Mirror, Mirror

1 Handedness

Each page of this activity has an independent variable that can move along a restricted domain (a triangle). You’ll transform the variable, using a different function on each page, and investigate whether the dependent variable has the same handedness (both clockwise or both counter-clockwise) or a different orientation compared to the independent variable.

(The mathematical term handedness distinguishes objects like your hands or your feet, which are opposite from each other even though they have the same shape. You distinguish your hands by calling them right and left. We will call triABC clockwise or counter-clockwise based on the way x travels as it varies from A to B to C.)

2 Explore Multiple Reflections

On the pages of this activity you’ll reflect the independent variable (along with its domain) two or three times. In each case you’ll see if you can find a function from a different transformation family that produces the exact same result as the combination of reflect functions you used.

3 Construct Multiple Reflections

On each page of this activity you’ll try to construct multiple reflect functions to produce the exact same result as other transformations. The functions you'll try to construct this way include a rotate function (page 2), a translate function (page 3), a glide reflection (page 4), and a dilate function (page 5). (Hint: all of these except one are possible.)

The Fine Print

Requirements:

These activities require web access using a browser that supports HTML5 and JavaScript. (That means almost any current browser.) No purchase is required, and there’s no advertising anywhere.

Release Information

Update History:

10 Apr 2018: Regularized vocabulary to use "handedness", revised given order of tool objects, and started the teacher notes.