Math CC7/8 – Feb. 13 Math Notebook: Things Needed Today (TNT):

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Presentation transcript:

Math CC7/8 – Feb. 13 Math Notebook: Things Needed Today (TNT): Pencil/Math Notebook/Calculator/Book Filling & Wrapping NEW Seats Today! Math Notebook: Topic: Finding Surface Area & Least Surface Area HW: F&W p. 16, #4-5, 22-23 & 25

What’s Happening Today? Do a short version of 1.2 Warm up Lesson 1.3 Begin HW?

Use worksheet 1.2 – 24 cube table

Find All Possible Arrangements Buddy/Truddy 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.

Possible Arrangements of 24 cubes Length Width Height Volume Surface Area 1 inch 24 inches 24 cubic inches 98 square inches 2 inches 12 inches 76 square inches 3 inches 8 inches 70 square inches 4 inches 6 inches 68 square inches 56 square inches 52 square inches

Different ways to solve for surface area Surface Area Recap ALWAYS label surface area as: units squared or units2 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

To find the volume of a polyhedron: 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

Warm Up Surface Area: Area of Front face = 21.5 x 5 = 107.5 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 Height = 5 cm Width = 10.5 cm Length = 21.5 cm

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 solid figures. They have 3 dimensions. Each side is flat surfaces (polygons) Height Radius Width Circumference Length Width or Length Radius Height Height Width Circumference Length

Nets A net is a two-dimensional shape that can be folded into a three-dimensional shape. Examples:

Question What are the dimensions of the rectangular prism that has the least surface area of a given volume?

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

Find All Possible Arrangements Buddy/ Truddy 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?

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 No! 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? Yes!

Find All Possible Arrangements Buddy/Truddy 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?

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!

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.

Homework: F&W 1.2-1.3 pg. 16 #4-5, #22-23 20 #25