Distance of Segments in the Coordinate Plane

1. Distance of Segments in the Coordinate Plane SPI 0506.4.5

2. Imagine with me……… We are all on a boat. A storm comes up and our boat wrecks on the shore of an island. We are stranded and looking for food. We find a poem and a map that apparently were left by pirates……

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4. To hunt for your treasure, a few things you must know~ This map is for those who are ready to show how to find ordered pairs on a coordinate grid And measuring distances is for really smart kids! ARGGGG! Sincerely, Pirate Pete

5. 5th grade students in the state of Tennessee should be able to…. find the length of vertical or horizontal line segments in the first quadrant of the coordinate system, including problems that require the use of fractions and decimals. Today Pirate Pete is going to help us master this skill!

6. Ahoy mateys……. When we finish our lesson today, Pirate Pete wants us to be able to say…… I CAN identify a coordinate grid. I CAN locate ordered pairs on a coordinate grid. I CAN find the distance between ordered pairs on a coordinate grid.

7. Click to learn more about graphing ordered pairs……..

8. x axis – a horizontal number line on a coordinate grid. x 0 1 2 3 4 5 6

9. y axis – a vertical number line on a coordinate grid. 6 y 5 4 3 2 1 0

10. Coordinates – an ordered pair of numbers that give the location of a point on a grid. (x-coordinate, y-coordinate) (3, 4) 6 5 (3,4) 4 y 3 2 1 x 0 0 1 2 3 4 5 6

11. Partner #1, point to the x-axisPartner #2, point to the y-axis.Work together to locate…. (x-coordinate, y-coordinate) (4, 2) 6 5 4 y 3 (4,2) 2 1 x 0 0 1 2 3 4 5 6

12. Try this one on your own, then compare with your partner…… (x-coordinate, y-coordinate) (5, 5) 6 (5,5) 5 4 y 3 2 1 x 0 0 1 2 3 4 5 6

13. Try this one on your own…… (x-coordinate, y-coordinate) (0, 3) 6 5 4 (0,3) y 3 2 1 x 0 0 1 2 3 4 5 6

14. Try this one on your own…… (x-coordinate, y-coordinate) (4, 0) 6 5 4 y 3 2 (4,0) 1 x 0 0 1 2 3 4 5 6

15. Find the coordinates for the points…. (x-coordinate, y-coordinate) 6 5 4 y (2,3) (5,3) 3 2 1 x 0 0 1 2 3 4 5 6

16. WORK WITH YOUR PARTNER Find the distance between the and the . The distance between the star and heart is 3 units. 6 5 4 y 3 2 1 x 0 0 1 2 3 4 5 6

17. Which letter is located at (2,4)? Point A is located at (2,4). y 6 5 A B 4 3 2 C D 1 x 0 0 1 2 3 4 5 6

18. Which letter is located at (4,2)? Point D is located at (4,2). y 6 5 A B 4 3 2 C D 1 x 0 0 1 2 3 4 5 6

19. With your hand against your chest, show with your fingers the length of line segment BD? The length of line segment BD is 2 units. y 6 5 A B 4 3 2 C D 1 x 0 0 1 2 3 4 5 6

20. What is the location of point Y? 3.5 4 W X 3 y 2.5 2 1.5 1 Z Y 0.5 0 x 0 0.5 1 1.5 2 2.5 3 3.5 4

21. The location of point Y is (4,0.5) 3.5 4 W X 3 y 2.5 2 1.5 1 Z Y 0.5 0 x 0 0.5 1 1.5 2 2.5 3 3.5 4

22. What is the length of line segment YZ? 3.5 4 W X 3 y 2.5 2 1.5 1 Z Y 0.5 0 x 0 0.5 1 1.5 2 2.5 3 3.5 4

23. 4 – 1.5 = 2.5 = length of YZ 3.5 4 W X 3 y 2.5 2 1.5 1 Z Y 0.5 0 x 0 0.5 1 1.5 2 2.5 3 3.5 4

25. Practice with Ordered Pairs(When you finish, please begin working on your treasure map. I will come to you to provide feedback.) 1.Put a yellow dot on the ordered pair (2,3). 2.Put a red dot on the ordered pair (4,6). 3.Put a green dot on the ordered pair (6,3). 4. Connect the ordered pairs. 5. What is the distance between the yellow and green vertices? 6. What shape have you drawn? Triangle

26. Pirate Pete is proud that his mateys can say with confidence…… I CAN identify a coordinate grid. I CAN locate ordered pairs on a coordinate grid. I CAN find the distance between ordered pairs on a coordinate grid.

27. Partner work using Pirate Pete’s Treasure Map(Please highlight any questions with which you and your partner need help.) • What is located at 5,2? • What is located at 2,4? • Which ordered pair names the location of the hamburger? • Which ordered pair names the location of the french fries? • Which ordered pair names the location of the treasure chest? • What is the length of the line segment from the skull bone to the rock? Is the line segment from the skull bone to the rock vertical or horizontal? • What is the length of the line segment from the rock to the treasure chest? Is the line segment from the skull bone to the treasure chest vertical or horizontal? • What is the length of the line segment from the treasure chest to the shark infested water? Is the line segment from the skull bone to the treasure chest vertical or horizontal? • What is the length of the line segment from the shark infested water to the skull bone? Is the line segment vertical or horizontal? • Pirate Pete’s riddle…..I spy 2 things on the map with a distance of 8 units. Which two things do I see? • What shape have you made as you have measured the distance between these four points? • What kind of angles are in this shape? • Why is it a rectangle and not a square? • Find the perimeter of the shape. • Find the area of the shape.

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29. It’s your time in the spotlightto SHOW WHAT YOU KNOW!!! with an TICKET

30. #1: This grid shows the locations in which LaShonda planted flowers and a tree in her backyard. Which is closest to the distance between the flowers and the tree? • 7.5 units • 7 units • 6.5 units • 6 units

31. #2: A coordinate grid is shown below. A vertical line segment that is 8 units long is drawn on the grid. Which list of coordinate pairs could represent the locations of the endpoints of this line segment? • (2,1),(2,8) • (8, 0), (8, 7) • (8,4),(1,4) • (4,9),(4,1)

32. TICKET DISCUSSION…

33. #1: This grid shows the locations in which LaShonda planted flowers and a tree in her backyard. Which is closest to the distance between the flowers and the tree? • 7.5 units • 7 units • 6.5 units • 6 units

34. This grid shows the locations in which LaShonda planted flowers and a tree in her backyard. Which is closest to the distance between the flowers and the tree? • 7.5 units • 7 units • 6.5 units • 6 units

35. #2: A coordinate grid is shown below. A vertical line segment that is 8 units long is drawn on the grid. Which list of coordinate pairs could represent the locations of the endpoints of this line segment? • (2,1),(2,8) • (8, 0), (8, 7) • (8,4),(1,4) • (4,9),(4,1)

36. A coordinate grid is shown below. A vertical line segment that is 8 units long is drawn on the grid. Which list of coordinate pairs could represent the locations of the endpoints of this line segment?EXPLAIN YOUR ANSWER IN SENTENCES ON THE BACK OF YOUR EXIT TICKET. • (2,1),(2,8) • (8, 0), (8, 7) • (8,4),(1,4) • (4,9),(4,1)

38. For tomorrow…be ready to connect the skills we used today in Math class to everyday life.HOW WILL YOU USE THIS? REAL WORLD CONNECTIONS

39. On the grid below, plot the points that have coordinates (B, 1), (B, 3), and (D, 5). Plot 3 more points on the grid so that when you connect all 6 points you will make a rectangle. List the coordinates for the 3 new points. _______   _______   _______ Connect the 6 points to show your rectangle.