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.

**Grade 5, decimals and decimal notation:**Zooming Decimals—Tenths, Hundredths, and Beyond (Students explore tenths, hundredths, and beyond on a “zooming” number line.) iPad compatible.**Grade 5, addition of fractions:**Fractions on a Number Line—Adding with Unlike Denominators (Students add fractions with unlike denominators on a number line.)**Grade 6, solving simple equations:**Balance–Solving for Unknowns (Students are introduced to solving for an unknown using a balance model.) iPad compatible.-
**Grade 7, fractions and decimals:**Color Calculator—Decimal Representations of Fractions (Students explore patterns using a calculator with color outputs of decimals.) iPad compatible. -
**Grade 7, area:**Parallel Pairs: Parallelogram and Triangle Area (Students explore the relationship between the areas of parallelograms and triangles.) -
**Grade 8, introducing functions:**ID the Suspects—Identify Functions (Students explore point variables to formulate a definition of function.) iPad compatible. -
**Grade 8, transformations, congruence, and similarity:**Reflection Challenges—The Reflection Family (Students explore reflections as functions.)