Classroom Resource

Translations and Reflections

Subject Area

Mathematics

Grade(s)

7, 8

Overview

Watch an animated demonstration of translating and reflecting a triangle on the coordinate plane in this video from KCPT. In the accompanying classroom activity, students watch the video and then consider the effect of translating and reflecting on the coordinates of the vertices of the triangle. Next, they draw translations and reflections of a triangle and identify the number of units and direction of translation as well as the lines of reflection in classmates drawings. To get the most from the lesson, students should be comfortable graphing points on the coordinate plane. Prior exposure to reflection is helpful.

Content Standards

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

MA19.8.23
Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two- dimensional figures.

Unpacked Content

Vocabulary

Coordinates
Congruent
Rotation
Reflection
Translation
Dilation
Scale factor

Knowledge

Students know:

What it means to translate, reflect, rotate, and dilate a figure.
How to perform a translation, reflection, rotation, and dilation of a figure.
How to apply (x, y) notation to describe the effects of a transformation.

Skills

Students are able to:

Select and apply the proper coordinate notation/rule when given a specific transformation for a figure.
Graph a pre-image/image for a figure on a coordinate plane when given a specific transformation or sequence of transformations.

Understanding

Students understand that:

the use of coordinates is also helpful in proving the congruence/proportionality between figures.
The relationships between coordinates of a preimage and its image for dilations represent scale factors learned in previous grade levels.

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.

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.43
Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two- dimensional figures. [Grade 8, 23]

Unpacked Content

Vocabulary

Coordinates
Congruent
Rotation
Reflection
Translation
Dilation
Scale factor

Knowledge

Students know:

what it means to translate, reflect, rotate, and dilate a figure.
how to perform a translation, reflection, rotation, and dilation of a figure.
how to apply (x, y) notation to describe the effects of a transformation.

Skills

Students are able to:

select and apply the proper coordinate notation/rule when given a specific transformation for a figure.
Graph a pre-image/image for a figure on a coordinate plane when given a specific transformation or sequence of transformations.

Understanding

Students understand that:

the use of coordinates is also helpful in proving the congruency/proportionality between figures.
The relationships between coordinates of a preimage and its image for dilations represent scale factors learned in previous grade levels.

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.

Interdisciplinary Connection(s)

Link to Resource

https://aptv.pbslearningmedia.org/resource/mkcpt.math.g.transreflections/transl…

Content Type / Source

CR Resource Type

Audio/Video

Resource Provider

ReadWriteThink

Accessibility

License

License Type

Comments or Notes

This resource contains an activity sheet.

Approved Date

2022-09-13

Curated by

Learning Resource Type

Translations and Reflections

Subject Area

Grade(s)

Overview

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

MA19.8.23 Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two- dimensional figures.

Vocabulary

Knowledge

Skills

Understanding

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

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.43 Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two- dimensional figures. [Grade 8, 23]

Vocabulary

Knowledge

Skills

Understanding

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

URL (web address)

CR Resource Type

Resource Provider

License Type

Comments or Notes

Approved Date

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.

MA19.8.23
Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two- dimensional figures.

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.

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.43
Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two- dimensional figures. [Grade 8, 23]

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]