lesson 3 homework practice dilations

Measuring Dilations

Lesson Narrative

This lesson gives students more opportunities to practice drawing dilations precisely by reasoning about the definition of a dilation (MP6). Students construct and compare several examples of dilations, and then measure corresponding lengths and distances in the dilated and original figure. Through experimentation, students conjecture that all distances and lengths in the scaled figure are increased or decreased according to the same ratio given by the scale factor.

In this lesson they justify that the distances to the center of the dilation from the scaled figure and from the original figure have the same ratio as the scale factor because of how dilations are defined. They also notice that the ratios of corresponding lengths within the original and scaled figure are the same as the scale factor, but that this fact doesn’t come directly from the definition. In this course, we don’t prove this relationship, instead we leave it as an assertion, justified only by experimentation.

Note on language: In previous courses, students may have learned that a ratio is an association between two or more quantities. However in more advanced work, such as this course, ratio is commonly used as a synonym for quotient (which some refer to as the value of the ratio ). This expanded use of the word ratio comes into play in this lesson when students are asked to write fractions representing ratios and notice connections between the fraction and the scale factor. In later lessons we will refer interchangeably to scale factor, ratio of side lengths, and use “ratio” to mean “the quotient of the side lengths.”

Learning Goals

Teacher Facing

• Comprehend that corresponding lengths in the original figure and image are in the same proportion.
• Determine that dilating by a scale factor of $k$ multiplies all lengths by $k$ (orally and in writing).

Student Facing

• Let’s dilate polygons.

Required Materials

• Geometry toolkits (HS)
• Rulers marked with centimeters

Learning Targets

• I know that when figures are dilated by a scale factor of $k$, all lengths in the figure are multiplied by $k$.

CCSS Standards

Building On

• HSG-SRT.A.1
• HSG-SRT.A.1.b

Building Towards

• HSG-SRT.A.2

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Describing Dilations

Help students deepen their understanding of dilations on the coordinate plane with this eighth-grade geometry worksheet! In Describing Dilations, learners are given coordinate planes that show a preimage and its dilated image. Students are asked to describe the dilations depicted on eight different coordinate planes. This worksheet is helpful practice for students as they learn about transformations on the coordinate plane. For practice completing and graphing dilations on the coordinate plane, having students complete the  Dilations on the Coordinate Plane  worksheet.

View aligned standards

Dilations Worksheets

What are Dilation Transformations? In mathematics, a dilation is a function from a metric space into itself that satisfies the identity for all points, where is the distance from to and is some positive real number. In Euclidean space, such a dilation is a similarity of the space. Dilations change the size but not the shape of an object or figure. OR A dilation is a transformation that produces an image that is the same shape as the original, but is a different size... A description of a dilation includes the scale factor (or ratio) and the center of the dilation. The center of dilation is a fixed point in the plane.

Basic Lesson

Guides students through recognizing dilations. Under a dilation, triangle A(0,0), B(0,2), C(4,0) becomes triangle A'(0,0), B'(0,4), C(8,0). What is the scale factor for this dilation? B(0,2) becomes after dilation B'(0,4) that means y coordinate changed 2 to 4.

Intermediate Lesson

Demonstrates the use of coordinates with dilations. Triangle ABC becomes A'B'C' after dilation as shown in figure. What is the scale factor?

Independent Practice 1

A really great activity for allowing students to understand the concepts of the Dilations.

Independent Practice 2

Students use Dilations in 20 assorted problems. The answers can be found below.

Homework Worksheet

Students are provided with 12 problems to achieve the concepts of Dilations.

This tests the students ability to understand Dilations.

Homework and Quiz Answer Key

Answers for the homework and quiz.

Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

Guides students through solving transformations in the form ofg dilations. If an image is 7 units in size, under a dilation of scale factor 3 what will be the size of figure after dilation?

Demonstrates the concept of advanced skill while solving these problems. Under a dilation, the picture shown at the left has been reduced in size just half of the image. What is the scalar factor.

A really great activity for allowing students to understand the concepts of the core skill that is lead here. The length of a pencil is 6 inches. Under a dilation of scale factor 2, the length of the large/small pencil is:?

Students work on 20 different assorted problems. The answers can be found below.

Students are provided with 12 problems to achieve the concepts we explored.

This tests the students ability to understand what we are studying here.

Answer Keys

Answers for all lessons and independent practice.

Question: Where did Christopher Complementary begin his journey?

Answer: At the Verta Seas.

• Inspiration

Properties of Dilations

New york state common core math grade 8, module 3, lesson 2, lesson 1 outcome lesson 2 outcome.

• Students learn how to use a compass and a ruler to perform dilations. • Students learn that dilations map lines to lines, segments to segments, and rays to rays. Students know that dilations are degree preserving.

Lesson 2 Summary

Dilations map lines to lines, rays to rays, and segments to segments. Dilations map angles to angles of the same degree.

NYS Math Module 3 Grade 8 Lesson 2

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Unit 7 – Dilations and Similarity

LESSON/HOMEWORK

LESSON VIDEO

EDITABLE LESSON

EDITABLE KEY

SMART NOTEBOOK

Dilations in the Coordinate Plane

Dilations and Angles

Similar Figures

Similarity Criteria

Reasoning with Similarity

More Similarity Reasoning

The Side Splitter Theorem

Partitioning a Line Segment

The Medians of a Triangle

Partitioning the Hypotenuse with an Altitude

Geometric Means

Proving the Pythagorean Theorem (No Homework)

Unit Review

Unit 7 Review

UNIT REVIEW

EDITABLE REVIEW

Unit 7 Assessment – Form A

EDITABLE ASSESSMENT

Unit 7 Exit Tickets

U07.AO.01 – Partitioning a Side with an Angle Bisector (Extended Activity)

EDITABLE RESOURCE

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