1. DO NOW: STUDY YOUR ANGLE NOTES Remember if you scored below a 70% on Friday’s exam you’re going to have to retake the test today and score above an 80% in order to not have to take it AGAIN Tuesday. Things to look up in your notes: What are vertical angles? What is AA Criterion? How do we find the new ordered pairs when we translate a shape using a vector? How do we find the new ordered pairs when we dilate a shape by a scale factor? Remember when it ask what type of “relationship” it’s referring to a type of angle (vertical, corresponding, adjacent, consecutive) We’re only going over #6 on the exam so don’t ask for the rest of the answers! Number 9 part B asks if the ANGLES are congruent not TRIANGLES

2. PYTHAGOREAN THEOREM Unit 8 Agenda: Monday, Feb 8 = Review Unit 7 Test Tuesday, Feb 9= Last chance to retake Unit 7 Exam and Slope Race Activity Wednesday, Feb 10 = Intro to Pythagorean Theorem and Slope Race Activity Thursday, Feb 11 = Real World Problems and solving for legs a/b (kids should be assembling their slope race ramps at home) Friday, Feb 12 = Pythagorean Theorem on a coordinate plane (last 10 minutes of class hot wheels race!) Monday, Feb 15 = NO SCHOOL!

3. BELL RINGER Tuesday February 9 th, 2016

4. For those of you who passed… We’re going to build ramps to race hot wheels cars!!!! Grab the Slope Race handout from the assignment table. The rest of you go to the POD with your exam and try again…Remember you need to get a 90% today to pass and if you don’t I’ll be calling home!

5. Do Now: On a Blank Sheet of Paper Pull out your Slope Race Project Worksheet and fill out Section 3!! I’m coming around checking to see if you have Section 1 and Section 2 done, then we’ll fill out Section 4 together as a class. Wednesday February 10 th, 2016

6. Do Now:

7. PYTHAGOREAN THEOREM Unit 8

8. Standard MAFS.8.G.2.6 (DOK 3): Explain a proof of the Pythagorean Theorem and its converse. Define key vocabulary: square root, Pythagorean Theorem, right triangle, legs a & b, hypotenuse, sides, right angle, converse, base, height, proof. Identify the legs and hypotenuse of a right triangle. Explain a proof of the Pythagorean Theorem.

9. Learning Scale: Level 1 I can recall specific vocabulary such as converse, coordinate system, dimension, distance, length, point, proof, Pythagorean theorem, side, and unknown. I can use the Pythagorean theorem to calculate an unknown side of a triangle.

10. Essential Question How does the area of a square relate to the Pythagorean Theorem?

11. Leg “a” Leg “b” hypotenuse Right angle What exactly is a right triangle? A right triangle is a triangle (3 sides and 3 angles) that contains a 90 degree angle. When looking at a right triangle, you will notice that it also has two sides a.k.a. two legs (Legs “a” and “b”) and a hypotenuse.

12. The Hypotenuse…

13. Let’s Watch a Video… it’s only 16 seconds! https://www.mathsisfun.com/pythagoras.html https://www.mathsisfun.com/pythagoras.html (this will allow us to get a visual to see how squares are related to Pythagorean Theorem) Note: “c” is ALWAYS the longest side!! “a” and “b” are ALWAYS the legs.

15. So what exactly is the Pythagorean Theorem?

16. Example: Find the length of the hypotenuse if a = 12 and b = 16. 12 16 ???

17. You Try! Find the length of the hypotenuse if a = 5 and b = 7. 7 5 ???

18. Whiteboards! (calculators permitted)

19. What is the length of the diagonal of a rectangle of length 3 and width 2? 3 2

20. Whiteboards! (calculators permitted) Which one of the following is NOT a right triangle?

21. Homework Explain how Figure 1 demonstrates the Pythagorean Theorem. The shaded triangle is a right triangle. 4 3 5 Figure 1 Figure 2 Is the shaded triangle of Figure 2 a right triangle? Explain how you know.

22. Do Now: You have 10 MINUTES to get your ramp done and then we’re racing our hot wheels! (if you need a ruler come see me, tape is on the front table, scissors are in the colored baskets on the short bookshelf) If you already finished your ramp complete the last section of your slope race packet (reflection ) and turn it into my basket.

23. Standard MAFS.8.G.2.7 (DOK 2): Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Recall the Pythagorean Theorem and its converse. Apply Pythagorean Theorem in solving real-world problems dealing with two and three dimensional shapes. Solve basic mathematical Pythagorean Theorem problems and its converse to find missing lengths of sides of triangles in two and three dimensions.

24. Learning Scale: Level 2 I can recall specific vocabulary such as converse, coordinate system, dimension, distance, length, point, proof, Pythagorean theorem, side, and unknown. I can use the Pythagorean theorem to calculate an unknown side of a triangle. I can recall the Pythagorean theorem and its converse.

25. Essential Question How does the area of a square relate to the Pythagorean Theorem?

26. Let’s Watch a Video! http://www.pbslearningmedia.org/resource/muen-math-g- pythagorean/pythagorean-theorem/ This video will help us see how the Pythagorean Theorem can be used in real life. Have you ever thought about a short-cut to walking or biking home? You’re using Pythagorean Theorem!

27. Let’s Find C! 1. What is A? 2. What is B? 3. What is our Pythagorean Theorem formula? 4. Let’s work it out on our whiteboards! 4 5

28. ANSWER… C = 6

29. Work this out…

30. Answer… 4

31. What about this??? 1. Draw your triangle. (Yes, you can do this!) 2. Find the lengths of your legs (A and B). 3. A = 5 and B = 3 Plug these into the formula.

32. ANSWER…

33. Homework Tuesday, February 16, 2016 If you didn’t finish the last section of the slope race packet (reflection) you need to complete that also!!! 1. 2. 3.

34. Homework Challenge! (If you turn this in tomorrow with the correct answer, I will give you extra credit on your Unit 8: Pythagorean Theorem test!)

36. Do Now: On a Blank Sheet of Paper Answer the Following 1. Write the number 123,000,000,000 in scientific notation. 2. Write 0.000001 in scientific notation. 3. Grab a white board with a grid on it and a dry erase marker.

37. Standard MAFS.8.G.2.8 (DOK 2): Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Recall the Pythagorean Theorem and its converse. Determine how to create a right triangle from two points on a coordinate graph. Use the Pythagorean Theorem to solve for the distance between the two points.

38. Learning Scale: Level 2 I can recall specific vocabulary such as converse, coordinate system, dimension, distance, length, point, proof, Pythagorean theorem, side, and unknown. I can use the Pythagorean theorem to calculate an unknown side of a triangle. I can recall the Pythagorean theorem and its converse. I can apply the Pythagorean theorem to find the distance between two points on a coordinate plane.

39. Essential Question How does the area of a square relate to the Pythagorean Theorem?

40. On the Coordinate Plane on your whiteboard, plot the following points: A (-1, 1) B (5, 3) C (2, -3) Find the distance from A to B. Find the distance from B to C. Find the distance from A to C. FSA Practice

41. Hint… You can draw right triangles between the points to figure out the hypotenuse for each! A (-1, 1) B (5, 3) C (2, -3) Find the distance from A to B. Find the distance from B to C. Find the distance from A to C.

42. FSA Practice Three points are on the coordinate plane shown. A(-5, 3), B(-3, 5). What is the distance between A (-5, 3) and B (-3, 5)?

43. FSA Practice Which set of numbers forms a right triangle? A.4.7, 3.6, 5.2 B.6, 8, 10 C.7, 3.2, 8 D.1, 2, 3

44. FSA Practice Triangle ABC is a right triangle. The length of one leg is 80 cm and the hypotenuse is 120 cm. What is the length of the other leg?

45. FSA Practice A figure is shown. The base of the shape is a square with side length b = 30 m. The height of the figure, h, is 10 m. What is the length of l?

46. FSA Practice

47. Hint…

49. Do Now: On Your Bellringer Sheet Get ready to take notes as we watch a video on the Pythagorean Theorem (I’m pressing play as soon as the bell rings!). After we watch the video you’ll need to answer the following: What are some real life situations where the Pythagorean theorem can be used?

50. Learning Scale: Level 2 I can recall specific vocabulary such as converse, coordinate system, dimension, distance, length, point, proof, Pythagorean theorem, side, and unknown. I can use the Pythagorean theorem to calculate an unknown side of a triangle. I can recall the Pythagorean theorem and its converse. I can apply the Pythagorean theorem to find the distance between two points on a coordinate plane. I can use the Pythagorean theorem to solve real world problems.

51. Warm-Up: Complete on a blank sheet of paper

52. Let’s watch a video on Pythagorean Theorem Proofs! Pull out your notes: Title the page “Pythagorean Theorem Proofs” Proof 1 4 3 5 Figure 1 A B C

53. Problem Based Learning: The Scenario AT&T is laying fiber optic lines for its U-Verse service, they’ve sent us a map outlining exactly what streets the new lines will be placed on in our area. It’s now our job to calculate the total amount of fiber optic lines (in miles) that the technician will need in order to install the U-verse service. Using the map, the information at the top, and your knowledge of the Pythagorean theorem, calculate the length of the streets in black in order to find out how many miles of line we will need total. Once you’ve come up with your answer write out a “Work Order” to AT&T stating how much fiber optic wiring they need to order. Challenge Question (FOR EXTRA CREDIT): The city is charging AT&T $4 for every 2,000 feet of fiber optic line used; what is the least amount of money the city can make off of this deal with AT&T?

54. The Details You will be working in groups of 4 on this assignment. Make sure each group member’s name is listed at the top of your group’s map Members will take turns working out the length of each street Using a color pencil or highlighter mark on your map the right triangles you ended up using for your calculations (see picture) Make sure to show your work! Only one person needs to write the “Work Order” on a separate sheet of paper (make sure everyone’s name is included!) and then staple this to your map when you turn it in.