Created on: September 10, 2008

Website Address: https://library.curriki.org/oer/Lesson--Rotation

TABLE OF CONTENTS

- Curriki Project Based Geometry
- Curriki Calculus: Applications of Derivatives
- Curriki Calculus: Integrals

- Selling Geometry
- Designing a Winner
- What's Your Angle, Pythagoras?
- TED Talk: House of the Future
- The Art of Triangles
- How Random Is My Life?
- Introduction to Angles
- Lesson -- Drawing right triangles from word problems
- Accessing Curriki Geometry Projects
- Introduction to Curriki Geometry

- Selling Geometry Resources
- Curriki Geometry Tools and Resources
- Lesson -- Rotation
- The World Runs on Symmetry
- Lesson -- Dilations and Isometry
- Lesson -- Composition of Transformations
- Cool Math 4 Kids: Tessellations
- Tessellations.org
- Euclid
- About Cloze Notes
- What's the point of Geometry? - Euclid
- Selling Geometry Project Teacher Edition
- Selling Geometry Project Student Packet

- Applications of Derivatives Table of Contents by Standard
- AD.1: Find the slope of a curve at a point.
- AD.2: Find a tangent line to a curve at a point and a local linear approximation.
- AD.3: Decide where functions are decreasing and increasing.
- AD.4: Solve real-world and other mathematical problems involving extrema.
- AD.5: Analyze real-world problems modeled by curves.
- AD.6: Find points of inflection of functions.
- AD.7: Use first and second derivatives to help sketch graphs.
- AD.8: Compare the corresponding characteristics of the graphs of f, f', and f".
- AD.9: Solve optimization real-world problems with and without technology.
- AD.10: Find average and instantaneous rates of change.
- AD.11: Find the velocity and acceleration of a particle moving in a straight line.
- AD.12: Model rates of change, including related rates problems.
- AD.13: Interpret a derivative as a rate of change in applications.
- AD.14 Geometric interpretation of differential equations via slope fields

Lesson: Performing Rotations

Prerequisite Knowledge: Students must have prior knowledge the coordinate plane. They must have knowledge regarding right angles.

Learning Objectives: Students will be able to identify a rotation. Students will be able to visualize a rotation about the coordinate plane. Students will be able to perform regular polygon rotations of 90, 180 and 270 degrees on a coordinate plane.

Key Ideas: Rotations of (x,y) about the origin

Rotation of 90 (-y,x)

Rotation of 180(-x,-y)

Rotation of 270 (y, -x)

Motivational Problem: Have each student take two pieces of patty paper. On both of the pieces, have the students draw an x and y axis in dark marker. On one piece of patty paper, have students draw a regular polygon in the first quadrant. In their notebooks ask them to sketch the polygon as they rotate the figure 90°, 180° and 270°.

This can be modeled by teacher using a transparency on the overhead.

Important Questions: What is a center of rotation? Explain why rotating 90 degrees clockwise is the same thing as rotating 270 counter clockwise.