1. 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!

2. 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:

3. Solve for Surface Area The following polyhedron is a cube. 12 feet Front = 12 x 12 = 144 SA= 144 x 6 = 864 square feet Why can I solve it this way??

4. What are the two key words that explain what you will explore today? SCALE FACTOR

5. 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) ? (1 dimension) What is the SA? What is the Volume? SA = 10 sq. in. Vol = 2 cubic in.

6. What happens when you double the length AND the width? What is the SA? What is the Volume? What happens when you double the length, the width, AND the height? (3 dimensions) What is the SA? What is the Volume? SA = 16 sq. in. Vol = 4 cubic in. SA = 24 sq. in. Vol = 8 cubic in. (2 dimensions)

7. 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?

8. 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.

9. 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.

10. 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.

11. 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.

12. 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.

13. 2. What growth patterns do you see in the volume and surface area?

14. 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?

15. 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

16. V = You can find these answers by multiplying the original box volume by the f 3 (V x 2 x 2 x 2) (V x 1.5 x 1.5 x 1.5) (V x 0.5 x 0.5 x 0.5) V = 4 x 8 x 12 = 384 cubic in.

17. 30 m = 3,000 cm 3,000 200 = 15 cm Work in Groups… 25 x 200 = 5,000 cm or 50 meters long

18. 20 cm 2 200 2 x = 800,000 cm or 80 m 2 2 100 cm 3 200 3 x = 800,000,000 cm or 800 m 3 3

19. Exit Ticket?

20. 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