Classroom Resource

Shifting Shapes

Subject Area

Mathematics

Grade(s)

7, 8

Overview

In this Desmos activity, students explore transformations of plane figures and describe these movements in everyday language using words like "slide," "shift," "turn," "spin," "flip," and "mirror." Students are not expected to use formal math vocabulary yet. This lesson provides both the intellectual need for agreeing upon a common language and the chance for students to experiment with different ways of describing some transformations in the plane. This activity should be used to help teach a lesson on transformations. This Desmo activity offers sample student responses and a teacher guide.

Content Standards

Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

MA19.7A.42
Verify experimentally the properties of rigid motions (rotations, reflections, and translations): lines are taken to lines, and line segments are taken to line segments of the same length; angles are taken to angles of the same measure; and parallel lines are taken to parallel lines.

Unpacked Content

Vocabulary

Congruent
Rotation
Reflection
Translation

Knowledge

Students know:

how to measure line segments and angles
That similar figures have congruent angles.
The definition/concept of what a figure does when it undergoes a rotation, reflection, and translation.
how to perform a translation, reflection, and rotation.

Skills

Students are able to:

verify by measuring and comparing lengths of a figure and its image that after a figure has been translated, reflected, or rotated its corresponding lines and line segments remain the same length.

Understanding

Students understand that:

congruent figures have the same shape and size.
Two figures in the plane are said to be congruent if there is a sequence of rigid motions that takes one figure onto the other.

Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

MA19.7A.42a
Given a pair of two-dimensional figures, determine if a series of rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are congruent; describe the transformation sequence that verifies a congruence relationship. [Grade 8, 22]

Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

MA19.7A.44
Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them. [Grade 8, 24]

Unpacked Content

Vocabulary

Translation
Reflection
Rotation
Dilation
Scale factor

Knowledge

Students know:

how to perform rigid transformations and dilations graphically and algebraically (applying coordinate rules).
What makes figures similar and congruent.

Skills

Students are able to:

use mathematical language to explain how transformations can be used to prove that two figures are similar or congruent.
Demonstrate/perform a series of transformations to prove or disprove that two figures are similar or congruent.

Understanding

Students understand that:

there is a proportional relationship between corresponding characteristics of the figures, such as lengths of line segments, and angle measures as they develop a definition for similarity between figures.
The coordinate plane can be used as tool because it gives a visual image of the relationship between the two figures.

Mathematics (2019) Grade(s): 8

MA19.8.22
Verify experimentally the properties of rigid motions (rotations, reflections, and translations): lines are taken to lines, and line segments are taken to line segments of the same length; angles are taken to angles of the same measure; and parallel lines are taken to parallel lines.

Unpacked Content

Vocabulary

Congruent
Rotation
Reflection
Translation

Knowledge

Students know:

How to measure line segments and angles.
That similar figures have congruent angles.
The definition/concept of what a figure does when it undergoes a rotation, reflection, and translation.
How to perform a translation, reflection, and rotation.

Skills

Students are able to:

verify by measuring and comparing lengths of a figure and its image that after a figure has been translated, reflected, or rotated its corresponding lines and line segments remain the same length.

Understanding

Students understand that:

congruent figures have the same shape and size.
Two figures in the plane are said to be congruent if there is a sequence of rigid motions that takes one figure onto the other.

Mathematics (2019) Grade(s): 8

MA19.8.22a
Given a pair of two-dimensional figures, determine if a series of rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are congruent; describe the transformation sequence that verifies a congruence relationship.

Mathematics (2019) Grade(s): 8

MA19.8.24
Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them.

Unpacked Content

Vocabulary

Translation
Reflection
Rotation
Dilation
Scale factor

Knowledge

Students know:

How to perform rigid transformations and dilations graphically and algebraically (applying coordinate rules).
What makes figures similar and congruent.

Skills

Students are able to:

Use mathematical language to explain how transformations can be used to prove that two figures are similar or congruent.
Demonstrate/perform a series of transformations to prove or disprove that two figures are similar or congruent.

Understanding

Students understand that:

There is a proportional relationship between corresponding characteristics of the figures, such as lengths of line segments, and angle measures as they develop a definition for similarity between figures.
The coordinate plane can be used as tool because it gives a visual image of the relationship between the two figures.

Interdisciplinary Connection(s)

Link to Resource

https://teacher.desmos.com/activitybuilder/custom/5d4380d4fc08cd0a943e099d

Content Type / Source

CR Resource Type

Interactive/Game

Resource Provider

Desmos.com

Accessibility

License

License Type

Custom

Custom License Type (URL)

https://www.desmos.com/terms

Comments or Notes

Desmos's mission is to help every student learn math and love learning math. Teachers can explore and enjoy Desmos collections of free digital math activities that include:

meaningful feedback by showing students what their answers mean, then give them the opportunity to improve their thinking and revise their work.
collaboration by using devices to connect students, not to isolate them. Students see their classmates' thinking. They ask each other questions and create challenges for each other.
invites students to solve challenging problems using the tools they already have. We create a need for new tools before we help students learn how to use them.

If the teacher does not have an account, he/she will need to create a FREE account. (More information on how Desmos works can be found at Getting Started.)

Once the teacher has selected an activity to run, he/she will need to click on the "Create Class Code" button. This will generate a unique class code and a link to view the dashboard. (More information can be found at Creating a Class Code.) Every new activity will need a new class code in order to start a session. Students cannot start the activity until they have the class code - so sessions can be started days, hours, or mere minutes before you plan to run the activity. When the teacher is ready to have students start, have the students go to student.desmos.com and enter the class code. Although it is not required, Desmos strongly encourages students to sign in with their Desmos Student Account. Signing in allows students to resume and view their past activity work.

Approved Date

2020-07-08

Curated by

yvetteakridge

Shifting Shapes

Subject Area

Grade(s)

Overview

MA19.7A.42
Verify experimentally the properties of rigid motions (rotations, reflections, and translations): lines are taken to lines, and line segments are taken to line segments of the same length; angles are taken to angles of the same measure; and parallel lines are taken to parallel lines.

Unpacked Content

UP:MA19.7A.42

Vocabulary

Knowledge

Skills

Understanding

MA19.7A.42a
Given a pair of two-dimensional figures, determine if a series of rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are congruent; describe the transformation sequence that verifies a congruence relationship. [Grade 8, 22]

MA19.7A.44
Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them. [Grade 8, 24]

Unpacked Content

UP:MA19.7A.44

Vocabulary

Knowledge

Skills

Understanding

MA19.8.22
Verify experimentally the properties of rigid motions (rotations, reflections, and translations): lines are taken to lines, and line segments are taken to line segments of the same length; angles are taken to angles of the same measure; and parallel lines are taken to parallel lines.

Unpacked Content

UP:MA19.8.22

Vocabulary

Knowledge

Skills

Understanding

MA19.8.22a
Given a pair of two-dimensional figures, determine if a series of rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are congruent; describe the transformation sequence that verifies a congruence relationship.

MA19.8.24
Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them.

Unpacked Content

UP:MA19.8.24

Vocabulary

Knowledge

Skills

Understanding

CR Resource Type

Resource Provider

License Type

Custom License Type (URL)

Comments or Notes

Approved Date

Learning Resource Type

Shifting Shapes

Subject Area

Grade(s)

Overview

MA19.7A.42 Verify experimentally the properties of rigid motions (rotations, reflections, and translations): lines are taken to lines, and line segments are taken to line segments of the same length; angles are taken to angles of the same measure; and parallel lines are taken to parallel lines.

Vocabulary

Knowledge

Skills

Understanding

MA19.7A.42a Given a pair of two-dimensional figures, determine if a series of rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are congruent; describe the transformation sequence that verifies a congruence relationship. [Grade 8, 22]

MA19.7A.44 Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them. [Grade 8, 24]

Vocabulary

Knowledge

Skills

Understanding

MA19.8.22 Verify experimentally the properties of rigid motions (rotations, reflections, and translations): lines are taken to lines, and line segments are taken to line segments of the same length; angles are taken to angles of the same measure; and parallel lines are taken to parallel lines.

Vocabulary

Knowledge

Skills

Understanding

MA19.8.22a Given a pair of two-dimensional figures, determine if a series of rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are congruent; describe the transformation sequence that verifies a congruence relationship.

MA19.8.24 Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them.

Vocabulary

Knowledge

Skills

Understanding

URL (web address)

CR Resource Type

Resource Provider

License Type

Custom License Type (URL)

Comments or Notes

Approved Date

MA19.7A.42
Verify experimentally the properties of rigid motions (rotations, reflections, and translations): lines are taken to lines, and line segments are taken to line segments of the same length; angles are taken to angles of the same measure; and parallel lines are taken to parallel lines.

MA19.7A.42a
Given a pair of two-dimensional figures, determine if a series of rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are congruent; describe the transformation sequence that verifies a congruence relationship. [Grade 8, 22]

MA19.7A.44
Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them. [Grade 8, 24]

MA19.8.22
Verify experimentally the properties of rigid motions (rotations, reflections, and translations): lines are taken to lines, and line segments are taken to line segments of the same length; angles are taken to angles of the same measure; and parallel lines are taken to parallel lines.

MA19.8.22a
Given a pair of two-dimensional figures, determine if a series of rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are congruent; describe the transformation sequence that verifies a congruence relationship.

MA19.8.24
Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them.