Measuring Polygon Side Lengths

Mrs. Thompson Level 1

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Lesson Overview (4 of 4)

Topic Background

For students interested in the history of mathematics you can point them to online resources that discuss the development of the Cartesian Plane by René Descartes in the 17th century.

Links:• https://www.khanacademy.org/math/algebra/introduction-to-algebra/ov

erview_hist_alg/v/descartes-and-cartesian-coordinates (note the above link mentions algebraic concepts quite a bit)

• http://4dlab.info/article_short_history_of_the_cartesian_coordinates.htm• http://mathematica.ludibunda.ch/mathematicians1.html (note the above

link mentions the Pythagorean theorem

Warm Up

Version 23

CONTENT OBJECTIVE: You will be able to measure the side lengths of a polygon on the coordinate plane without counting.LANGUAGE OBJECTIVE: Students will talk about the x- and y-coordinates of points.

Answer

Find the length of the line segment.

Then write a paragraph explaining how you found the line segment. Be specific and include all details.

Agenda:

1) Warm Up (5 min, individual): Explain how to measure side length 2) Launch (15 min, whole class): New method for measuring side length

3) Explore/Practice (25 min, partner): Using both methods

4) Summary (5 min, whole class): Why (and when) use the new method?

5) Assessment (5 min, individual): Exit ticket

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CONTENT OBJECTIVE: You will be able to measure the side lengths of a polygon on the coordinate plane without counting.LANGUAGE OBJECTIVE: Students will talk about the x- and y-coordinates of points.

Handout: Launch, p.1

Agenda8

2 units

Handout: Launch, p.1

Agenda9

3 units

Handout: Launch, p.1

Agenda10

4 units

Handout: Launch, p.1

Agenda11

Questions: 1. What coordinate stays the same in each of the three examples? 2. What coordinate changes in each of the three examples? 3. What is the relationship between the coordinate that changes and the length of the line segment?

(1,2) (3,2)(1,2) (3,2)

2 units

3 – 1 = 2 units

Scaffold

Handout: Launch, p.1

Agenda14

Questions: 1. What coordinate stays the same in each of the three examples?

2. What coordinate changes in each of the three examples?

3. What is the relationship between the coordinate that changes and the length of the line segment?

Answer

Handout: Launch, p.1

Agenda16

3 – 1 =

2 units

2

Handout: Launch, p.1

Agenda17

4 – 1 =

3 units

3

Handout: Launch, p.1

Agenda18

5 – 1 =

4 units

4

Handout: Launch, p.2

Agenda19

4 units

Handout: Launch, p.2

Agenda20

3 units

Handout: Launch, p.2

Agenda21

2 units

Handout: Launch, p.2

Agenda22

Questions: 1. What coordinate stays the same in each of the three examples? 2. What coordinate changes in each of the three examples? 3. What is the relationship between the coordinate that changes and the length of the line segment?

(2,4)

(2,0)

(2,4)

(2,0)

4 units

4 – 0 = 4 units

Scaffold

Handout: Launch, p.2

Agenda25

Questions: 1. What coordinate stays the same in each of the three examples?

2. What coordinate changes in each of the three examples?

3. What is the relationship between the coordinate that changes and the length of the line segment?

Answer

Handout: Launch, p.2

Agenda27

4 – 0 =4 units

4

Handout: Launch, p.2

Agenda28

3 – 0 =

3 units

3

Handout: Launch, p.2

Agenda29

2 – 0 =

2 units

2

Handout: Launch, p.3

Agenda30

Summary: Another way to measure a horizontal or vertical line segment is by…

Answer

Handout: Launch, p.3

Agenda32

Answer

Handout: Practice

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Agenda

Page 1Page 2Page 3

Handout: Practice, p.1

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Agenda

Polygon D

Answer

Handout: Practice, p.2

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Agenda

2. Give the coordinates of three points that lie on a horizontal line with the point (–2, 7). Explain how you know that all three points lie on the same line with (–2,7).

3. Give the coordinates of three points that lie on a vertical line with the point (–2, 7). Explain how you know that all three points lie on the same line with (–2,7).

Answer

Handout: Practice, p.4

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AgendaAnswer

Set #3

Perimeter is ________________.

Handout: Practice, p.4

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Agenda

6. You are told that a rectangle has vertices at the following coordinates:

To find the side lengths of the rectangle would you rather use Method #1: Counting on the Coordinate Plane or Method #2: Calculating Using Coordinates? Explain why you would use that method.

(Note: you do not need to find the side lengths, just explain which strategy you would prefer and why)

Handout: Exit Ticket

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Agenda

1) Individually work on the exit ticket.

2) When you turn in your exit ticket, collect a homework handout.

3) Have a great day!