1. Measuring Polygon Side Lengths Mrs. Thompson Level 1 1

2. 2 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 17 th century. Links: https://www.khanacademy.org/math/algebra/introduction-to- algebra/overview_hist_alg/v/descartes-and-cartesian-coordinates (note the above link mentions algebraic concepts quite a bit) https://www.khanacademy.org/math/algebra/introduction-to- algebra/overview_hist_alg/v/descartes-and-cartesian-coordinates 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 http://mathematica.ludibunda.ch/mathematicians1.html

3. Warm Up Version 2 3 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.

4. Warm Up (version 2) 4 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.

5. Warm Up (version 2, Answer) Version 2 5 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. Length = 9 units Explanation: Determine scale of axis. This tell you how to skip count. Start at one endpoint and skip count to the other endpoint. Jump from one gridline to the next till you reach the endpoint.

6. Warm Up (Answer) Version 2 6 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. Length = 4 units Explanation: Determine scale of axis. This tell you how to skip count. Start at one endpoint and skip count to the other endpoint. Jump from one gridline to the next till you reach the endpoint.

7. 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 7 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.

8. Handout: Launch, p.1 Agenda 8 2 units

9. Handout: Launch, p.1 Agenda 9 3 units

10. Handout: Launch, p.1 Agenda 10 4 units

11. Handout: Launch, p.1 Agenda 11 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

12. Handout: Launch, p.1 Agenda 12 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)(4,2) (1,2)(4,2) 3 units 4 – 1 = 3 units

13. Handout: Launch, p.1 Agenda 13 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)(5,2) (1,2)(5,2) 4 units 5 – 1 = 4 units

14. Handout: Launch, p.1 Agenda 14 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

15. Handout: Launch, p.1 Agenda 15 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? The y-coordinate was the same in each example. The x-coordinate changed in each example. If you subtract the coordinates the smaller x-coordinate from the larger one you get the length of the line segment.

16. Handout: Launch, p.1 Agenda 16 3 – 1 = 2 units 2

17. Handout: Launch, p.1 Agenda 17 4 – 1 = 3 units 3

18. Handout: Launch, p.1 Agenda 18 5 – 1 = 4 units 4

19. Handout: Launch, p.2 Agenda 19 4 units

20. Handout: Launch, p.2 Agenda 20 3 units

21. Handout: Launch, p.2 Agenda 21 2 units

22. Handout: Launch, p.2 Agenda 22 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

23. Handout: Launch, p.2 Agenda 23 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? (2,3) (2,0) (2,3) (2,0) 3 units 3 – 0 = 3 units

24. Handout: Launch, p.2 Agenda 24 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? (2,2) (2,0) (2,2) (2,0) 2 units 2 – 0 = 2 units

25. Handout: Launch, p.2 Agenda 25 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

26. Handout: Launch, p.2 Agenda 26 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? The x-coordinate was the same in each example. The y-coordinate changed in each example. If you subtract the coordinates the smaller y-coordinate from the larger one you get the length of the line segment.

27. Handout: Launch, p.2 Agenda 27 4 – 0 = 4 units 4

28. Handout: Launch, p.2 Agenda 28 3 – 0 = 3 units 3

29. Handout: Launch, p.2 Agenda 29 2 – 0 = 2 units 2

30. Handout: Launch, p.3 Agenda 30 Summary: Another way to measure a horizontal or vertical line segment is by… Answer

31. Handout: Launch, p.3 Agenda 31 Summary: Another way to measure a horizontal or vertical line segment is by… …subtract the smaller coordinate that changes from the bigger coordinate that changes between the two endpoints of a line segment (or polygon side). We can call this Method #2: Calculating Using Coordinates.

32. Handout: Launch, p.3 Agenda 32 Answer

33. Handout: Launch, p.3 Agenda 33 4 – 2 = 2 units 5 – 3 = 2 units 5 – 4 = 1 unit 3 – 1 = 2 units 5 – 2 = 3 units 5 – 1 = 4 units

34. Handout: Practice 34 Agenda

35. Handout: Practice, p.1 35 Agenda Polygon D Answer

36. Handout: Practice, p.1 36 Agenda Polygon D

37. Handout: Practice, p.2 37 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

38. Handout: Practice, p.2 38 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). Any point with the a y-coordinate of 7 because points that have the same y-coordinate are horizontal since since they are all the same distance away from the x-axis. Any point with the an x-coordinate of –2 because points that have the same x-coordinate are vertical since since they are all the same distance away from the y-axis.

39. Handout: Practice, p.4 39 Agenda Answer Set #3 Perimeter is ________________.

40. Handout: Practice, p.4 40 Agenda Set #3 Perimeter is 38 units.

41. Handout: Practice, p.4 41 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)

42. Handout: Exit Ticket 42 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!