1. 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

2. Tasks for Today
Finish/Summarize 1.2?
Warm up
Lesson 1.3
Begin HW?

3. 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.

4. 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.

5. 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

6. 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

7. 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

8. 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

9. 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

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

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

13. 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?

14. 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!

15. 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

16. 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!

17. 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.