EQ: GMD.1 What is Cavalieri's Principle?

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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 1 1. Warm Up 2. GMD.4 Quiz 3. Notes 4. Practice 5. Closure 70 Cavalieri's Principle 71 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: In order to prepare for the quiz, take a few minutes to review pages 68 69 in your IAN. Look over the GMD.4 practice sheet 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?

GMD.4 Quiz

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. tes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes Quick Recap... Summary: How many cones does it take to fill a cylinder with the same height and base area? https://www.youtube.com/watch?v=0zacau4sgym How many pyramids does it take to fill a prism with the same height and base area? https://www.youtube.com/watch?v=oudjy6vj8pw

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...

EQ: GMD.1 How do the volumes of different shapes compare? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 14, Lesson 2 1. Warm Up 2. GMD.1 Quiz 3. Notes 4. Volume Practice 5. Closure 72 Comparing Volumes 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 u Warm Up: In order to prepare for the quiz, take a few minutes to review pages 70 71 in your IAN. Also look at the GMD.1 Practice Sheet. Then, self assess with the following questions: 1. Can you explain Cavalieri's Principle in your own words? 2. Do you understand the relationship between cones and cylinders? Do you understand the relationship between prisms and pyramids?

GMD.1 Quiz!

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 How to find the radius of a 3D object Step 1: Find the Circumference. Step 2: Divide that number by 2. Then, divide your answer by pi. notes notes notes notes notes notes notes notes notes notes Summary: Your final answer is your radius round to the nearest tenth!

ss Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity

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...

EQ: GMD.1 How do the volumes of different shapes compare? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 14, Lesson 3 1. Warm Up 2. Left Side Practice 3. Closure 72 Comparing Volumes Not a new page! Use the same ones as yesterday, please! 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 u 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?

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?

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...

EQ: GMD.1 How do the volumes of different shapes compare? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 14, Lesson 4 1. Warm Up 2. Left Side Practice 3. Volume Practice *IAN Check/Choice Board/2D Project/Study Guide 74 Comparing Volumes 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 u Warm Up: Given the picture below, find its volume. Be sure to show your work and include units!

ss Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity Left Side Practice 1. The mass of an unknown substance is 35 grams. You find that its volume is 110 cm 3. What is its density? 2. Copper has a density of 8.92 g/cm 3. If you measure 60 grams of copper, what will its volume be? 3. An area of land can be approximated by a rectangle with a length of 20.4 miles and a width of 12.3 miles. Currently, there is a herd of about 3,416 buffalo that roam this area of land. What is the population density of buffalo/mi 2? 4. A town has an area of 179 square miles. The current population density of the town is 15 people per square mile. What is the population of the town? 5. To start making some money, you decide to buy soap in bulk and make candles like the ones shown below. If you bought a block 2,000 in 3, how many candles can you make? diameter = 3 in height = 4 in

ss Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity

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...

EQ: GMD.1 How do the volumes of different shapes compare? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 14, Lesson 5 1. Warm Up 2. TI NSpire Activity 3. Choice Board/2D Project/ Study Guide 74 Comparing Volumes not a new page! 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 u Warm Up: Suppose the figure below was dilated by a factor of 4. Part A: What will the area of the dilated figure be? Part B: What will the perimeter of the dilated figure be?

ity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity TI NSpire Activity

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... Left Side...

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