1. Warm - up Are You In or Out? Power point 3D Guided Practice Fill ‘er Up Independent Practice Can You Hold It? Measurement

2. Are You In or Out? (Warm Up) You’ve been asked to design a race track that is 50 miles long and 20 miles wide. If the ends are in the shape of a semi-circle, what is the perimeter of the track AND how much turf is inside? Hint: drawing a picture might help.

3. Are You In or Out? (Warm Up) You’ve been asked to design a race track that is 50 miles long and 20 miles wide. If the ends are in the shape of a semi-circle, what is the perimeter of the track AND how much turf is inside? Hint: drawing a picture might help. 50 miles 20 miles Area: Rectangle 50 x 20 = 1000 miles² Two semi-circles of the same diameter will make a whole circle; therefore, A = πr² A = 3.14 · 10² A = 3.14 · 100 A = 314 miles² The perimeter is 162.8 miles and the area is 1314 miles². Perimeter: Circumference = πd = 3.14 · 20 = 62.8 miles Rectangular = 50 + 50 = 100 miles

4. 3D What are dimensions? What do they tell us? What is the difference between two-dimensional and three-dimensional? Dimension refer to a direction. Length, l, tells me how long an object is, width, w, tells me how wide the object is, and height, h, tells me how tall the object is. Two-dimensional objects are flat in nature – they have length and width. For example, a piece of paper is two-dimensional, it has length and width. They only occupy space - area. Three-dimensional objects have not only length and width, but also height. A box has three measurements; length, width, and height. It occupies space and has capacity – the ability to hold or contain - volume.

5. 3D Three-dimensional Identify which are two-dimensional versus three-dimensional. 2D 3D

6. 3D Three-dimensional Let’s look at the volume or capacity of an object – specifically a rectangular prism and a cube. For any prism, we start with the base shape and then multiply height. Our first example will be a rectangular prism. Our base shape is a rectangle.

7. 3D Three-dimensional As previously stated, we start with the base shape and then multiply height. Our next example will be a cube. Therefore, our base shape is a square.

8. 3D Three-dimensional What would happen if you were given the volume of the prism and asked to find one of the dimensions? How would you begin to solve that problem? 1. Identify the shape. Let’s practice with the figure on the right. 2. Write down the equation/formula for finding its volume. 3. Substitute in the values you know. 4. Solve for the unknown. Rectangular Prism V = Bh 3 cm 5 cm V = 135 cm³ 135 = 5 · 3 · h V = l · w · h 135 = 15 · h 9 cm = h simplify divide substitute

9. 3D Three-dimensional What would happen if you were given the volume of the prism and asked to find one of the dimensions? How would you begin to solve that problem? 1. Identify the shape. Let’s practice with the figure on the right. 2. Write down the equation/formula for finding its volume. 3. Substitute in the values you know. 4. Solve for the unknown. Cube V = Bh 4 m V = 64 mm³ 64 = s · 4 · 4 V = s · s · s 64 = s · 16 4 mm = s simplify divide substitute

10. Fill ‘er Up (Guided Practice) Jalissa just purchased an aquarium and wants to fill it half way with water. How much water will she need to accomplish this? 14 inches 16 inches 10 inches SHAPE: Rectangular Prism EQUATION: V = Bh; where B is the area of the base V = 224 in² · 5 in. B = l x w B = 14 x 16 B = 224 in² V = 1120 inches³ Jalissa needs 1120 cubic inches of water.

11. Fill ‘er Up (Guided Practice) SHAPE: Cube EQUATION: V = Bh; where B is the area of the base V = 121 in² · 11 in. B = s x s = s ² B = 11 x 11 B = 121 in² V = 1331 inches³ 11 inches The Johnson family is going green; they have added recycling to their list of family activities. The container, shown on the right, has been designated for recycling is a cube. Calculate how much paper the container will hold. The Johnson family filled the container with 1331 cubic inches of paper.

12. Fill ‘er Up (Guided Practice) Donnie found a large empty box. The dimensions of the box are 5ft by 6ft by 3ft. He also found 50 smaller cubes with which he could build things. The dimensions of the smaller cubes are 12 inches wide. His father saw him playing with the different prisms. His question to Donnie was, “ Can all of the smaller cubes fit inside the large empty box you found?”

13. Fill ‘er Up (Guided Practice) Donnie found a large empty box. The dimensions of the box are 5ft by 6ft by 3ft. He also found 50 smaller cubes with which he could build things. The dimensions of the smaller cubes where 12 inches wide. His father saw him playing with the different prisms. His question to Donnie was, “ Can all of the smaller cubes fit inside the large empty box you found?” Large empty box V = Bh V = l · w · h V = 5 · 6 · 3 V = 90 ft 3 Smaller cubes V = Bh V = s · s· s V = 1 · 1· 1 V = 1 ft 3 Yes. 90 ÷ 1 = 90

14. Can You Hold It? (Independent Practice) The standard shipping container has the interior dimensions of 39’ “ in length, 7’ 8 “ in width, and 7’9 “ in height and a weight of 56,000 pounds. You are planning to ship large artifacts in crates that measures 90” in length, 30” in width, and 48” in height and weigh a total of 350 pounds. How many crates can you pack without exceeding the weight limit of the shipping container? How much space is left for packing materials?

15. Can You Hold It? (Independent Practice) Important facts: Dimensions of shipping container: 39’ “ x 7’ 8 “ x 7’ 9 “ Dimensions of crate: 90” x 30” x 48” watch your units V shipping container = Bh V = 468.375 · 92.375 · 93.375 V = 43,266.14 · 93.375 V = 4,039,975.88 in 3 V crate = Bh V = 90 · 30 · 48 V = 2700 · 48 V = 129,600 in 3

16. Can You Hold It? (Independent Practice) V shipping container = V crate 4,039,975.88 in 3 129,600 in 3 = 31.17 Total weight: 975 · 31 = 30,225 lbs Weight difference: 56,000 - 30,225 = 25,775 lbs Space for packing material