LearnZillion Illustrative Mathematics

Grade 8

Unit 9

Adapted from Open Up Resources under Creative Commons Attribution 4.0 International License. https://creativecommons.org/licenses/by/4.0 

All adaptations copyright LearnZillion, 2018 

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ContributorsWriting Team

Susan Addington

Ashli Black, Grade 8 Lead

Alicia Chiasson

Mimi Cukier

Nik Doran, Engineering Lead

Lisa Englard

Sadie Estrella

Kristin Gray

Donna Gustafson

Arias Hathaway

Bowen Kerins, Assessment Lead

Henry Kranendonk

Brigitte Lahme

Chuck Larrieu Casias

William McCallum, Shukongojin

Cam McLeman

Michelle Mourtgos, Grade 7 Lead

Mike Nakamaye

Kate Nowak, Instructional Lead

Roxy Peck, Statistics Lead

David Petersen

Sarah Pikcilingis

Liz Ramirez, Supports Lead

Lizzy Skousen

Yenche Tioanda, Grade 6 Lead

Kristin Umland, Content Lead

Supports for Students with Special Needs

Bridget Dunbar

Andrew Gael

Anthony Rodriguez

Supports for English Language Learners

Vinci Daro

Jack Dieckmann

James Malamut

Sara Rutherford-Quach

Renae Skarin

Steven Weiss

Jeff Zwiers

Digital Activities Development

Jed Butler

John Golden

Carrie Ott

Jen Silverman, Lead

Copy Editing

Emily Flanagan

Carolyn Hemmings

Tiana Hynes

Cathy Kessel, Lead

Nicole Lipitz

Robert Puchalik

Project Management

Aubrey Neihaus

Olivia Mitchell Russell, Lead

Engineering

Dan Blaker

Eric Connally

Jon Norstrom

Brendan Shean

Teacher Professional Learning

Vanessa Cerrahoglu

Craig Schneider

Jennifer Wilson

Alt Text

Donna Gustafson

Kia Johnson-Portee, Lead

Deb Barnum

Gretchen Hovan

Mary Cummins

Image Development

Josh Alves

Rob Chang

Rodney Cooke

Tiffany Davis

Jessica Haase

Christina Jackyra, Lead

Caroline Marks

Megan Phillips

Siavash Tehrani

Support Team

Madeleine Lowry

Nick Silverman

Melody Spencer

Alex Silverman

Hannah Winkler

Table of Contents

Unit 9: Putting it All Together

Lesson 1: What Influences Temperature? ..........................................200

Lesson 2: Tessellations of the Plane ...................................................208

Unit 9 200 Lesson 1

Unit 9 201 Lesson 1

Unit 9 202 Lesson 1

Unit 9 203 Lesson 1

Unit 9 204 Lesson 1

Unit 9 205 Lesson 1

Unit 9 206 Lesson 1

Unit 9 207 Lesson 1

Unit 9 208 Lesson 2

2.2: Tessellations

1. Pick one of the shapes. Create a

tessellation by tracing copies of your

shape. Make sure to use the same

shape as your partner.

2. Compare your tessellation to your

partner's. How are they similar? How

are they different?

3. If possible, make a third tessellation

of the plane with your shape

(different from the ones you and your

partner already created). If not

possible, explain why it is not

possible.

.____I__ ___ / 6

Unit 9 209 Lesson 2

Unit 9 210 Lesson 2

2.4: Regular Tessellations

1. For each shape (triangle, square, pentagon, hexagon, and

octagon), decide if you can use that shape to make a regular

tessellation of the plane. Explain your reasoning.

2. For the polygons that do not work what goes wrong? Explain your reasoning.

Unit 9 211 Lesson 2

Unit 9 212 Lesson 2

2.6: Regular Tessellation for Other Polygons

1. Can you make a regular tessellation of the plane using regular polygons with 7 sides?

What about 9 sides? 1 O sides? 11 sides? 12 sides? Explain.

2. How does the measure of each angle in a square compare to the measure of each

angle in an equilateral triangle? How does the measure of each angle in a regular

8-sided polygon compare to the measure of each angle in a regular 7-sided polygon?

3. What happens to the angles in a regular polygon as you add more sides?

Unit 9 213 Lesson 2

4. Which polygons can be used to make regular tessellations of the plane?

2.7: Triangle Tessellations

Your teacher will assign you one of the three triangles. You can use

the picture to draw copies of the triangle on tracing paper. Your goal

is to find a tessellation of the plane with copies of the triangle.

2.8: Quadrilateral Tessellations

1. Can you make a tessellation of the plane with copies of the trapezoid? Explain.

2. Choose and trace a copy of one of the other two quadrilaterals. Next, trace images of

the quadrilateral rotated 180 degrees around the midpoint of each side. What do

you notice?

Unit 9 214 Lesson 2

3. Can you make a tessellation of the plane with copies of the quadrilateral from the

previous problem? Explain your reasoning.

2.9: Pentagonal Tessellations

1. Can you tessellate the plane with copies of the pentagon? Explain

why or why not. Note that the two sides making angle A are

congruent.

Pause your work here.

2. Take one pentagon and rotate it 120 degrees clockwise about the vertex at angle A,

and trace the new pentagon. Next, rotate the pentagon 240 degrees clockwise about

the vertex at angle A, and trace the new pentagon.

3. Explain why the three pentagons make a full circle at the central vertex.

4. Explain why the shape that the three pentagons make is a hexagon (i.e., the sides

that look like they are straight really are straight).

Lesson 2 Glossary Terms

• tessellation

Unit 9 215 Lesson 2

Licensing and attribution for images appearing in this unit appears below.

Additional Attribution: ‘Notice and Wonder’ and ‘I Notice/I Wonder’ are trademarks of the National Council of Teachers of Mathematics, reflecting approaches developed by the Math Forum (http://mathforum.org), and used here with permission.

Lesson 1.2: Is Temperature a Function of Latitude?, Map of Washington adapted from the website American Fact Finder by the United States Census Bureau. Public Domain. https://factfinder.census.gov

Image Attribution

IM Unit Title Page(8).pdfIM Gr 8, 7-9.pdfIM Student Workbooks Table of Contents(12).pdfIM Gr 8, 7-9IM Gr 8, 7-9IM Gr 8, 7-9IM Gr 8, 7-9IM Gr 8, 7-9Copy of IM Student Workbooks Table of Contents(18).pdfIM Gr 8, 7-9IM Gr 8, 7-9IM Gr 8, 7-9Copy of IM Student Workbooks Table of Contents(19).pdfIM Gr 8, 7-9