1. FILLING & WRAPPING 1.3 3) Warm-up:
1) Learning Target: I will determine how to design a box with the least packaging material, given the volume of a box.
2) HW Inv. 1 Day 2:FW 1.3 Finish pg. 7 and Correct with the EDpuzzle *WDYE Retake this Thursday, 3/30 in Math Lab
3) 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

2. 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

3. 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) .

4. 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

5. 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.
Height
Radius
Width
Circumference
Length
Width or Length
Width
Length
Height

6. 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.

8. p. 4

9. Find All Possible Arrangements
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.

10. 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

11. 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?
The one closest to a cube requires the least material. The one furthest from a cube requires the most material.
C. Which box shape would you recommend for shipping the
Mug Wump characters? Explain your reasoning.
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.
D. Why do you think the shipping directions called for 24 rather than 26 Mug Wump characters in a box?
There are only a few possible ways to build a box that is 26 in3. 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.

12. p. 5
You discovered that 24 blocks can be packaged in different ways that use varying amounts of packaging material. By using less material, a company can save money, reduce waste, and conserve natural resources. Which rectangular arrangement of cubes uses the least amount of packaging material?

13. Find All Possible Arrangements
Group Task:
Given 8 cubes find all possible arrangements for a rectangular prism.
Fill in the packet 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 in
1 in
8 in³
34 in²
4 in
2 in
28 in²
24 in²
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) ?
No!
Yes!

15. Possible Arrangements of 8 cubes
Length
Width
Height
Volume
Surface Area
8 in
1 in
8 in³
34 in²
4 in
2 in
28 in²
24 in²
1. Which arrangement had the most surface area and used the most packaging material for 8 cubes?
2. Which arrangement had the least surface area and used the least packaging material for 8 cubes?
a. What is the name of that prism?
8 in x 1 in x 1 in
2 in x 2 in x 2 in
cube

16. Find All Possible Arrangements
Group Task:
Find all possible arrangements for 27 cubes .
Fill in the packet 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?

17. Possible Arrangements of 27 cubes
Length
Width
Height
Volume
Surface Area
27 in
1 in
27 in³
110 in²
9 in
3 in
78 in²
54 in²
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!
3. Which arrangement (set of dimensions) used the least packaging material for 27 cubes?
a. What is the name of this type of prism?
3 in x 3 in x 3 in
cube

18. 4. Without solving for the surface area, how could you tell simply by looking at the dimensions which prism will have the least amount of surface area?
The shape closest to a cube has the least amount of surface area.
5. The dimensions for a box with 12 unit cubes are listed below.
12 x 1 x x 3 x x 2 x 1 3 x 2 x 2
a. Which set of dimensions will require the least amount of material or have the smallest surface area? How do you know?
3 x 2 x 2
Because they are the closest dimensions to a cube.

19. FILLING & WRAPPING 1.3
Did I meet my Learning Target? I will determine how to design a box with the least packaging material, given the volume of a box.
HOMEWORK: Inv. 1 Day 2:FW 1.3 Finish pg. 7 and Correct with the EDpuzzle
*Remember: WDYE Retake this Thursday, 3/30 in Math Lab