document.docx382 LessonMEAS3 (3 Instructional Days)Proportional Change

8(10)  Two-dimensional shapes. The student applies mathematical process standards to develop transformational geometry concepts. The student is expected to:(D)  model the effect on linear and area measurements of dilated two-dimensional shapes. Supporting

The student will know… The student will be able to… that a proportional change occurs in

the perimeter and/or area of a pre-image when a scale factor is applied to the dimensions.

describe the effects on area and perimeter (including scale factor) when the dimensions of a two-dimensional figure are changed proportionally.

estimate and/or determine the area and/or perimeter of a new two-dimensional figure when the dimensions of the original figure are changed proportionally.

Technology TEKS:8(1) Creativity and innovation. The student uses creative thinking and innovative processes to construct knowledge, generate new ideas, and create products. The student is expected to:(C)  explore complex systems or issues using models, simulations, and new technologies to develop hypotheses, modify input, and analyze results; and8(3) Research and information fluency. The student acquires, analyzes, and manages content from

digital resources. The student is expected to:(D) process data and communicate results.8(4) Critical thinking, problem solving, and decision making. The student makes informed

decisions by applying critical-thinking and problem-solving skills. The student is expected to:(C) collect and analyze data to identify solutions and make informed decisions;(E) make informed decisions and support reasoning;

ELPS:(2) Cross-curricular second language acquisition/listening. The student is expected to:(D) monitor understanding of spoken language during classroom instruction and interactions and seekclarification as needed;(2) Cross-curricular second language acquisition/listening. The student is expected to:(I) demonstrate listening comprehension of increasingly complex spoken English by followingdirections, retelling or summarizing spoken messages, responding to questions and requests,collaborating with peers, and taking notes commensurate with content and grade-level needs.(3) Cross-curricular second language acquisition/speaking. The student is expected to:(D) speak using grade-level content area vocabulary in context to internalize new English words andbuild academic language proficiency;(3) Cross-curricular second language acquisition/speaking. The student is expected to:(E) share information in cooperative learning interactions;(5) Cross-curricular second language acquisition/writing. The student is expected to:(B) write using newly acquired basic vocabulary and content-based grade-level vocabulary;

Materials Glue Scissors ISN Dark Green, Lite Green, and Red colored pencils 1 copy of Proportional Change recording document per student (Day 1) 1 copy of Proportional Change ISN entry per student on white paper (Day 1) 1 copy of Proportional Change Practice per student (Day 1) 1 dry erase marker, dry erase board and eraser per student (Day 2) 1 copy of What’s the Change? per student (Day 2) 1 copy of Let’s Adjust alternative assessment per student (Day 3)

Procedure:Day 1:

document.docxUse the MATH_0382_MEAS3_MAT_PROPORTIONALCHANGE_02 Geometer’s Sketchpad file (GSP) and MATH_0382_MEAS3_MAT_PROPCHANGEISN_02 to guide this lesson. Use the Proportional Change recording document for this lesson.

Tab 1:Use a scale factor of one to demonstrate what happens to the perimeter and area of the image. Allow students to write this information onto the recording document.

Use this column to write your own notes.

Tab 2:Use a scale factor larger than one to demonstrate what happens to the perimeter and area of the image. Discuss the difference between the scale factor for perimeter and area. Allow students to write this information onto the recording document.

Tab 3:Use a scale factor smaller than one to demonstrate what happens to the perimeter and area of the image. Discuss the difference between the scale factor for perimeter and area. Allow students to write this information onto the recording document.Tab 4:This is a repeat of the concept in Tab 3 but with a different figure. Repeat the same process with students as outlined in Tab 3 notes.

document.docxTab 5:This is a repeat of the concept in Tab 2 but with a different figure. Repeat the same process with students as outlined in Tab 2 notes.

Slide 1:This slide guides the students with setting up their ISN entry.

Slide 2:This slide provides the student with the process on how to find proportional change of perimeter above their ISN foldable.

Slide 3:This slide provides the student with the process on how to find proportional change of area below their ISN foldable.

Assign students Proportional Change Practice as Independent Practice/Homework

Procedure

document.docxDay 2:Use MATH_0382_MEAS3_MAT_LETSBEPROPORTIONAL_02 to guide this lesson.Provide students with a dry erase marker, dry erase board, and eraser for this lesson or the optional recording document, Let’s Be Proportional.

Prezi Home page:Introduction slide.

Use this column to write your own notes.

Slide 1:This slide allows the student to practice finding the perimeter of an image while using a scale factor. Student should complete the practice on a dry erase board, then confirm their answer with the teacher.

D. 40 units

Slide 2:This slide allows the student to understand the concept of the effects of the scale factor on the area of a figure.

C. The image’s area is ¼ as large as the pre-image’s area

Slide 3:This slide allows the student to practice finding the scale factor used to create the area of an image.

D. 1/16

document.docxSlide 4:This slide allows the student to practice finding the perimeter and area of an image.

D. P=48 units and A=144units2

Slide 5:This slide allows the student to practice deciding what is not true about proportional change of perimeter and area.

A. The image’s perimeter and area will be 5 times larger

Slide 6:This slide allows the student to practice finding area of the image using a scale factor.

B. 6 units2

Slide 7:This slide allows the student to practice finding the perimeter and area of the figure using a scale factor.

B. 8 units and 4 units2

document.docxSlide 8:This slide allows the student to practice finding the area of a figure using a scale factor.

C. 512 units2

Assign the students What’s the Change? as independent practice/homework.

Procedure:

document.docxDay 3:There is no presentation for this day in the lesson.

Let’s Adjust!

1) This is an alternate assessment. Allow students to work in small groups of 2 or 3.2) Each group of students receives 1 copy of the assessment including 2 pieces of graph paper, attached.3) Students will create a scale factor and a pre-image and image for proportional change of perimeter and area.4) Students will answer any corresponding questions, including who’s correct on the back.

Proportional ChangeTab 1: Rectangle centered at the origin

Scale Factor

Side Lengths Perimeter Area

Pre-Image Image Pre-Image Image Pre-Image Image

document.docxCD = C’D’ =

DE = D’E’ =

EF = E’F’ =

FC = F’C’ = ______ (______) = _____ Original Perimeter (SF) = New Perimeter

____ (____)(____) = ____Original Area (SF) (SF) = New Area

How did the scale factor affect the new perimeter and new area of the figure?______________________________________________________________________________

Tab 2: Rectangle in quadrant 4Scale Factor

Side Lengths Perimeter Area

Pre-Image Image Pre-Image Image Pre-Image ImageCD = C’D’ =

DE = D’E’ =

EF = E’F’ =

FC = F’C’ = ______ (______) = _____ Original Perimeter (SF) = New Perimeter

____ (____)(____) = ____Original Area (SF) (SF) = New Area

How did the scale factor affect the new perimeter and new area of the figure?

____________________________________________________________________________________________________

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Tab 3: Rectangle in quadrant 1Scale Factor

Side Lengths Perimeter Area

Pre-Image Image Pre-Image Image Pre-Image ImageCD = C’D’ =

DE = D’E’ =

EF = E’F’ =

FC = F’C’ = ______ (______) = _____ Original Perimeter (SF) = New Perimeter

____ (____)(____) = ____Original Area (SF) (SF) = New Area

How did the scale factor affect the new perimeter and new area of the figure?

______________________________________________________________________________

Tab 4: Right TriangleScale Factor

Side Lengths Perimeter Area

Pre-Image Image Pre-Image Image Pre-Image ImageCE = C’E’ =

EF = E’F’ =

FC = F’C’ =

______ (______) = _____ Original Perimeter (SF) = New Perimeter

____ (____)(____) = ____Original Area (SF) (SF) = New Area

document.docxHow did the scale factor affect the new perimeter and new area of the figure?______________________________________________________________________________

Tab 5: Right TriangleScale Factor

Side Lengths Perimeter Area

Pre-Image Image Pre-Image Image Pre-Image ImageEF = E’F’ =

GC = G’C’ =

______ (______) = _____ Original Perimeter (SF) = New Perimeter

____ (____)(____) = ____Original Area (SF) (SF) = New Area

How did the scale factor affect the new perimeter and new area of the figure?______________________________________________________________________________

Main Idea of Proportional Change

Why is the scale factor multiplied once when the perimeter is being changed proportionally?

_____________________________________________________________________________

Why is the scale factor multiplied twice when the area is being changed proportionally?_____________________________________________________________________________

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Proportional ChangeISN Suggestion

MaterialsISNScissorsGlue/tapeProportional Change ISN Entry

Have students cut out the large rectangle leaving the smaller rectangle attached. Provide students with a dark and light green colored pencil to represent area and a red colored pencil to represent perimeter. Students should color the small rectangle dark green and the large rectangle light green. Have students trace the outside of each rectangle with the red colored pencil. Students will then paste the foldable on the right side of their notebook. See example below.

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Proportional Change ISN Entry

3 (1.5) = _____

5 (1.5)

5

3 in

3 (1.5) = _____

5 (1.5)

5

3 in

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Name: _______________________Date: _______________________

Proportional Change Practice_____1.Rectangle ABCD is similar to rectangle A’B’C’D’.

If the perimeter of rectangle ABCD is 18 units and it is dilated by a scale factor of 2, what is the perimeter of rectangle A’B’C’D’?

A. 10 units C. 18 unitsB. 28 units D. 36 units

_____2. If the length of a side of a square is increased from 4 to 8, which of the following statements is true?A. Both the area and perimeter are doubled.B. Both the area and perimeter are quadrupled.C. The perimeter is doubled and the area is quadrupled.D. The perimeter is quadrupled and the area is doubled.

_____3. If the side lengths of the square below are tripled, what is NOT true about its perimeter and area?

A. The scale factor from the pre-image to the image is 3.B. The image’s perimeter will be three times larger and the area will be 9 times larger

than the pre-image.C. The image’s perimeter will be 72 mm and the area will be 324 mm. D. The image’s perimeter and area will be three times larger than the pre-image.

5 units

C’ D’

B’A’

D C

BA

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_____4.Rectangle DEFG is similar to rectangle D’E’F’G’.

If the pre-image area of rectangle DEFG is 80 units and it is dilated by a scale factor of ½, what is true about the image’s perimeter?A. The image’s perimeter is twice as large as the pre-image’s perimeter.B. The image’s perimeter is half as large as the pre-image’s perimeter.C. The image’s perimeter is ¼ as large as the pre-image’s perimeter.D. Cannot be determined.

_____5. A 24 x 32 inch photograph is reduced so that each side is one-fourth the original size. What is the number of square inches in the smaller photograph and the new perimeter length?

A. 48 cm2 / 28 cm C. 6 cm2 / 8 cmB. 28 cm2 / 48 cm D. 768 cm2 / 112 cm

_____6. The sides’ measures of two squares are shown below. The area of the smaller square is 81 square feet. What is the area of the larger square?

A. 9 cm2 C. 384 cm2

B. 27 cm2 D. 729 cm2

20 units G F

ED

G’ F’

E’D’

document.docxANSWER KEY

1. D. 36 units2. C. The perimeter is doubled and the area is quadrupled.3. D. The image’s perimeter and area will be three times larger than the pre-image.4. B. The image’s perimeter is half as large as the pre-image’s perimeter.5. A. 48 cm2 / 28 cm6. D. 729 cm2

Name: _____________________Date: _____________________

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Slide 2A 6x4 rectangle is dilated by a scale factor of 2. What is the perimeter of rectangle A’B’C’D’?

A. 24 units C. 48 unitsB. 20 units D. 40 units

Slide 3

A pre-image is dilated by a scale factor of . Which of the following is true?

A. The image’s area is 2 times the pre-image’s area.

B. The image’s area is the pre-image’s area.

C. The image’s area is the pre-image’s area.D. The image’s area is 4 times the pre-image’s area.

Slide 4Square STUV is dilated to create square S’T’U’V’. If the area of the pre-image is 64 and the area of the image is 4, what is the scale factor of the areas from the pre-image to the image?

A. B. 4C. 16

D.

Slide 5

2 in1 in

4 in

2 in

document.docxThe perimeter of a square is 12 units and the area is 9 units2. What is the new perimeter and the new area of the image?

A. P = 48 units C. P = 16 unitsA = 36 units2 A = 36 units2

B. P = 16 units D. P = 48 unitsA = 144 units2 A = 144 units2

Slide 6If the side lengths of the pre-image are dilated by a scale factor of 5, what is not true about the perimeter and area of the image?

A. The image’s perimeter and area will be 5 times larger.B. The image’s perimeter is 160 ft and the area is 1600 ft2.C. Motion rule is (x, y) (5x, 5y)D. The image’s perimeter will be 5 times larger and the area will be 25

times larger.

Slide 7The perimeter of the pre-image is 30 units, while the perimeter of the image is 10 units. If the area of the pre-image is 56 units2, approximately what is the area of the image?

A. 168 units2 C. 19 units2

B. 6 units2 D. not here

Slide 8

What is the perimeter and area of the image if the pre-image below is dilated by ?

4XX

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A. 32 units and 64 units2

B. 8 units and 4 units2

C. 8 units and 16 units2

D. 4 units and 8 units2

Slide 9The perimeter of the pre-image is 24 units while the perimeter of the image is 96 units. If the area of the pre-image is 32 units2, what is the area of the image?

A. 256 units2 C. 512 units2

B. 128 units2 D. 96 units2

Name: _____________________ Date: _____________________

What's the Change?

document.docx1) Pre-image JLMN measures 5.5 cm by 7 cm. The pre-image is dilated by a scale factor of 2.5. What

is the perimeter and area of the image?

2) Image A'B'C'D' has a perimeter of 37. The pre-image has a perimeter of 74. What scale factor was used to change the perimeter of the pre-image?

3) The pre-image below is dilated by a scale factor of 3.5. What is the perimeter and area of the image?

4) Pre-image HAWK has a perimeter of 174 ft. If the pre-image is dilated by 1/3, what is the perimeter of the image?

5) What is true about the pre-image and image below?

A) The perimeter and area are dilated by a scale factor of 4.5.

B) The perimeter of the image is 32 units and the area of the image is 63 units2.

C) The perimeter is dilated by a scale factor of 4.5 and area is dilated by a scale factor of 20.25.

D) The perimeter of the image is 144 units and the area of the image is 283.5 units2.

What's the Change? KEY1) Perimeter = 62.5 cm

Area = 240.625 cm2

2)

11 units11 units

7 units

9 units 7(4.5) units

9(4.5) units

document.docx3) Perimeter = 154 units

Area = 1482.25 units2

4) 58 ft.

5) C

Names: ________________________ __________________________ ______________________Date: _______________________

I. Draw and label a polygon with 4 sides using the given graph paper.

What is the perimeter of the pre-image? ___________ 3 points

Reduce the polygon by a scale factor of __________. 4 pointsComplete the following table with the vertex ordered pairs. 10 points

Pre-Image Vertex

Ordered Pair

Image

Vertex

Ordered Pair

Let’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s AdjustLet’s Adjust

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Draw and label the reduced image with the pre-image.

What is the perimeter of the image? ___________ 3 points

II. Draw and label a polygon with 4 sides using the given graph paper.

What is the area of the pre-image? _____________ 3 points

Enlarge the polygon by a scale factor of __________. 4 points

Draw and label the enlarged image with the pre-image.

What is the area of the image? _____________ 3 points

Explain: (5 points)What is another way to solve for proportional change of the perimeter?________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

III. Who’s correct? (15 points)Kameron and Sofia solved the following proportional change problem:

The pre-image is dilated by a scale factor of 3.5. What is the area of the image?Kameron’s Process Sofia’s Process

2

2

3 4 12

12 3.5 42.5

x cm

x cm

2

2

3 4 12

12 3.5 3.5 147

x cm

x x cm

Complete the following table with the vertex ordered pairs. 10 points

Pre-Image Vertex

Ordered Pair

Image

Vertex

Ordered Pair

(your choice)

(your choice)

Show Process: 10 points

Complete the following table with the vertex ordered pairs. 10 points

Pre-Image Vertex

Order Pair

Image

Vertex

Order Pair

4 cm3 cm

Show Process: 10 points

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Circle the student’s name who completed the process incorrectly. What is the correct process for solving proportional change of area and why?________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

The pre-image is dilated by a scale factor of 3.5. What is the area of the image?Kameron’s Process Sofia’s Process

2

2

3 4 12

12 3.5 42.5

x cm

x cm

2

2

3 4 12

12 3.5 3.5 147

x cm

x x cm

document.docxPerimeter 10 points

document.docxArea 10 points

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Let’s Adjust KeyAnswers for part I, II and III will vary depending on the process they choose, the scale factor and shapes the student creates.

IV. Who’s correct? (15 points)Kameron and Sofia solved the following proportional change problem:

Circle the student’s name who completed the process incorrectly. What is the correct process for solving proportional change of area and why?Sofia’s process is correct when solving for proportional change of area because you have to multiple both sides of the rectangle, pre-image, by the scale factor of 3.5.

4 cm3 cm

The pre-image is dilated by a scale factor of 3.5. What is the area of the image?Kameron’s Process Sofia’s Process

2

2

3 4 12

12 3.5 42.5

x cm

x cm

2

2

3 4 12

12 3.5 3.5 147

x cm

x x cm