Post on 01-Jan-2016
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 2
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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.
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
Agenda
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2 units
Handout: Launch, p.1
Agenda
9
3 units
Handout: Launch, p.1
Agenda
10
4 units
Handout: Launch, p.1
Agenda
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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
Agenda
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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
Agenda
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3 – 1 =
2 units
2
Handout: Launch, p.1
Agenda
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4 – 1 =
3 units
3
Handout: Launch, p.1
Agenda
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5 – 1 =
4 units
4
Handout: Launch, p.2
Agenda
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4 units
Handout: Launch, p.2
Agenda
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3 units
Handout: Launch, p.2
Agenda
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2 units
Handout: Launch, p.2
Agenda
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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
Agenda
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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
Agenda
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4 – 0 =4 units
4
Handout: Launch, p.2
Agenda
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3 – 0 =
3 units
3
Handout: Launch, p.2
Agenda
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2 – 0 =
2 units
2
Handout: Launch, p.3
Agenda
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Summary: Another way to measure a horizontal or vertical line segment is by…
Answer
Handout: Launch, p.3
Agenda
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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!