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Graphing and Describing 90° and 270° Rotations about the Origin (0, 0), Study notes of Reasoning

University of Providence (UP)Reasoning

A lesson plan for teaching students how to graph and describe 90° and 270° rotations about the origin in two-dimensional coordinates. It includes CC standards, mathematical practices, teacher input, and student notes. The lesson covers guided practices for rotating figures 90° clockwise and counter-clockwise, as well as using rules to rotate 90° and 270°.

Typology: Study notes

2021/2022

Uploaded on 09/27/2022

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Graphing and Describing 90° and 270° Rotations about the Origin (0, 0)

1 | P a g e

Teacher Lesson Plan

Lesson: Day 6 – Supplement Lesson

Graphing and Describing 90° and 270° Rotations about the Origin (0, 0)

CC Standards

8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional

figures using coordinates.

Objective

TSW… Graph and Describe 90° and 270° rotations about the origin.

Mathematical Practices

#1 Make sense of problems and persevere in solving them.

#6 Attend to precision.

#7 Look for and make use of structure.

#8 Look for and express regularity in repeated reasoning.

Note to teachers:

Be sure to teach this lesson from the PowerPoint, not the student notes. You will be missing part of the

lesson otherwise.

Teacher Input

Bellwork: Review bellwork.

Homework: Review important problems assigned the previous night.

Introduction: Introduce as directed on the PowerPoint.

Lesson: Teach as directed in the PowerPoint. Be sure to look at the notes on each slide for additional

instruction and answers.

Practice

Classwork

Homework

Click on each link below to watch a YouTube video that explains how to graph using rules (around origin).

180 degree rotations (3:58) https://www.youtube.com/watch?v=8ZeeDYIlNFk

90 degree clockwise rotations (13:33) https://www.youtube.com/watch?v=LwGmA9F3hbw

90 degree CCW rotations (12:57) https://www.youtube.com/watch?v=4Q70ZHVFKPc

Note… The above videos are included in the PowerPoint so that you can show them to your students if you are able to.

The last two videos are longer. There is a portion at the end of the video that you can skip if necessary.

All 3 rotations: https://www.youtube.com/watch?v=9dSnm6CSoSs

Note…This video can be shown on a Review Day.

Partial preview of the text

Download Graphing and Describing 90° and 270° Rotations about the Origin (0, 0) and more Study notes Reasoning in PDF only on Docsity!

Teacher Lesson Plan Lesson: Day 6 – Supplement Lesson Graphing and Describing 90° and 270° Rotations about the Origin (0, 0)

CC Standards 8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Objective TSW… Graph and Describe 90° and 270° rotations about the origin.

Mathematical Practices #1 Make sense of problems and persevere in solving them. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

Note to teachers: Be sure to teach this lesson from the PowerPoint, not the student notes. You will be missing part of the lesson otherwise.

Teacher Input Bellwork: Review bellwork. Homework: Review important problems assigned the previous night. Introduction: Introduce as directed on the PowerPoint. Lesson: Teach as directed in the PowerPoint. Be sure to look at the notes on each slide for additional instruction and answers.

Practice Classwork Homework

Click on each link below to watch a YouTube video that explains how to graph using rules (around origin).

180 degree rotations (3:58) https://www.youtube.com/watch?v=8ZeeDYIlNFk 90 degree clockwise rotations (13:33) https://www.youtube.com/watch?v=LwGmA9F3hbw 90 degree CCW rotations (12:57) https://www.youtube.com/watch?v=4Q70ZHVFKPc

Note… The above videos are included in the PowerPoint so that you can show them to your students if you are able to. The last two videos are longer. There is a portion at the end of the video that you can skip if necessary.

All 3 rotations: https://www.youtube.com/watch?v=9dSnm6CSoSs Note…This video can be shown on a Review Day.

Section 1: Rotating 90º about the Origin

Guided Practice #1 You Try #

Rotate ∆EFG 90º clockwise. Rotate ∆QRS 90º clockwise.

Pre-image Image Pre-image Image

Guided Practice #2 You Try # Rotate Figure EFGH 90° counter - clockwise. Rotate Figure EFGH 90° counter - clockwise.

Pre-image Image Pre-image Image

Student Notes

Guided Practice #3 You Try #

Rotate ∆EFG 90º clockwise. Rotate ∆QRS 90º clockwise.

Pre-image Image Pre-image Image

Guided Practice #4 You Try # Rotate Figure EFGH 90° counter - clockwise. Rotate Figure EFGH 90° counter - clockwise.

Pre-image Image Pre-image Image

Name______________________________________ Date________ Period ____

90 ° Rotations

Classwork

Homework

Using RULES to Rotate 90° about the Origin.

90 º CLOCKWISE

90º COUNTER-Clockwise

Rules for Rotating 270 º

 If asked to rotate 270° clockwise… use the rule for 90° CCW.

 If asked to rotate 270° counter-clockwise… use the rule for 90° clockwise.

RULE:

 Swap the x and y values;  Change the sign of the 2nd^ coordinate to the opposite. (x, y) → (y, - x) EXAMPLE: Pre - image Image A( 3 , 5 ) A’(5, - 3) B( 4 , 1 ) B’(1, - 4) C( 2 , 1 ) C’( 1 , - 2 )

RULE:

 Swap the x and y values;  Change the sign of the 1st coordinate to the opposite. (x, y) → ( - y, x) EXAMPLE: Pre - image Image A( 1 , 2 ) A’( - 2, 1) B( 2 , 3 ) B’( - 3, 2) C( 3 , 1 ) C’( - 1, 3)

Guided Practice #3 You Try # Rotate ∆EFG 90º clockwise. Rotate ∆QRS 90º clockwise.

Guided Practice #4 You Try # Rotate Figure EFGH 90° counter - clockwise. Rotate Figure EFGH 90° counter - clockwise.

Pre-Image Image E(-6, - 6) E’(6, - 6) F(-1, - 6) F’(6, - 1) G(3, - 3) G’(3, 3) H(-3, - 3) H’(3, - 3)

Pre-Image Image E(-4, 5) E’(-5, - 4 ) F(-3, 2) F’(-2, - 3 ) G(-1, 2) G’(-2, - 1 ) H(2, 4) H’(-4, 2)

Graphing and Describing 90° and 270° Rotations about the Origin (0, 0), Study notes of Reasoning

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Partial preview of the text

Download Graphing and Describing 90° and 270° Rotations about the Origin (0, 0) and more Study notes Reasoning in PDF only on Docsity!

RULE:

RULE:

Classwork answer key not provided.