Quick Start Expectations 1.Fill in planner and HWRS HW: F&W p. 16-24, #3-4, 17-19, 31 2.On desk: journal, vocab toolkit, calculator, bin, pencil 3.Warm.

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Quick Start Expectations 1.Fill in planner and HWRS HW: F&W p , #3-4, 17-19, 31 2.On desk: journal, vocab toolkit, calculator, bin, pencil 3.Warm Up: Find the surface area and volume of this rectangular prism: SA = 2(3x4) + 2(4x5) + 2(3x5) = = 94 units 2 V = 3units x 4units x 5 units = 60 units 3

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Group Task: – Given 24 cubes and a lab sheet, find 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. Find All Possible Arrangements

Possible Arrangements of 24 cubes LengthWidthHeightVolumeSurface Area 1 inch 24 inches24 cubic inches98 square inches 1 inch2 inches12 inches24 cubic inches76 square inches 1 inch3 inches8 inches24 cubic inches70 square inches 1 inch4 inches6 inches24 cubic inches68 square inches 2 inches 6 inches24 cubic inches56 square inches 2 inches3 inches4 inches24 cubic inches52 square inches

B. Which arrangement of cubes requires the box that can be made with the least material? Which requires the box that needs the most material? C. Which box shape would you recommend for shipping the Mug Wump characters? Explain your reasoning. D. Why do you think the shipping directions called for 24 rather than 26 Mug Wump characters in a box? The one closest to a cube requires the least material. The one furthest from a cube requires the most material. 2 in. x 3 in. x 4 in. It has the smallest surface area, so it would use the least material to create the box. So, it would cost less to produce. There are only a few possible ways to build a box that is 26 in 3. It could be 1x2x13 or 1x1x26. Both of those are long and slender, so they’d be expensive compared to a box that is shaped more like a cube.

Recap Always label surface area as: units squared or units 2 because surface area only measures two dimensions (length and width). Different ways to solve for surface area: – 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).

Volume Recap Volume is always labeled as: – units cubed or units 3 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

HW: F&W p , #3-4, 17-19, 31