Starting with Sketchpad Activities on Day One in Grades 5-8

In the Dynamic Number project, one of our goals has been to create activities in which students actually experience mathematical objects by creating them, manipulating them, and investigating them. (George Lakoff and Rafael Núñez describe, in Where Mathematics Comes From, how students’ abstract mathematical concepts are grounded in their sensory-motor experiences.)

With Sketchpad, such experiences have been available in the geometric realm for many years, but our project’s focus was to make it as easy and effective to experience numeric objects (integers, fractions and decimals) and early algebra objects (variables, equations and functions).

That effort produced all of the activities I listed in my previous post on grades 2-5 and all but one of the grade 5-8 activities I’ve listed below. These include activities to zoom the number line to investigate decimals; to create fractions in using number line, rectangular, and circular representations; to connect common fractions with their decimal representations; to use a balance model to solve equations; and to explore variables and functions using a two-dimensional (geometric) representation.

Every one of these activities is designed for students to manipulate and investigate mathematical objects, and in a number of them students themselves create the mathematical objects that they modify and explore. (Update: Many of the Dynamic Number activities are now available for use in your web browser with no need to install Sketchpad. See here.)

In my next post, I’ll recommend some Dynamic Number activities for high school use.

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