In my previous two posts, I listed some of the new Dynamic Number project activities (for grades 2-5 and grades 5-8) that engage students in manipulating and investigating dynamic mathematical objects from day one.
In this post I’ll list several similar activities suitable for high school mathematics. The first three address familiar topics: binomial multiplication, factoring of trinomials, and angles in polygons. The remaining four need a bit of explanation.
One of our Dynamic Number focus areas was beginning algebra, which led us not only to develop algebra-readiness activities for younger students, but also to rethink how we introduce variables and functions to students. Common Core standard G-CO2 requires students to “describe transformations as functions that take points in the plane as inputs and give other points as output.” We used this “Geometric Functions” approach to create 12 Sketchpad activities (including the four listed below), with the goal of making variables and functions concrete and engaging for students.
As we developed these Geometric Functions activities, we realized three things about functions in two dimensions. (a) Students find it easy to use a mouse or finger to manipulate input variables on a 2D plane, and they find it easy to observe and trace output variables on a 2D screen. (b) Directly constructing, manipulating, and observing 2D variables makes function concepts more concrete and memorable for students. (c) The activities develop the deep connection between functions and geometric transformations, which is particularly useful in addressing the Common Core’s increased emphasis on both of these topics.
I’ll have more to say about these activities in a future post (I’ll also be presenting at NCTM’s Baltimore Regional Conference in October and at NCTM’s Annual Meeting in April.)
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Algebra, binomial multiplication: Binomial Multiplication, Part One (Students use virtual algebra tiles to model binomial multiplication.) iPad compatible. -
Algebra, factoring trinomials: Factoring Games, Part One (Students factor quadratic expressions using virtual algebra tiles.) iPad compatible. -
Geometry, angles in polygons: Exterior Angles in a Polygon (Students construct a convex polygon and make a conjecture about the sum of the measures of its exterior angles.) 
Functions, introducing functions: ID the Suspects—Identify Functions (Students explore point variables to formulate a definition of function.) iPad compatible.
Functions, transformations, and congruence: Reflection Challenges—The Reflection Family (Students explore reflections as functions.)
Functions, build new functions from existing functions: Transform Twice—Function Composition (Students compose geometric functions and investigate their behavior.)
Geometry, transformations and functions: Special Effects—A Swirling Transformation (Students create a new function family, the swirl, with fascinating behavior.)