EQ: GPE.7 How do I find the perimeter and area of polygons?

Transcription

1 EQ: GPE.7 How do I find the perimeter and area of polygons? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 14, Lesson 1 1. Warm Up 2. Investigation 3. Left Side practice 4. 2 D project 5. Closure 72 Area and Perimeter of Polygons 73 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm Warm Up: If the triangle shown below is dilated by a scale factor of 4, what is its new area? To determine how much of each item to buy, tell whether you need to know the area or the perimeter. Explain. 1. wallpaper for a bedroom 2. fencing for a backyard 3. paint for a basement floor. 1

2 vity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity Left Side Practice Use the given vertices: A(4, 1), B(5,6), C(1,3). Part A: Graph the triangle. Part B: Using the distance formula or Pythagorean Theorem, classify the triangle as scalene, isosceles, or equilateral. Part C: Find the perimeter to the nearest whole number. 2

3 A: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity Investigation: Which shape gives the largest area? Everyone has been given the same length of string. Using all of the string but don't stretch it you will make 4 shapes on your coordinate plane. Once you have made each shape, estimate its area by counting the squares inside, or by using a formula. Record all of your data in your IAN (left side). Shape Square Triangle Rectangle Circle Area 3

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6 s Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity 6

7 Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Right Side... Write a summary that answers the essential question. Left Side... To determine how much of each item to buy, tell whether you need to know the area or the perimeter. Explain. 1. wallpaper for a bedroom 2. fencing for a backyard 3. paint for a basement floor. 7

8 EQ: GMD.4 How do I identify cross sections of 3D figures? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 14, Lesson 2 1. Warm Up 2. GPE.7 Quiz 3. Intro activity 4. Practice 5. Closure 74 Cross Section of 3D Figure 75 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm Warm Up: To prepare for the quiz, take a few minutes to look over pages in your IAN. Then, self assess with the following questions: 1. Do you know how to find the perimeter of a triangle on a coordinate plane? 2. Do you know the definitions of scalene, isosceles, and equilateral? 3. Do you know how to find the area of irregular shapes on a coordinate plane? 4. Do you remember which shape always produces the largest area? 5. Do you remember how dilations affect area? Honors: Find the area of the Triangle 8

9 GPE.7 Quiz 9

10 Week 14.2D 3D Shapes v.2.notebook Intro Activity Write your guesses in your IAN (left side). What is the cross section of a sphere? What is the cross section of a prism? What is the cross section created by a plane parallel to the bases of a cylinder? What is the cross section created by a plane perpendicular to the bases of a cylinder? 10

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13 Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Right Side... Write a summary that answers the essential question. Left Side... 13

14 EQ: GMD.1 What is Cavalieri's Principle? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 14, Lesson 3 1. Warm Up 2. Demo 3. Notes 4. Practice 5. Closure 76 Cavalieri's Principle 77 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm Warm Up: 1. Given the following figure, (a) Draw the cross section that is parallel to the base. (b) Draw the cross section that is perpendicular to the base. 2. What 3 dimensional figure is formed by the rotation of each around the given line? 14

15 Demonstration 1. (a) Look at the formulas for the volumes of prisms and pyramids. Write 3 things you notice. (b) How many pyramids do you think would fit into a prism with the same dimensions? 2. (a) Look at the formulas for the volumes of cones and cylinders. Write 3 things you notice. (b) How many cones do you think would fit into one cylinder with the same dimensions? 15

16 notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes Cavalieri's Principle If two 3 dimensional figures have the same height and the same cross sectional area at every level, then they have the same volume. notes notes notes notes notes notes notes notes notes notes Summary: 16

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19 EQ: GMD.1 What is Cavalieri's Principle? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 14, Lesson 4 1. Warm Up 2. GMD.4 Quiz 3. Practice 4. 2D Project or Choice Board 5. Closure 78 Cavalieri's Principle 79 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm u Warm Up: In order to prepare for the quiz, take a few minutes to review pages in your IAN. Look over the practice sheet GMD. 4 Cross Sections Practice, as well. Then, self assess with the following questions: 1. Do you know how to identify and draw the cross sections for different 3D shapes? 2. Do you know how to sketch the 2D shape that forms a 3D shape when rotated? 19

20 GMD.4 Quiz 20

21 Left Side Practice 1. You are at a festival and have a choice of 2 cups to purchase your beverage: a cylinder or a cone. Both have the same height and radius. If they are the same price, which is the better deal? Why? 2. A cylindrical vase is 5 inches tall and has a radius of 3 inches. What is the volume of water that the vase can hold? 3. A rectangular prism has a length of 4 cm, a width of 5 cm and a height of 10 cm. What volume of packing peanuts can fit inside? ss Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity 4. A toy ball can hold a volume of 615cm 3. What is the radius of the ball? 21

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23 Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Right Side... Write a summary that answers the essential question. Left Side... 23