# 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 ››

# Creating Animated Factorization Diagrams

Last year, I had the pleasure of co-organizing a geometry-focused coaching collaborative led by Metamorphosis, a New York-based organization that offers professional content coaching to transform the mindset and practices of teachers and administrators. I had so much fun that I decided to do it again! My workshop partners were Metamorphosis staffers Toni Cameron, Ariel Dlugasch, and … Continue Reading ››

In my very first Sine of the Times blog post from January 2012, I wrote about the paucity of fractions that young learners typically encounter in their math classes. While they might construct visual representations of 1/2, 2/3, and 8/12, it's unlikely they'll create models of 7/31, 36/19, or 5/101. That's a shame because without … Continue Reading ››

# Stars, Polygons, and Multiples

I've always found my collaborations with teachers to be a great inspiration for curriculum development, and that was especially true of my work with Wendy Lovetro, an elementary-school teacher in Brooklyn, NY. Wendy coordinated an after-school math club at her school, and I used the setting as an opportunity to develop and field test Sketchpad activities for the … Continue Reading ››

# Raz’s Magic Multiplying Machine

Here is a question you don't hear very often: What does it feel like to experience multiplication in our bodies? It's a strange question because our typical exposure to multiplication is numerical. I give you two numbers—say, 3 and 5—and you tell me their product, 15. But multiplication need need not be so static and concrete. Back … Continue Reading ››

# Decomposing Number Challenges

The mental arithmetic game 'Make 20' begins with students sitting in a circle. The teacher picks a student to call out a random number between 0 and 20. Students raise their hands, and whoever is chosen by the teacher must say what number, when added to the first, makes 20. The game continues in this manner, with students picking random … Continue Reading ››

# Adding and Subtracting on a Dynamic Number Chart

Below (and here) is a collection of four interactive number charts that we first introduced in our NSF-funded Dynamic Number project. Start by asking students to press the four directional arrows and to explore what they do. The right arrow, for example, moves the shaded square to the right, and wraps the square to the next row up … Continue Reading ››

# Estimating Angle Measurement

Angles are a thorny concept to teach because of the fundamentally different ways in which they can be used and understood. In the article What's Your Angle on Angles?, the authors divide the concept of angle into three main groups: angle-as-figure, angle-as-wedge, and angle-as-turn. In the Web Sketchpad game below (and here), we focus on angle-as-turn. Given an … Continue Reading ››

# An Equivalent Fractions Game

In my recent posts, I've introduced interactive models for comparing fractions and multiplying fractions. To continue the fraction theme, below (and here) is a Web Sketchpad model in which the need for equivalent fractions arises naturally through the rules of a game. The model displays two arrays. Dragging the four points changes the arrays' dimensions. The goal is to drag … Continue Reading ››

# A Compendium of Elementary Web Sketchpad Activities

Below is a complete list of all the interactive elementary-themed activities we've offered on our Sine of the Times blog. Most of these activities grew out of the work that we did during our NSF-funded Dynamic Number project. The list includes links to our original blog posts as well as links that take you directly … Continue Reading ››