ALEX Classroom Resource

  

Sketchy Dilations

  Classroom Resource Information  

Title:

 Sketchy Dilations

URL:

 https://teacher.desmos.com/activitybuilder/custom/5e13560bbefb180dcd92d427

Content Source:

 Other
Desmos
Type: Learning Activity

Overview:

In this Desmos lesson, students are informally introduced to dilations through experimenting with "sketching machines" that allow them to adjust various parts of a drawing to see the effect on the pre-image. Students are then introduced to similarity as the result of dilation. This activity should be used to help teach a lesson on transformations. This Desmos activity offers sample student responses and a teacher guide.

 

Content Standard(s):
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
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: dilation, transform, transformations
License Type: Custom Permission Type
See Terms: https://www.desmos.com/terms
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityText Resources: Content is organized under headings and subheadings
Comments

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.

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. 

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Author: YVETTE AKRIDGE
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