Lesson plan

# Lesson 4: Making the Moves

teaches Alabama State Standards 8-23.
teaches Arizona State Standards 8.G.A.1
teaches Common Core State Standards MP7 http://corestandards.org/Math/Practice/MP7
teaches Common Core State Standards MP6 http://corestandards.org/Math/Practice/MP6
teaches Common Core State Standards MP5 http://corestandards.org/Math/Practice/MP5
teaches Common Core State Standards 8.G.A.1 http://corestandards.org/Math/Content/8/G/A/1
teaches Georgia State Standards MGSE8.G.1.
teaches Minnesota State Standards 7.3.2.4.
teaches New York State Standards NY-8.G.1.
teaches Ohio State Standards 8.G.1.
teaches Pennsylvania State Standards CC.2.3.8.A.2.

# Lesson 4: Making the Moves

In the previous lesson, students were introduced to the terms “translation,” “rotation,” and “reflection.” In this lesson, students understand that:

• A translation is determined by two points that specify the distance and direction of the translation.
• A rotation is determined by a point, angle of rotation, and a direction of rotation.
• A reflection is determined by a line.

These moves are called transformations for the first time and students draw images of figures under these transformations. They also study where shapes go under sequences of these transformations and identify the steps in a sequence of transformations that takes one figure to another. Note the subtle shift in language. In the previous lesson, one shape “moves” to the other shape—it is as if the original shape has agency and does the moving. In this lesson, the transformation “takes” one shape to the other shape—this language choice centers the transformation itself as an object of study.

Students using the print version may make use of tracing paper to experiment moving shapes. Students using the digital version have access to geogebra applets with which to perform transformations. Whenever students choose to make use of an appropriate tool, they are engaging in MP5. Students are also likely starting to begin thinking strategically about which transformations will take one figure to another, identifying properties of the shapes that indicate whether a translation, rotation, reflection or sequence of these will achieve this goal (MP7).

Lesson overview

• 4.1 Warm-up: Reflection Quick Image (5 minutes)
• 4.2 Activity: Make That Move (15 minutes)
• There is a digital applet in this activity.
• 4.3 Activity: A to B to C (15 minutes)
• Includes "Are you Ready for More?" extension problem
• There is a digital applet in this activity.
• Lesson Synthesis
• 4.4 Cool-down: What Does It Take? (5 minutes)

Learning goals:

• Comprehend that a “transformation” is a translation, rotation, reflection, or a combination of these.
• Draw a transformation of a figure using information given orally.
• Explain (orally) the “sequence of transformations” that “takes” one figure to its image.
• Identify (orally and in writing) the features that determine a translation, rotation, or reflection.

Learning goals (student facing):

• Let’s draw and describe translations, rotations, and reflections.

Learning targets (student facing):

• I can use the terms translation, rotation, and reflection to precisely describe transformations.

Required materials:

• pre-printed cards, cut from copies of the blackline master
• geometry toolkits

Required preparation:

• Print and cut up cards from the Make that Move blackline master.
• Prepare 1 set of cards for every 4 students.

Glossary:

• sequence of transformations - A sequence of transformations is a set of translations, rotations, reflections, and dilations on a figure. The transformations are performed in a given order. This diagram shows a sequence of transformations to move Figure A to Figure C. First, A is translated to the right to make B. Next, B is reflected across line $$\ell$$ to make C.

• transformation - A transformation is a translation, rotation, reflection, or dilation, or a combination of these.
• Access the complete Grade 8 glossary.

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.