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## U nit 5: Geometry

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**Unit 5: Geometry**Week 1 SPIs 4.1 & intro 4.2**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?**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.**Math Rockstars!**• 5th Period • Katelynn • Aliciah • Aliyah • Brandon • Vicki • Wesley**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**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**Weekly Agenda**• Wednesday – Rules Review/ Pythagorean Theorem Introduction • Thursday – Applying the Pythagorean Theorem • Friday – Quiz!**Rules**• Same as last semester. • Questions?**Procedures**• Do Now • Supplies • Bathroom • Asking / Answering Questions**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.**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.**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.**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.**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.**Today’s Objective**• SWBAT defineand identify hypotenuse, leg, and right triangle and state the Pythagorean theorem.**BrainPOP!**• BrainPOP!**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**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**Why Use the Pythagorean Theorem?**• The goal of the Pythagorean theorem is to find the missing side of a RIGHT TRIANGLE. a2 + b2 = c2**C**A B Identifying Parts of a Triangle • Ex.1: ID each side as leg or hypotenuse.**E**F D Identifying Parts of a Triangle • Ex.2: ID each side as leg or hypotenuse.**L**N M Identifying Parts of a Triangle • Ex.3: ID each side as leg or hypotenuse.**T**W V Identifying Parts of a Triangle • Ex.4: ID each side as leg or hypotenuse.**Identifying Parts of a Triangle**• Ex.5: ID each side as leg or hypotenuse. x 5 13**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**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**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.**Do Now – (2/2), (√9), (20 - 7)**• State the Pythagorean theorem (formula). • Identify the variables in the Pythagorean theorem.**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.**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**Today’s Objective**• SWBAT determine the missing side of a triangle given information, picture, or a coordinate plane.**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**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.**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.**Using the Pythagorean Theorem**• Watch as I walk through this one. • Ex. 1: Solve for the missing side. x 6 8**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?**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)**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?**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?**Using the Pythagorean Theorem**• Work on this one with your partner. • Ex. 6: Solve for the missing side. c 16 ft d 40 ft**Using the Pythagorean Theorem**• Work on this one with your partner. • Ex. 7: Solve for the missing side. x 5 13**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)**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)**Using the Pythagorean Theorem**• Work on this onewith your partner. • Ex. 10: Whatis the length ofthe hypotenuse?**Using the Pythagorean Theorem**• Work on this one ON YOUR OWN. • Ex. 11: Solve for the missing side. 5 m 13**Using the Pythagorean Theorem**• Work on this one ON YOUR OWN. • Ex. 12: Solve for the missing side. 5 m 13**Using the Pythagorean Theorem**• Work on this one ON YOUR OWN. • Ex. 13: Solve for the missing side. 26 5 d**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?