ALEX Classroom Resource

  

Translations and Reflections

  Classroom Resource Information  

Title:

 Translations and Reflections

URL:

 https://aptv.pbslearningmedia.org/resource/mkcpt.math.g.transreflections/translations-and-reflections/

Content Source:

 ReadWriteThink
Type: Audio/Video

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 Standard(s):
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
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.

a. 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]
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Confirm characteristics of the figures, such as lengths of line segments, angle measures and parallel lines as they develop a definition for congruent figures.
  • Use mathematical vocabulary to distinguish between a pair of congruent figures, noting that the figure prior to the transformation is called the preimage and the post-transformation figure is called the image.
  • Examine two figures to identify the rigid transformation(s) that produced the image from the pre-image. they can recognize the symbol for congruency (≅) and write statements of congruence.
Teacher 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.
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
43. Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two-dimensional figures. [Grade 8, 23]
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Describe the changes occurring to the x- and y-coordinates of a figure after a transformation.
Teacher 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.
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
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
Evidence Of Student Attainment:
Students:
  • Explain how transformations can be used to prove that two figures are similar.
  • Describe a sequence of transformations to prove or disprove that two figures are similar or congruent.
Teacher 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.
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 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.

a. 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.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Confirm characteristics of the figures. such as lengths of line segments, angle measures, and parallel lines as they develop a definition for congruent figures.
  • Use mathematical vocabulary to distinguish between a pair of congruent figures, noting that the figure prior to the transformation is called the preimage and the post-transformation figure is called the image.
  • Examine two figures to identify the rigid transformation(s) that produced the image from the pre-image. they can recognize the symbol for congruency (≅) and write statements of congruence.
Teacher 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.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.22.1: Define rotation, reflection, and translation.
M.8.22.2: Recognize translations (slides), rotations (turns), and reflections (flips).
M.8.22.3: Distinguish between lines and line segments.
M.8.22.4: Demonstrate how to measure length.
M.8.22.5: Demonstrate how to use a protractor to measure angles.
M.8.22.6: Identify parallel lines.
M.8.22.7: Define congruent and sequence.
M.8.22.8: Compare translations to reflections.
M.8.22.9: Compare reflections to rotations.
M.8.22.10: Compare rotations to translations.
M.8.22.11: Identify attributes of two-dimensional figures.
M.8.22.12: Identify congruent figures.

Prior Knowledge Skills:
  • Define ordered pairs.
  • Name the pairs of integers and/or rational numbers of a point on a coordinate plane.
  • Demonstrate when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
  • Identify which signs indicate the location of a point in a coordinate plane.
  • Recall how to plot ordered pairs on a coordinate plane.
  • Define reflections.
  • Define reflections.
  • Calculate the distances between points having the same first or second coordinate using absolute value.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.22 Identify 3 different transformations (e.g., reflection, rotation, translation).
Mathematics
MA2019 (2019)
Grade: 8
23. Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two-dimensional figures.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Describe the changes occurring to the x-and y-coordinates of a figure after a transformation.
Teacher 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.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.23.1: Define dilation.
M.8.23.2: Recall how to find scale factor.
M.8.23.3: Give examples of scale drawings.
M.8.23.4: Recognize translations.
M.8.23.5: Recognize reflections.
M.8.23.6: Recognize rotations.

Prior Knowledge Skills:
  • Define scale, scale drawings, length, area, and geometric figures.
  • Locate/use scale on a map.
  • Identify proportional relationships.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.23 Recognize the reflection (across the x or y axis) and translation (across quadrants) of a two dimensional figure on a coordinate plane (limited to non-equilateral rectangles and triangles).
Mathematics
MA2019 (2019)
Grade: 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
Evidence Of Student Attainment:
Students:
  • Explain how transformations can be used to prove that two figures are similar.
  • Describe a sequence of transformations to prove or disprove that two figures are similar or congruent.
Teacher 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.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.24.1: Define similar.
M.8.24.2: Recognize dilations.
M.8.24.3: Recognize translations.
M.8.24.4: Recognize rotations.
M.8.24.5: Recognize reflections.
M.8.24.6: Identify similar figures.
M.8.24.7: Analyze an image and its dilation to determine if the two figures are similar.

Prior Knowledge Skills:
  • Define ordered pairs.
  • Name the pairs of integers and/or rational numbers of a point on a coordinate plane.
  • Demonstrate when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
  • Identify which signs indicate the location of a point in a coordinate plane.
  • Recall how to plot ordered pairs on a coordinate plane.
  • Define reflections.
  • Calculate the distances between points having the same first or second coordinate using absolute value.
Tags: reflection, translation, vertices
License Type: Public Domain
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityVideo resources: includes closed captioning or subtitles
Comments

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  This resource provided by:  
Author: Kristy Lacks
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