Thinkport | Finding Reflections in Landscape Architecture

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

7, 8

Overview

Learn about reflections through examples from landscape architecture in this video from MPT. In the accompanying classroom activity, students identify reflection lines in photographs of designed landscapes. Next, they draw a triangle and graph its reflections over the x-axis and y-axis. They then consider changes in coordinates that result from these reflections. To get the most from the lesson, students should be comfortable graphing in all four quadrants of the coordinate plane. For a longer self-paced student tutorial using this media, see "Transformations in Landscaping" on Thinkport from Maryland Public Television.

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.

UP:MA19.8.22

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

MA19.8.24

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.

UP:MA19.8.24

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.

UP:MA19.7A.42

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.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]

UP:MA19.7A.44

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.

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

PD
https://aptv.pbslearningmedia.org/resource/mmpt-math-g-findingreflectiions/find…

Comments or Notes

This resource contains an activity entitled Finding Reflections in Landscape Architecture - Activity.

Approved Date

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