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Title: FW 1.3 Finding Least & Greatest Surface Area
Math CC7/8 – Be Prepared Unit: Filling and Wrapping On Desk: Journal: Date: 1/30/2019 Title: FW 1.3 Finding Least & Greatest Surface Area 3) Sign off neighbor's HW from last night. 4) Warm Up: Turn In: Check Family Access. Are you missing anything? What is the Surface Area of this Kleenex Box? Dimensions: 21.5 cm x 10.5 cm x 5cm In Your Planner: HW: p. 16 #4, 5, 22, 23, 25 Height = 5 cm Width = 10.5 cm Length = 21.5 cm
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Tasks for Today Finish/Summarize 1.2? Warm up Lesson 1.3 Begin HW?
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Find All Possible Arrangements
Group Task: Given 24 cubes and a lab sheet, find at least 3 possible arrangements. Fill in the lab sheet as you are working. Find the volume for each arrangement. Find the surface area for each arrangement.
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Possible Arrangements of 24 cubes
Length Width Height Volume Surface Area 1 inch 24 inches 24 cubic in. 98 sq. in. 2 inches 12 inches 76 sq. in. 3 inches 8 inches 70 sq. in. 4 inches 6 inches 68 sq. in. 56 sq. in. 52 sq. in.
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Surface Area Recap Always label surface area as: units squared or units2 surface area only measures two dimensions (L and W). Different ways to solve for surface area (SA): Solve for the area of all six faces and add them all together OR Solve for the area of three of the faces (for example, top, front, and right), add the areas together, and multiply by two (because there are two pairs of faces that are equivalent) . OR Double the love method
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Volume Recap Volume is always labeled as:
units cubed or units3 because we use three dimensions to solve for volume. To find the volume of a polyhedron: Count how many inch cubes fit in the box. OR Find the area of the base and multiply it by the height of the polyhedron. Volume = Bh (B = area of base , h = height) OR Volume of a Rectangular Prism = Length x Width x Height
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What is the Surface Area of this Kleenex Box?
Warm-up: What is the Surface Area of this Kleenex Box? Dimensions: 21.5 cm x 10.5 cm x 5cm Height = 5 cm Width = 10.5 cm Length = 21.5 cm
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Warm Up Kleenex Box -Dimensions: 21.5 cm x 10.5 cm x 5cm Surface Area:
Area of Front face = 21.5 x 5 = 107.5 Area of Top face = 21.5 x 10.5 = Area of Right face = 10.5 x 5 = 52.5 Total Surface Area = 2 ( ) = sq. cm Height = 5 cm Width = 10.5 cm Length = 21.5 cm
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What does it mean to be 3-dimensional?
Lines are one-dimensional. They only have length. Polygons and circles are 2-dimensional because they have 2 dimensions. Polyhedrons are 3-dimensional. They have 3 dimensions. Height Radius Width Circumference Length Width or Length Radius Height Height Width Circumference Length
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Nets A net is a two-dimensional shape that can be folded into a three-dimensional shape. Examples:
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Use worksheet - Finding the Least Surface Area (8 & 27 cubes)
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Find All Possible Arrangements
Group Task: Given 8 cubes find all possible arrangements for a rectangular prism. Fill in the lab sheet as you are working. Find the volume for each arrangement. Find the surface area for each arrangement. Think about the following: Which arrangement gives you the greatest SA? Which arrangement gives you the least SA?
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Possible Arrangements of 8 cubes
Length Width Height Volume Surface Area 8 inches 1 inch 8 cubic inches 34 sq inches 4 inches 2 inches 28 sq inches 24 sq inches Does it matter which order the dimensions are in? Is (8 in x 1 in x 1 in) the same rectangular prism as (1 in x 1 in x 8 in), or (1 in x 8 in x 1 in) ? Which arrangement had the most surface area? Why? Which arrangement had the least surface area? Why? No! Yes!
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Find All Possible Arrangements
Group Task: Find all possible arrangements for 27 cubes . Fill in the lab sheet as you are working. Find the volume for each arrangement. Find the surface area for each arrangement. Think about the following: Which arrangement gives you the greatest SA? Which arrangement gives you the least SA? Answer the questions on the second lab sheet. Be ready for a Class Discussion
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Possible Arrangements of 27 cubes
Length Width Height Volume Surface Area 27 inches 1 inch 27 cubic inches 110 sq inches 9 inches 3 inches 78 sq inches 54 sq inches Does it matter which order the dimensions are in? No! 27 x 1 x 1 1 x 27 x 1 1 x 1 x 27 Same SA and Volume!
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Answers to Lab Sheet 8 cubes = 2 in x 2 in x 2in
The name for these types of prisms is a cube. 24 cubes = 2 in x 3 in x 4 in The shape closest to a cube has the least amount of surface area. a. 12 in x 1 in x 1 in will have the most surface area because it is least like a cube. b. 3 in x 2 in x 2 in will have the least surface area because it is most like a cube.
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