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3. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING LESSON GOALS When given geometric formulas, compute volume and surface area of rectangular prisms. Solve for the side lengths or height, when given volume or surface area. (Q.5.a) When given geometric formulas, compute volume and surface area of cylinders. Solve for height, radius, or diameter when given volume or surface area. (Q.5.b) When given geometric formulas, compute volume and surface area of right prisms. Solve for the side lengths or height, when given volume or surface area. (Q.5.c)

4. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING 4 Think & work alone Think, Pair, Share Cooperative Learning in Small Groups WHAT YOU WILL DO IN THIS LESSON

5. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING GEOMETRY REVIEW ROUND ROBIN 5

6. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING 2014 GED ® Webinar Series How do you think finding the area of a 2-D figure would be different from finding the surface area of a 3-D figure? Does it make sense to find the volume of a 2-D figure? Explain why or why not. What are you actually finding when asked to find the volume of a 3-D figure? What are the units of measure? In your own words, write a definition for the surface area and volume of a 3-D figure. 2-D VERSES 3-D: QUESTIONS TO PONDER 6

7. UNDERSTANDING SURFACE AREA FORMULAS https://www.youtube.com/watch ?v=wdDLXCypg4Y 7

8. UNDERSTANDING VOLUME OF PRISMS AND CYLINDERS https://www.youtube.com/watch ?v=OYY4ZkhpqGU 8

9. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING GED TEST FORMULA SHEET 9

10. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING THE SOLVE METHOD 10 S tudy the problem (What am I trying to find?) O rganize the facts (What do I know?) L ine up a plan (What steps will I take?) V erify your plan with action (How will I carry out my plan?) E xamine the results (Does my answer make sense? If not, rework.) Always double check!

11. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING S – STUDY THE PROBLEM 11 What is the problem asking me to do? Find the question. Find the surface area and the volume of a box whose base measures 12 inches by 5 inches and whose height is 6 inches. Find the surface area and volume of the box.

12. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING O – ORGANIZE THE FACTS 12 What do I know? Find the surface area and the volume of a box whose base measures 12 inches by 5 inches and whose height is 6 inches. Dimensions of the box: l = 12 inches w = 5 inches h = 6 inches

13. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING L – LINE UP A PLAN 13 What steps will I take? 1.To find the surface area, use the formula: SA = ph + 2B 2.To find the volume, use the formula: V = Bh 3.Since the area of the base (B) is in both formulas and the base is a rectangle, find B by using the B = bh first. 4.Then, you need to find the perimeter of the base by using p = 2l +2w. 5. Next substitute the known values for B and p into the formulas with the known height (h = 6). 6.Use the order of operations to simplify the equations in the formulas and arrive at the final answers.

14. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING V – VERIFY YOUR PLAN WITH ACTION 14 B = bh = 12 inches x 5 inches = 60 in 2 p = 2l + 2w = 2(12) + 2(5) = 24 + 10 = 34 inches SA = ph + 2B = 34(6) + 2(60) = 204 + 120 = 324 in 2 V = Bh = 60(6) = 360 in 3

15. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING E – EXAMINE THE RESULTS 15 Does my answer make sense? Since the surface areas of the top and bottom of the box would be 2(60) = 120, you would think that your answer of 324 for all 6 sides of the box is reasonable. It is also reasonable for the volume of the box to be 360 in 3 since it is not much more than the surface area number was because it is the same box.

16. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING USING THE SOLVE METHOD 16 XYZ Company stores its waste in cylindrical barrels that have a radius of 2 feet and a height of 5.5 feet. Last month the company filled 20 barrels with waste. What was the total volume of waste that the company produced last month? If the metal the barrels were made of cost them $2.00 per square foot, what was the total cost of the metal to make the 20 barrels?

17. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING LESSON GOALS When given geometric formulas, compute volume and surface area of rectangular prisms. Solve for the side lengths or height, when given volume or surface area. (Q.5.a) When given geometric formulas, compute volume and surface area of cylinders. Solve for height, radius, or diameter when given volume or surface area. (Q.5.b) When given geometric formulas, compute volume and surface area of right prisms. Solve for the side lengths or height, when given volume or surface area. (Q.5.c)

18. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING SOLVING FOR OTHER UNKNOWNS 18 The surface area of a container shaped like a rectangular prism is 864 cm 2. It has a width of 4 cm and a length of 12 cm. Find the height of the container.

19. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING S – STUDY THE PROBLEM 19 What is the problem asking me to do? Find the question. Find the height of the rectangular prism. The surface area of a container shaped like a rectangular prism is 864 cm 2. It has a width of 4 cm and a length of 12 cm. Find the height of the container.

20. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING O – ORGANIZE THE FACTS 20 What do I know? The surface area of a container shaped like a rectangular prism is 864 cm 2. It has a width of 4 cm and a length of 12 cm. Find the height of the container. Container is a rectangular prism with the following: SA = 864 sq. cm w = 4 cm l = 12 cm

21. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING L – LINE UP A PLAN 21 What steps will I take? 1. Use the formula: SA = ph + 2B 2. Find the perimeter of the base by using p = 2l +2w. 3. Find B (area of the base) using B = lw. 4. Substitute the known values for B and p into the formula with the known surface area. 5. Solve the resulting equation for h.

22. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING V – VERIFY YOUR PLAN WITH ACTION 22 p = 2l + 2w = 2(12) + 2(4) = 24 + 8 = 32 B = lw = 12 (4) = 48 SA = ph + 2B 864 = 32h + 2(48) 864 = 32h + 96 768 = 32h 24 = h

23. INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING E – EXAMINE THE RESULTS 23 Does my answer make sense? To see if my answer makes sense, I am going to see if this height, with the given dimensions of the base, result in the given surface area. Does 864 = 32h + 96 if h = 24? 864 = 32(24) + 96 864 = 768 + 96 864 = 864 Yes, my answer makes sense!