1. NOTE TO TEACHERS 1.THE LESSON ON THE POWERPOINT IS ONE THAT ACCOMPLISHES THE SAME GOAL AS Inv. 3.3, IN THE BOOK. WE BELIEVE IT IS MORE EFFECTIVE. 2.The 4 slides after the warmup are review, and can be used at your discretion.

2. Quick Start Expectations 1.Fill in planner and HWRS HW: F&W p. 16 & 22, #5-7, 23 2.Get a signature on HWRS 3.On desk: journal, HWRS, pencil, pen 4.Warm Up: next slide… back of HWRS

3. 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 = 225.75 Area of Right face = 10.5 x 5 = 52.5 Total Surface Area = 2 (107.5 + 225.75 + 52.5) = 771.5 sq. cm Warm Up Height = 5 cm Width = 10.5 cm Length = 21.5 cm 1.Fill in planner and HWRS HW: F&W p. 16 & 22, #5-7, 23

4. 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 and spheres are 3-dimensional. They have 3 dimensions. Width Length Radius Circumference Width or Length Height Width Length Height

5. Nets A net is a two-dimensional shape that can be folded into a three-dimensional shape. Examples: Our online tool can help you see how nets fold into rect. prisms.

6. 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). OR – Double the love method

7. 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

9. Use worksheet - Finding the Least Surface Area (8 & 27 cubes)

10. 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? Be ready for a Shuffle Quiz!

11. Possible Arrangements of 8 cubes LengthWidthHeightVolumeSurface Area 8 inches1 inch 8 cubic inches34 square inches 4 inches2 inches1 inch8 cubic inches28 square inches 2 inches 8 cubic inches24 square 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!

12. 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 back of your lab sheet. – Be ready for a Shuffle Quiz!

13. Possible Arrangements of 27 cubes LengthWidthHeightVolumeSurface Area 27 inches1 inch 27 cubic inches110 square inches 9 inches3 inches1 inch27 cubic inches78 square inches 3 inches 27 cubic inches54 square inches Does it matter which order the dimensions are in? 27 x 1 x 1 1 x 27 x 1 1 x 1 x 27 Same SA and Volume! No!

14. Answers to Lab Sheet 1.8 cubes = 2 in x 2 in x 2in 27 cubes = 3 in x 3 in x 3 in 2.The name for these types of prisms is a cube. 3.24 cubes = 2 in x 3 in x 4 in 4.The shape closest to a cube has the least amount of surface area. 5.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.