Transcript FW 1.4 Scaling Up Prisms-3.pptx

TEACHER NOTES
Plan this lesson well. Three-dimensional scale
factor can be confusing.
The packet is on slides: 8-14
Slides 3-7 and 15-19 are also valuable.
Use all/some of what works best for you!
FILLING & WRAPPING 1.4- Scaling Up Prisms
Learning Target: I will analyze the impact of scale factor on
surface area and volume.
HW: Do FW Investigation 1 packet Pg. 10
Zelda Puzzle and CORRECT online
**QUIZ TOMORROW!**
*WDYE Retake TOMORROW, 3/24, in Math Lab
Warm-up:
Solve for Surface Area
The following polyhedron is a cube.
Front = 12 x 12 = 144
SA= 144 x 6 = 864 square feet
Why can I solve it this way??
12 feet
What are the two key words that explain
what you will explore today?
SCALE FACTOR
Calculate the Surface Area and the Volume of a 1 x 1 x 1
rectangular prism.
SA = 6 sq. in.
Vol = 1 cubic in.
What happens when you double the length(only)?
• What is the SA?
SA = 10 sq. in.
• What is the Volume?
Vol = 2 cubic in.
(1 dimension)
What happens when you double the length AND the width?
• What is the SA?
(2 dimensions)
SA = 16 sq. in.
• What is the Volume?
Vol = 4 cubic in.
What happens when you double the length, the width,
AND the height? (3 dimensions)
• What is the SA?
SA = 24 sq. in.
• What is the Volume?
Vol = 8 cubic in.
What happens to the SA…
• when you apply a scale factor of 2?
 All 3 dimensions are multiplied by 2.
 What is the relationship between the original SA and
the new SA?
 What is the relationship between the scale factor and
how many times larger the SA is?
What happens to the Volume…
• when you apply a scale factor of 2?
 All 3 dimensions are multiplied by 2.
 What is the relationship between the original
Vol. and the new Vol.?
 What is the relationship between the scale factor
and how many times larger the Vol. is?
FW 1.4: Scaling Up Prisms
Recipe for a 1-2-3 Compost Box
• Start with an open rectangular wood box that is
1 foot _________, 2 feet _________, and 3 feet _______.
This is a 1-2-3 box.
• Mix 10 pounds of shredded newspaper with 15 quarts of
water. Put the mixture in the 1-2-3 box.
• Add a few handfuls of soil.
• Add about 1,000 red worms (about 1 pound).
• Every day, mix collected kitchen waste with the soil in
the box. The worms will do the rest of the work, turning
the waste into new soil. A 1-2-3 box will decompose
about _______ pound of garbage a day.
A. Use graph paper to make a scale model of the 1-2-3 box that will
decompose 0.5 pound of garbage each day.
Make a sketch of the box and label the dimensions.
B. Assume that the number of worms used increases to match the
increase in box volume.
1. What changes in the dimensions of the basic design would
produce a box that could compost 1 pound of garbage each day?
Make a sketch of the new box and label the dimensions.
2. What changes in the dimensions of the basic design would produce
a box that could compost 2 pounds of garbage each day?
Make a sketch of the new box and label the dimensions.
3. What changes in the dimensions of the basic design would produce
a box that could compost 5 pounds of garbage each day?
Make a sketch of the new box and label the dimensions.
C. The Science Club wants to scale up the basic 1-2-3 design to a larger
box that is similar in shape.
1. Complete the following table that shows the cost and capacity
of several larger boxes.
2. What growth patterns do you see in the volume and surface area?
D. Suppose a large compost box is similar to a 1-2-3 box with scale
factor f.
1. How is the surface area of the large box related to that of the 1-2-3
box?
2. How is the volume of the 4-8-12 box related to that of the 1-2-3
box?
3. How is the amount of decomposed garbage related to the volume of
the 1-2-3 box?
Together as a class…
Double any ONE of the dimensions – length, width or height
Triple any ONE of the dimensions – length, width or height
Halving any ONE of the dimensions – length, width or height
V = 4 x 8 x 12 = 384 cubic in.
V=
(V x 2 x 2 x 2)
V=
(V x 1.5 x 1.5 x 1.5)
V=
(V x 0.5 x 0.5 x 0.5)
You can find these answers by multiplying the
3
original box volume by the
f
Work in Groups…
25 x 200 = 5,000 cm or 50 meters long
30 m = 3,000 cm
3,000
200
= 15 cm
2
2
2
20 cm x 200 = 800,000 cm or 80 m
3
100 cm
x 200
3
3
2
3
= 800,000,000 cm or 800 m
Exit Ticket?
FILLING & WRAPPING 1.4- Scaling Up Prisms
Did I reach my Learning Target? I will analyze
the impact of scale factor on surface area and volume.
HW: Do FW Investigation 1 packet Pg. 10
Zelda Puzzle and CORRECT online
**QUIZ TOMORROW!**
*WDYE Retake TOMORROW, 3/24, in Math Lab