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Students will learn new functions that mimic the geometric transformations of rotation and reflection.

Lesson Goals

Students will be able to:

  • Demonstrate understanding of rotations

  • Demonstrate understanding of reflections over the x- and y- axis

Student-Facing Lesson Goals

  • I can transform images using rotations.

  • I can transform images using reflections.

Key Points for the Facilitator

  • It’s important that students use non-symmetrical images so that they can see the transformations. Text images work well for this!

  • Students should notice that rotations are counterclockwise unless the rotation angle is negative.

Prerequisites

  • Students should be familiar with Circles of Evaluation.

Materials

Connection Activities

Math Standards (CCSS)

CS Standards (CSTA)

  • CS Standards here.
Glossary
accessor functions

functions to extract values from a data structure

axis

a number line on a scatter plot, used to place points that represent pairs of values in data sets

contract

a statement of the name, domain, and range of a function

function

a mathematical object that consumes inputs and produces an output

🔗Get Ready:

Before the lesson, the facilitator should use the text function to create an image of their name in large letters. Have the image (but not the code) visible to students as they enter. (Use the slider between the Definitions and Interactions windows to hide the code.)

For example: (text "Ms. Frizzle" 100 "orange")

Students should have their computer, contracts page, and pencil.

🔗Launch: (5 min)

As students enter, ask them if they remember the function used to create the name on display. Ask students to create a similar text image for themselves, referring to their contracts page if necessary.

🔗Explore: (10 min)

Inform students that there are three new functions to investigate today, and it’s their job to explore and learn all they can about these new functions and their contracts.

Students try out reflect-x, reflect-y, and rotate on the image of their name, writing down their observations.

🔗Discuss: (10 min)

  • What is the contract for rotate? rotate: Number Image -> Image

  • What is the contract for reflect-x? reflect-x: Image -> Image, same for reflect-y

  • How do reflections and rotations have in common? They are both functions, they both transform, or change, images, they both preserve congruence (isometry)

  • How is a reflection different from a rotation? A reflection produces a mirror image, a rotation is like a turn while a reflection is like a flip

  • How do we measure rotations? Rotations can be measured in degrees or radians, measured counterclockwise

  • Is there a way to use reflections to get the same result as a rotation? A reflection over both the x- and y- axes produces an image that is the same as if we had rotated the image 180 degrees

🔗Practice: (10 min)

“Match My Moves” activity - students get a pre-image and image and figure out the transformations needed to get from the pre-image to the image.

🔗Create/Apply: (5 min)

Create/Apply task

🔗Some demo text only

Test of vocab items:

accessor functions

axis

These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, and 1738598). CCbadge Bootstrap:Cosmology by Jack Kepler, Ike Newton, and Al Einstein is licensed under a Creative Commons 4.0 Unported License. Based on a work at www.BootstrapWorld.org. Permissions beyond the scope of this license may be available by contacting schanzer@BootstrapWorld.org.