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1 PBL, Projects, and Activities downloaded from NextLesson are provided on an online platform. driving question *example lesson teacher guide, answer keys, links, and rubrics share with students customize steps notes links, documents, videos and more The preview that follows includes the teacher guide and teacher resources only for this lesson.

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3 Project Title: Geological Engineer Standard Focus: Geometry & Spatial Sense Time Range: 2-4 Days Supplies: Basic Stuff Topics of Focus: - Volume - Composite Volume - Using Formulas Benchmarks: Geometry 7.G Geometry 8.G 6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Geometric Measurement and Dimension Modeling with Geometry Modeling with Geometry Procedures: G-GMD G-MG G-MG 3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. 1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). 3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). A) Task 1: Material Volume -- Students use authentic density and costs of raw materials to solve problems that involve volumes of geometric shapes. Let students calculate the volume, the weight and cost of these materials to determine the most valuable. B) Task 2: Composite Solids Students will be introduced to composite figures under the same premise as the first one. C) Task 3: Geological Engineer Students look at four different fictional sites. I have included four volumes for students to calculate and measure in the same way they have in the previous assignments. The student s goal is to prioritize the sites based on the cost, profit and length of time it will take to complete the project. The volume and value answers will be the same, but prioritizing will vary. Student may put a premium on the fastest to complete projects, others may put it on overall profit. That s for them to decide, debate and support Math it Up!

4 Mineral Pounds per 1 Cubic Foot (Density) 2014 Cost Aluminum lbs $0.91/lbs Coal 87 lbs $0.033/lbs Copper lbs $3.24/lbs Crude Oil 53 lbs $18.02/lbs Gold lbs $19,060/lbs Iron ore lbs $0.0561/ lbs Lead lbs $1.04/lbs Natural Gas 1,027 btu $3,800,000/btu Nickel lbs $8.65/lbs Platinum lbs $21,546.9/lbs Silver lbs $302.5/lbs Zinc lbs $1.09/lbs Sources: Coyotesteel.com & Infomine.com

5 All minerals and metals are not created equal. Geological engineers use mathematical modeling to estimate the amount of materials underground. Through careful analysis and decision making, they decide where to dig and how to extract the raw material. In this assignment, there are two different masses of materials and it is your job to determine which mass is the largest and which is the most valuable. Use the table of Raw Material Values to calculate the weight and value of the material to determine the best place to dig. -For Example- Mineral Pounds per 1 Cubic Foot (Density) 2014 Cost Aluminum lbs $0.91/lbs Coal 87 lbs $0.033/lbs Copper lbs $3.24/lbs Crude Oil 53 lbs $18.02/lbs Gold lbs $19,060/lbs Iron ore lbs $0.056/ lbs Lead lbs $1.04/lbs Natural Gas 1,027 btu $3,800,000/btu Nickel lbs $8.65/lbs Platinum lbs $21,547/lbs Silver lbs $302.50/lbs Zinc lbs $1.09/lbs 24 ft 3 24 ft 3 x lbs = lbs lbs x $0.91/lbs = $ What is the difference in the value of the materials?

6 What is the difference in the value of the materials? What is the difference in the value of the materials?

7 What is the difference in the value of the materials? What is the difference in the value of the materials?

8 In the real world, mathematical models are rarely pure geometric solids. Composite solids are combinations of common geometric solids. In general with composite solid problems, volumes are added (think ice cream cone), but in some cases they can be subtracted (think ring). In this assignment, you must calculate the volume of the composite materials and estimate its value. Use the table of Raw Material Values to calculate the weight and value of the material to determine the best place to dig. Cost of Extraction: $1,000,000 Pounds: What is the expected profit of the project? Does it make sense to do it? Value: Cost of Extraction: $50,000 Pounds: What is the expected profit of the project? Does it make sense to do it? Value:

9 Cost of Extraction: $1,000,000,000 Pounds: Value: What is the expected profit of the project? Does it make sense to do it? Cost of Extraction: $1,600,000 Pounds: Value: What is the expected profit of the project? Does it make sense to do it? Cost of Extraction: $5,000,000,000 Pounds: Value: What is the expected profit of the project? Does it make sense to do it?

10 Mining and drilling for natural resources is a necessary evil of our modern lifestyle. With increased attention to the environmental impact of these activities, greater attempts are made to extract the natural resources in the most responsible way. Time and costs do factor in these projects. If a geological engineer doesn t believe that the value of the resources are worth the cost of extracting it, then it doesn t make sense to do. In this project, a geological engineer has to evaluate models from four different excavation sites. Help them estimate the amount of raw material and its value using the Raw Material Values table. Once you have completed the analysis of the sites, answer the questions and finalize your report in the space below. Which site is the most cost effective? Division Mountain (Canada - Coal) Cost of Excavation Value of Raw Materials Profit Years Suggested Priority Nkamouna (Cameroon - Nickel) Jabal Sayid (Saudi Arabia - Copper) Cerro Negro (Argentina - Gold) Which site has to most valuable raw materials? Is it the site that would have the highest profit? Why or why not? Are there any sites that you would not recommend to use? Explain your reasoning. Write a paragraph summary of findings and your recommendations that can be sent to your supervisor. Be sure to include evidence from your calculations to support your opinion.

11 Division Mountain (Canada) Cost of Extraction: $240,000,000 Background: In the mountain are pockets of coal deposits. The dig must be into a mountain without polluting a nearby stream. Given these challenges it will be a year project. Piece 1: Piece 2: Piece 3: Piece 4: Total

12 Nkamouna (Cameroon) Cost of Extraction: $15,000,000 Background: A clearing has already been made, the layers of sediment will prove a challege to dig through, but underneath are rich nickel deposits. It will likely be a 5-6 year project. Piece 1: Piece 2: Piece 3: Piece 4: Total

13 Jabal Sayid (Saudi Arabia) Cost of Extraction: $280,000,000 Background: The dig is in a barren area, but the sediment is some of the hardest in the world and will be at least a 25 year long project. There are large copper deposits which could make it worth it. Piece 1: Piece 2: Piece 3: Piece 4: Total

14 Cerro Negro (Argentina) Cost of Extraction: $1,487,000,000,000 Background: A dig for these gold deposits would take place in a densely forested area and cannot disrupt the tropical rain forest or pollute the rivers. It is estimated that this would be at least a 40 year project. Piece 1: Piece 2: Piece 3: Piece 4: Total

15 Thank you for being my Math Friend! If you liked this 21 st Century Math Project You might like others. (Click the logo) Math it Up. Boomdiggy.

16 All minerals and metals are not created equal. Geological engineers use mathematical modeling to estimate the amount of materials underground. Through careful analysis and decision making, they decide where to dig and how to extract the raw material. In this assignment, there are two different masses of materials and it is your job to determine which mass is the largest and which is the most valuable. Use the table of Raw Material Values to calculate the weight and value of the material to determine the best place to dig. -For Example- Mineral Pounds per 1 Cubic Foot (Density) 2014 Cost Aluminum lbs $0.91/lbs Coal 87 lbs $0.033/lbs Copper lbs $3.24/lbs Crude Oil 53 lbs $18.02/lbs Gold lbs $19,060/lbs Iron ore lbs $0.056/ lbs Lead lbs $1.04/lbs Natural Gas 1,027 btu $3,800,000/btu Nickel lbs $8.65/lbs Platinum lbs $21,547/lbs Silver lbs $302.50/lbs Zinc lbs $1.09/lbs 24 ft 3 24 ft 3 x lbs = lbs lbs x $0.91/lbs = $ ft ft 3 3, lbs 176,931 lbs $73,562, $53,521, What is the difference in the value of the materials? Although the Silver is ft 3 more and over 173,000 lbs heavier, the gold is over $20,000,000 more valuable.

17 ft ft 3 680, lbs 250, lbs $38,125.1 $260, What is the difference in the value of the materials? The lead is $222,002 more valuable than the iron ore although it is almost less than quarter the volume ft ft lb lb $12, $6, What is the difference in the value of the materials? The copper is over twice as valuable, but is also over 5 times heavier than the nickel.

18 ft ft 3 121, lbs lbs $4, $ What is the difference in the value of the materials? The coal is $300 more valuable, but is also over 121,397 pounds heavier 242,784.8 ft ,867,594.7 lbs 59, btus $231,874, $225,999,566, What is the difference in the value of the materials? The Natural Gas is over $225,700,000,000 more valuable although it has a volume of ft 3 less.

19 In the real world, mathematical models are rarely pure geometric solids. Composite solids are combinations of common geometric solids. In general with composite solid problems, volumes are added (think ice cream cone), but in some cases they can be subtracted (think ring). In this assignment, you must calculate the volume of the composite materials and estimate its value. Use the table of Raw Material Values to calculate the weight and value of the material to determine the best place to dig. Cost of Extraction: $1,000, =1312 Pounds: 584,233.6 lbs Value: $636, What is the expected profit of the project? Does it make sense to do it? The profit would be $363,185. It would seem to make sense to do it. Cost of Extraction: $50, ft 3 Pounds: 703, lbs Value: $39, What is the expected profit of the project? Does it make sense to do it? This would not make sense because the cost of extraction is over 10,000 more than the value of the iron.

20 Cost of Extraction: Pounds: Value: $1,000,000, = , lbs 7,070,926, What is the expected profit of the project? Does it make sense to do it? The project would have a profit of over 6 billion dollars. It would make sense to do it. Cost of Extraction: Pounds: Value: $1,600, = 11, ,017, lbs $1,836, What is the expected profit of the project? Does it make sense to do it? The profit would be 236, so it could be worthwhile. Cost of Extraction: Pounds: Value: $5,000,000, ,799,387.8= 1,413,716,694 ft 3 122,993,352,400 lbs $4,058,780,629 What is the expected profit of the project? Does it make sense to do it? This project would be estimated to lose nearly $1,000,000,000.

21 Mining and drilling for natural resources is a necessary evil of our modern lifestyle. With increased attention to the environmental impact of these activities, greater attempts are made to extract the natural resources in the most responsible way. Time and costs do factor in these projects. If a geological engineer doesn t believe that the value of the resources are worth the cost of extracting it, then it doesn t make sense to do. In this project, a geological engineer has to evaluate models from four different excavation sites. Help them estimate the amount of raw material and its value using the Raw Material Values table. Once you have completed the analysis of the sites, answer the questions and finalize your report in the space below. Which site is the most cost effective? Division Mountain (Canada - Coal) Nkamouna (Cameroon - Nickel) Jabal Sayid (Saudi Arabia - Copper) Cerro Negro (Argentina - Gold) Cost of Excavation Value of Raw Materials Profit Years Suggested Priority $240,000,000 $241,988, $1,988, varies $15,000,000 54,253, ,253, ,000,000 1,487,000,000,0 00,000 $1,173,376, ,487,736,4 38, ,376, ,438, Which site has to most valuable raw materials? Is it the site that would have the highest profit? Why or why not? Cerro Negro has the most valuable raw materials, but it does not have the largest profit because it is a more complicated dig and will take longer. Are there any sites that you would not recommend to use? Explain your reasoning. Division Mountain may not be as fruitful of a profit. Write a paragraph summary of findings and your recommendations that can be sent to your supervisor. Be sure to include evidence from your calculations to support your opinion. Varies

22 Division Mountain (Canada) Cost of Extraction: $240,000,000 Background: In the mountain are pockets of coal deposits. The dig must be into a mountain without polluting a nearby stream. Given these challenges it will be a year project. Piece 1: double cone Piece 2: Triangular Prism 31,646, ,968,135 2,753,225, ,227,745 90,856, ,747, Piece 3: Cylinder Piece 4: Pyramid/prism 14,665, ,007,072 1,275,906, ,523,615,264 42,104, $83,279, Total $241,988,197.43

23 Nkamouna (Cameroon) Cost of Extraction: $15,000,000 Background: A clearing has already been made, the layers of sediment will prove a challege to dig through, but underneath are rich nickel deposits. It will likely be a 5-6 year project. Piece 1: Cylinder Piece 2: Pyramid ,142, , ,182, ,025, Piece 3: Prism with half cylinder Piece 4: Double prism , ,200, ,009, ,035, Total 54,253,091.94

24 Jabal Sayid (Saudi Arabia) Cost of Extraction: $280,000,000 Background: The dig is in a barren area, but the sediment is some of the hardest in the world and will be at least a 25 year long project. There are large copper deposits which could make it worth it. Piece 1: Cone Piece 2: Ring 75, , ,025, ,779, $136,162, $174,245, Piece 3: Composite looks like a camera Piece 4: Prism 207, , ,442, ,905,192.5 $377,274, ,692,823.7 Total $1,173,376,413.34

25 Cerro Negro (Argentina) Cost of Extraction: $1,487,000,000,000 Background: A dig for these gold deposits would take place in a densely forested area and cannot disrupt the tropical rain forest or pollute the rivers. It is estimated that this would be at least a 40 year project. Piece 1: Sphere Piece 2: Cylinder 11, , ,862, ,811, ,228,048, ,241,162,700 Piece 3: Double Prism Piece 4: pencil , ,174, ,206, ,505,116, ,762,110,500 Total 1,487,736,438,212

26 Teacher Guide Geological Engineer -- Mining Raw Materials Volume Project How do geological engineer determine the optimal places to mine? Lesson Duration: 2-4 Days Lesson Type: POL Audience: Classmates, Teachers

27 Overview All minerals and metals are not created equal. Geological engineers use mathematical modeling to estimate the amount of materials underground. Through careful analysis and decision making, they decide where to dig and how to extract the raw material in the safest way for the environment. Bring volume to life in this project. Although mineral deposits are never in the shape of actual geometric figures, the concept is the same. - In Material Volume students use authentic density and costs of raw materials to solve problems that involve volumes of geometric shapes. Let students calculate the volume, the weight and cost of these materials to determine the most valuable. -- In Composite Solids students will be introduced to composite figures under the same premise as the first one. -- In Geological Engineer students look at four different fictional sites. There are four sites included for students to calculate and measure in the same way they have in the previous assignments. The student s goal is to prioritize the sites based on the cost, profit and length of time it will take to complete the project. The volume and value answers will be the same, but prioritizing will vary.

28 Common Core Standards CCSS.Math.Content.7.G.B.6 CCSS.Math.Content.8.G.C.9 CCSS.Math.Content.HSG-GMD.A.3 CCSS.Math.Content.HSG-MG.A.1 CCSS.Math.Content.HSG-MG.A.3 CCSS.Math.Practice.MP1 CCSS.Math.Practice.MP2 CCSS.Math.Practice.MP3 CCSS.Math.Practice.MP4 CCSS.Math.Practice.MP6 CCSS.Math.Practice.MP7 21st Century Skills Critical Thinking/Problem Solving Skills Communication Skills Collaboration Skills Social Skills Self-Monitoring And Self-Direction Skills Ethics/Civic Responsibility Lesson Plan

29 Step 1: Material Volume In Material Volume students use authentic density and costs of raw materials from the "Raw Material Values" handout to solve problems that involve volumes of geometric shapes. Students will calculate the volume, the weight and cost of these materials to determine the most valuable. Students should be able to do this independently, but may benefit from seeing one as an example. You can show the short Geological Engineering video to give students a brief introduction to the career. Note: the full teacher guide including an answer key is downloadable in the Teacher Resources above. Step 2: Composite Solids In "Composite Solids" students will be introduced to composite figures under the same premise as the "Material Volume" assignment. Students will need to use the "Raw Material Values" handout. In each case, an estimated project cost is included and the goal is to estimate the overall profit of each project.

30 Step 3: Geological Engineer In Geological Engineer students look at four different fictional sites. At each site, there are four volumes for students to calculate and measure in the same way they have in the previous assignments. The student s goal is to prioritize the sites based on the cost, profit and length of time it will take to complete the project. The volume and value answers will be the same, but prioritizing will vary. Student may put a premium on the fastest to complete projects, others may put it on overall profit. That s for them to decide, debate and support. It may work well for students to work with a partner or small groups given the amount of work in this project. Once they complete "Geological Engineer", you can have your students complete a Rank & Reason task where they are asked to prioritize their rankings. Students can complete the Rank & Reason by logging in individually or by logging in as a group (using the Group option under Advanced Features). Alternative ways of completing the ranking are to project the ranking below on the board for students to come up, drag an option and then justify verbally to the class; or to use the printable version of the activity in the Teacher Resources above. Students will be able to compare with other students or with the class average and see other justifications. This feature can be turned off under Advanced Options.

31 Login Directions (Google) Student: 1. If you are on a computer shared with any other students, confirm they are signed out of Google. Do this by going to drive.google.com and sign out the other student.! 2. Go to nextlesson.org. 3. Select Sign Up in the upper right corner of the site. 3. Select Student. 4. Select the red, Sign in with Google button. You will be required to enter your school Google username and password. 5. If your teacher has already given you a project code, enter it in the pop-up window requesting the code. If a pop-up window does not appear, select the Join Lesson button on the top of the page and enter the code.

32 Log In Directions (non-google) Student Log In: 1. Go to nextlesson.org. 2. Select Log In in the upper right corner of the site. 3. Select Student. 6. Select the orange, Log in with username button. 7. Enter your username and password. That s it! You should be able to access NextLesson.