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U nit 5: Geometry

U nit 5: Geometry

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U nit 5: Geometry

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  1. Unit 5: Geometry Week 1 SPIs 4.1 & intro 4.2

  2. Welcome back! 

  3. Do Now – √1, √4, √169 • Please pick up your guided notes, sit in your assigned seat, and respond to the following SILENTLY & INDEPENDENTLY: • What are you most proud of last semester? • What is your academic goal for this 9 weeks? • What are you SPECIFICALLY going to do to reach that goal? • What must you change about yourself to reach that goal?

  4. Unit 4 Exams • They were passed back before Christmas break. If you did not receive yours, you will shortly. • If you did not put your stars on the wall, please do so at the end of class. • Averages and shout outs are on the next slide.

  5. Class Averages

  6. Math Rockstars! • 5th Period • Katelynn • Aliciah • Aliyah • Brandon • Vicki • Wesley

  7. 100% Math All-Stars! • 3rd Period • Jacob J. • Carlos • Luke • Tyler R • Marshala • 5th Period • Tristan • Torez • Lekendric • Tyun • Kaylan • Jr. • Enrique • Robynn • Christian • Anneliese • Himani • JuWaun • Mario • 6th Period • Quinton • Shatonya • Jaycee • Dasha • Ellie • 7th Period • Autumn • Chris

  8. 85% or High Mathletes • 3rd Period • Gerardo • Kiara • Mackenzie • Cordarius • Khylee • Dez • JaWaun • 5th Period • Solomon • Reggie • Abdul • Olivia • Lauren • Jalen • Belen • Ceirsten • 6th Period • Brandon • Tylesha • Dorian C. • Jalen • Antonio • Jayla • Brittni • James • Mallory • 7th Period • Grace • Khadija • Shaquanna • Zakiya • Odalis • Whitney • Kameron • Esmeralda • Lataryl • Tinaya • Willie • Jordan

  9. Weekly Agenda • Wednesday – Rules Review/ Pythagorean Theorem Introduction • Thursday – Applying the Pythagorean Theorem • Friday – Quiz!

  10. Rules • Same as last semester. • Questions?

  11. Procedures • Do Now • Supplies • Bathroom • Asking / Answering Questions

  12. Do Now • There will no longer be details to sit down silently & work independently. • You all have shown me you know what to do before, therefore I will not include it. • If you are not working, that will be a consequence. • I will be tracking consequences on the board &/or on my clipboard, as usual. • The do now will no longer take more than 6 – 7 minutes to complete, so please get started immediately! • Urgency and timing is key to reaching our objective for the day.

  13. Supplies • Each student is responsible for bringing supplies to the classroom including: • Binder • Paper • Pencil • Eraser • I will help you if you do not have your supplies, but if it is a daily occurrences, points will be deducted from your weekly quiz grade. • Failure to bring in supplies not only wastes learning time for you and for others, but also hurts your grade.

  14. Restroom Passes • You have one EMERGENCY restroom pass for this 9 weeks. • Do not ask, UNLESS IT IS AN EMERGENCY! • If you have already used your restroom pass, you will not be permitted to go to the restroom UNDER ANY CIRCUMSTANCES. • Remember, the pass is for emergencies ONLY so please make sure you really want to use it before going.

  15. Asking / Answering Questions • All students are to raise their pointer finger when they want to answer a question SILENTLY. • You will not be called on if you are moving around in your chair or making noises. • All students are to raise their hand with 5 fingers if they want to ask a question. • Students will not be addressed if they do otherwise and will be given a silent consequence. • All students must raise 3 fingers for any other concern. • Students ARE NOT to get out of their seats to get a tissue or sharpen their pencil. • All students will be called on. • If you have answered multiple questions and I am no longer calling on you, please do not get upset.

  16. Unit 5 • We last stopped at unit 4, where we dealt with slope, y-intercepts, and slope intercept form. • From there, we are going to start on geometry in unit 5. Geometry is so important because it is ~20% of the TCAP! • Unit 5 will last 3 weeks and include: Pythagorean theorem and angles. • Our unit 5 exam will be JANUARY 18th, 2013.

  17. Today’s Objective • SWBAT defineand identify hypotenuse, leg, and right triangle and state the Pythagorean theorem.

  18. BrainPOP! • BrainPOP!

  19. Pythagorean Theorem • Before we get started with our new unit, we must introduce some new vocabulary. • Right Triangle–a triangle that has 2 legs and a hypotenuse. • Right Angle– an angle that measures 90°. • Indicated by a _____ in a triangle. • Legs – the shorter sides in a right triangle. • A & B in the diagram C A B

  20. Pythagorean Theorem • Hypotenuse– the side of a right triangle that is opposite of the right angle. • The LONGEST SIDE of a right triangle. • C in the diagram. • Pythagorean Theorem – states the sum of the squares of the length of the two legs is equal to the square of the length of the hypotenuse. • ONLY WORKS WITH A RIGHT TRIANGLE • a2 + b2 = c2 • Where a & b are the legs & c is the hypotenuse

  21. Why Use the Pythagorean Theorem? • The goal of the Pythagorean theorem is to find the missing side of a RIGHT TRIANGLE. a2 + b2 = c2

  22. C A B Identifying Parts of a Triangle • Ex.1: ID each side as leg or hypotenuse.

  23. E F D Identifying Parts of a Triangle • Ex.2: ID each side as leg or hypotenuse.

  24. L N M Identifying Parts of a Triangle • Ex.3: ID each side as leg or hypotenuse.

  25. T W V Identifying Parts of a Triangle • Ex.4: ID each side as leg or hypotenuse.

  26. Identifying Parts of a Triangle • Ex.5: ID each side as leg or hypotenuse. x 5 13

  27. Exit Ticket • Each of you will complete your exit ticket on a note card. • You will complete the exit ticket in 5 minutes and it must be turned in before you can exit the classroom. • You must work SILENTLY and INDEPENDENTLY. • HOMEWORK – Worksheet

  28. Exit Ticket • What is the difference between a leg and a hypotenuse? • Given the triangle below, ID the legs and hypotenuse. • Explain how you identified the hypotenuse. • Write the Pythagorean theorem out and identify each variable. Homework - Worksheet S Q Z

  29. q s z Do Now – (2/2), (√9), (20 - 7) • State the Pythagorean theorem (formula). • Identify the variables in the Pythagorean theorem. • Using the triangle, identify each side of the triangle. • Explain how you determined which side was the hypotenuse.

  30. Do Now – (2/2), (√9), (20 - 7) • State the Pythagorean theorem (formula). • Identify the variables in the Pythagorean theorem.

  31. q s z Do Now – (2/2), (√9), (20 - 7) • Using the triangle, identify each side of the triangle. • Explain how you determined which side was the hypotenuse.

  32. Today’s Agenda • Do Now – 7 minutes • Agenda/Objective -1 minute • Pythagorean Theorem Problem INM – 15 minutes • Pythagorean Theorem GP – 10 minutes • Pythagorean Theorem INM – 10 minutes • Exit Ticket – 5 minutes

  33. Today’s Objective • SWBAT determine the missing side of a triangle given information, picture, or a coordinate plane.

  34. Review of Pythagorean Theorem • For any right triangle, the square of the hypotenuse is equal to the sum of the squares of the lengths of the legs. • The hypotenuse is the longest side opposite of the right angle. • The formula for determining the missing side of a triangle is as follows: • Where a and b are the legs and c is the hypotenuse. a2 + b2 = c2

  35. Using the Pythagorean Theorem • There are different ways you can use the Pythagorean theorem. • Today, we will review problems given a picture, given a coordinate plane, or make our own triangle to solve given information.

  36. Using the Pythagorean Theorem General Steps to Solve for a Missing Side • Check to make sure the triangle is a right triangle. • If it is, write the Pythagorean theorem equation (a2 + b2 = c2) • Identify the hypotenuse (across from the right angle) and label it ‘c’. • Label the legs (the other sides) ‘a’ and ‘b’. • Substitute your numbers in the equation and solve for the missing side.

  37. Using the Pythagorean Theorem • Watch as I walk through this one. • Ex. 1: Solve for the missing side. x 6 8

  38. Using the Pythagorean Theorem • Follow along as I walk through this one. • Ex. 2: A right triangle has a hypotenuse of 13 centimeters. One of the legs is 5 centimeters. What is the length of the other leg?

  39. Using the Pythagorean Theorem • Follow along as I walk through this one. • Ex. 3: Mr. Lowe is measuring his TV. The TV is 36 inches wide and 24 inches tall. What is the length of the diagonal on the TV? (HINT: Draw a picture)

  40. Using the Pythagorean Theorem • Follow along as I walk through this one. • Ex. 4: A student designed a flag for KBMS and the diagonal distance is 5 ft. If the length of the flag is 4 ft, what is the width?

  41. Using the Pythagorean Theorem • Work on this one with your partner. • Ex. 5: The following picture shows 2 paths from Nora’s house to her friends. Based on the diagram, what is the length of the route from Nora’s house to her friends using Hill Drive?

  42. Using the Pythagorean Theorem • Work on this one with your partner. • Ex. 6: Solve for the missing side. c 16 ft d 40 ft

  43. Using the Pythagorean Theorem • Work on this one with your partner. • Ex. 7: Solve for the missing side. x 5 13

  44. Using the Pythagorean Theorem • Work on this one with your partner. • Ex. 8: Dasha lives 15 miles east of Jayla. Jayla lives 26 miles north of Quinton. How far does Quinton live from Dasha? (HINT: Draw a picture)

  45. Using the Pythagorean Theorem • Work on this one with your partner. • Ex. 9: Firefighters have a 40 foot extension ladder. In order to reach 28 feet up a building, how far away from the building should the foot of the ladder be placed? (HINT: Draw a picture)

  46. Using the Pythagorean Theorem • Work on this onewith your partner. • Ex. 10: Whatis the length ofthe hypotenuse?

  47. Using the Pythagorean Theorem • Work on this one ON YOUR OWN. • Ex. 11: Solve for the missing side. 5 m 13

  48. Using the Pythagorean Theorem • Work on this one ON YOUR OWN. • Ex. 12: Solve for the missing side. 5 m 13

  49. Using the Pythagorean Theorem • Work on this one ON YOUR OWN. • Ex. 13: Solve for the missing side. 26 5 d

  50. Using the Pythagorean Theorem • Work on this one ON YOUR OWN. • Ex. 14: A painting in the shape of a right triangle is 5 inches high and 12 inches long. What is the length of the diagonal of the painting?