember in school. "Why must my kids study more than one way to multiply? Isn't memorizing their multiplication facts enough?" is a frequent lament. James Tanton, Mathematician in Residence at the … Continue Reading ››
Educational Technology, Math Software

Algebra Cross Number Puzzles

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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 ››
Educational Technology, Elementary Mathematics, Math Software

Cross Number Puzzles

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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 ››
Educational Technology, Geometry, Math Software

Enhancing Web Sketchpad

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As a longtime Sketchpad fan, one of the most interesting features of Web Sketchpad (WSP) for me is the way its behavior can be customized. WSP makes it possible to add JavaScript to a web page in order to interact directly with objects in the sketch. For instance, a JavaScript function could use the locations … Continue Reading ››
Educational Technology, Elementary Mathematics, Math Software

Exploring Multiples on a Dynamic Number Grid

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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 choose … Continue Reading ››

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