Human Tree: Dilations

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

7, 8, 9, 10, 11, 12

Overview

Watch as the National Museum of Mathematics uses an image of a visitor to create a "Human Tree" using dilations. This video focuses on how similar figures can create dilations and how exponents can be used in an equation to express the proportional relationship in fractals. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers.

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.

UP:MA19.8.23

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.

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.43

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

UP:MA19.7A.43

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]

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.
Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.26

Verify experimentally the properties of dilations given by a center and a scale factor.

UP:MA19.GDA.26

Vocabulary

  • Dilations
  • Center
  • Scale factor

Knowledge

Students know:
  • Methods for finding the length of line segments (both in a coordinate plane and through measurement).
  • Dilations may be performed on polygons by drawing lines through the center of dilation and each vertex of the polygon then marking off a line segment changed from the original by the scale factor.

Skills

Students are able to:
  • Accurately create a new image from a center of dilation, a scale factor, and an image.
  • Accurately find the length of line segments and ratios of line segments.
  • Communicate with logical reasoning a conjecture of generalization from experimental results.

Understanding

Students understand that:
  • A dilation uses a center and line segments through vertex points to create an image which is similar to the original image but in a ratio specified by the scale factor.
  • The ratio of the line segment formed from the center of dilation to a vertex in the new image and the corresponding vertex in the original image is equal to the scale factor.

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

PD
https://aptv.pbslearningmedia.org/resource/mgbh.math.rp.humantree8/human-tree-d…

Comments or Notes

This resource contains an activity.

Approved Date

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