COMMUNITY LEARNING CENTER LESSON PLAN

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1 COMMUNITY LEARNING CENTER LESSON PLAN Level (preged or GED): Content Area (RLA, Math, Science, Social Studies): General Topic: GED Math Geometry Specific Lesson Title: Surface Area and Volume of pyramids, cones, spheres, and composite solids (Lesson 1 Estimated Time: 180 minutes CCRS (List College & Career Readiness Standards) CCR Standards CCRS Level D: Geometry 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. Anchor(s) & Level(s) GED Assessment Anchors Q.5.d When given geometric formulas, compute volume and surface area of right pyramids and cones. Solve for side lengths, height, radius, or diameter when given volume or surface area. Q.5.e When given geometric formulas, compute volume and surface area of spheres. Solve for radius or diameter when given the surface area. Q.5.f Compute surface area and volume of composite 3-D geometric figures, given geometric formulas as needed. Practice(s) MP 3 FOUNDATION SKILLS FRAMEWORK: W 5.5 (APPLIES MATH CONCEPTS TO UNDERSTAND AND SOLVE PROBLEMS) OBJECTIVES (After completing the lesson, what will student be able to show/do?) SWBAT: Define and identify right pyramids, cones, and spheres. Find surface area and volume of right pyramids, cones, and spheres. Given volume or surface area, solve for side length, height, radius, or diameter. Find surface area and volume of composite solid geometric figures MATERIALS (What print and electronic resources will be needed to conduct the lesson?) Kaplan New GED Test Strategies, Practice, and Review Steck-Vaughn GED: Test Preparation Student Workbook Mathematical Reasoning TI-30xs MultiView calculators GED Mathematics formula sheet: Surface area of mixed solids worksheet: Volume of mixed solids worksheet: Printable surface area worksheets for various shapes included in the lesson, including composite solids: Printable volume worksheets for various shapes included in the lesson, including composite solids: CLASSROOM ACTIVITIES OR PROCEDURES (What specific steps will you follow to execute the lesson? What will you say and do? Teacher/Developer: [Type text] Date: [Type text]

2 What will the learners do?) Pre-lesson activities (30 minutes) Review homework and answer questions. Discuss problems from exit ticket that students had trouble with. Lesson (2 hours plus 10 minute break) Surface area and volume of pyramids, cones, and spheres Direct students to appropriate formulas and discuss. Demonstrate calculation of volume and surface area with each of the three shapes. Demonstrate solving for height, radius, or side length when volume or surface area are given (ex. Steck-Vaungh p. 154 #1-2, 6- Provide time for guided practice. Ask students to discuss and explain thought process in solving the problem. Suggested resources: Kaplan p. 391 Steck-Vaughn p Surface area of mixed solids worksheet: Printable surface area worksheets for various shapes included in the lesson Printable volume worksheets for various shapes included in the lesson Surface area and volume of composite solids Discuss composite solids provide visual model if possible. Discuss strategy of dividing composite solid into known geometric figures to find volume, and strategy of subtracting overlapping areas to find surface area. Kaplan p. 397 Steck-Vaughn p Printable surface area worksheets (scroll down for composite solids) Printable volume worksheets (scroll down for composite solids) Geometry review Have students complete the geometry review in Kaplan p , or provide another mixed review of geometry concepts learned. You can choose to approach this as an opportunity for further guided practice or as an assessment where students work independently. Closure (20 minutes) - Ask students to recap vocabulary and concepts learned today. - Assign homework - Collect work completed on geometry review ASSESSMENT ACTIVITIES (How will you know that the learners have met the objectives for this lesson?) Q.1.b. Perform addition, subtraction, multiplication, and division on rational numbers. - check geometry review. HOMEWORK Finish any guided practice not completed during class. Teacher/Developer: [Type text] Date: [Type text]

3 2014 GED Test Resources Mathematics Formula Sheet & Explanation The 2014 GED Mathematical Reasoning test contains a formula sheet, which displays formulas relating to geometric measurement and certain algebra concepts. Formulas are provided to testtakers so that they may focus on application, rather than the memorization, of formulas. Area of a: square A = s 2 rectangle parallelogram triangle A = lw A = bh A =!! bh trapezoid A =! h(b1 + b! circle A = πr 2 Perimeter of a: square rectangle P = 4s P = 2l + 2w triangle P = s 1 + s 2 + s 3 Circumference of a circle C = 2πr OR C = πd; π 3.14 Surface area and volume of a: rectangular prism SA = 2lw + 2lh + 2wh V = lwh right prism SA = ph + 2B V = Bh cylinder SA = 2πrh + 2πr 2 V = πr 2 h pyramid SA =!! ps + B V =!! Bh cone SA = πrs + πr 2 V =!! πr2 h sphere SA = 4πr 2 V =!! πr3 Data mean median (p = perimeter of base with area B; π 3.1 mean is equal to the total of the values of a data set, divided by the number of elements in the data set median is the middle value in an odd number of ordered values of a data set, or the mean of the two middle values in an even number of ordered values in a data set Algebra slope of a line slope-intercept form of the equation of a line point-slope form of the equation of a line standard form of a quadratic equation! =!!!!!!!! y = mx + b y y 1 = m(x x y = ax 2 + bx + c quadratic formula! =! ±!! 4!" 2! Pythagorean theorem a 2 + b 2 = c 2 simple interest distance formula total cost I = Prt (I = interest, P = principal, r = rate, t = time) d = rt total cost = (number of units) (price per unit) GEDtestingservice.com GED.com GED and GED Testing Service are registered trademarks of the American Council on Education. They may not be used or reproduced without the express written permission of ACE or GED Testing Service. The GED and GED Testing Service brands are administered by GED Testing Service LLC under license from the American Council on Education. Copyright 2014 GED Testing Service LLC. All rights reserved.

4 Name : Score : Surface Area - Cone ES1 Find the surface area of each cone. Round the answer to nearest tenth. ( use π = 3.14 ) 3 m 7 m 12 ft 7 ft 14 m 9 in 3 cm 5 cm 18 ft 14 ft 6 in 8) 9) 8 m 9 in 18 m 12 cm 8 in 5 cm

5 Name : Score : Answer key Surface Area - Cone ES1 Find the surface area of each cone. Round the answer to nearest tenth. ( use π = 3.14 ) 3 m 7 m 12 ft 7 ft 14 m 94.2 m ft m2 9 in 3 cm 5 cm 18 ft 14 ft 6 in 83.2 cm ft2 113 in2 8) 9) 8 m 9 in 18 m 12 cm 8 in 5 cm in m cm2

6 13 in 7 in Name : Score : Volume - Cylinder ES1 Find the exact volume of each cylinder. 13 in 5 m 11 m 4 in 9 cm 15 ft 7 ft 11 cm 8) 9) 7 m 3 m 10) The cross-section of a pipe has a width of 6 centimeter and height of 15 centimeter. Calculate the volume of the pipe.

7 13 in 7 in Name : Score : Answer Key Volume - Cylinder ES1 Find the exact volume of each cylinder. 13 in 396π m3 208π in3 225π cm3 5 m 11 m 4 in 9 cm 15 ft 7 ft 45π m3 735π ft3 128π mm3 11 cm 8) 9) 7 m 3 m 275π cm3 637π in3 63π m3 10) The cross-section of a pipe has a width of 6 centimeter and height of 15 centimeter. Calculate the volume of the pipe. 135π cm3

8 Name : Score : Volume of Rectangular Pyramid Sheet 1 Find the volume of each rectangular pyramid. Round the answer to two decimal places. 29 m 14 cm 13 cm 6 cm 21 m 21 m 17 ft 32 ft 11 in 35 m 24 ft 18 in 5 in 22 m 21 m 3 cm 8) 9) 19 in 28 m 50 ft 32 ft 32 ft 15 in 15 in 27 m 23 m

9 Name : Score : Answer Key Volume of Rectangular Pyramid Sheet 1 Find the volume of each rectangular pyramid. Round the answer to two decimal places. 29 m 14 cm 13 cm 6 cm 21 m 21 m 17 ft 32 ft 364 cm m ft3 11 in 35 m 24 ft 18 in 5 in 22 m 21 m 3 cm 330 in m3 80 cm3 8) 9) 19 in 28 m 50 ft 32 ft 32 ft 15 in 15 in 27 m 23 m ft in3 5793

10 Name : Score : Volume - Mixed Shapes ES1 Find the exact volume of each shape. 18 ft 18 in 14 ft 8) 9) 8 m 18 m 5 cm 2 cm 3 ft 12 cm 20 cm 5 ft 8 ft 6 ft 15 in 10 ft 5 ft

11 Name : Score : Answer Key Volume - Mixed Shapes ES1 Find the exact volume of each shape. 18 ft 18 in 14 ft 294π ft3 972π in3 100 cm3 960 cm3 144 ft3 128π mm3 8) 9) 8 m 18 m 5 cm 2 cm 3 ft 12 cm 20 cm 5 ft 8 ft 6 ft 15 in 10 ft 5 ft 2250π in3 250 ft3 384π m3

12 5 mm 4 mm Name : Score : Volume - Compound Shapes Sheet 1 Find the volume of each figure. Round the answer to two decimal places. ( use π = 3.14 ) 9 ft 12 ft 6 ft 11 m 16 ft 4 ft 5 in 12 cm 8 in 14 in 9 in 5 mm 13 mm 7 mm 15 cm

13 4 mm Name : Score : Answer Key Volume - Compound Shapes Sheet 1 Find the volume of each figure. Round the answer to two decimal places. ( use π = 3.14 ) 9 ft 12 ft 6 ft 11 m 16 ft 4 ft 600 ft in 12 cm 8 in 14 in 9 in cm in3 5 mm 5 mm 13 mm 7 mm 15 cm 539 mm cm3

Volume of Cylinders. Volume of Cones. Example Find the volume of the cylinder. Round to the nearest tenth.

Volume of Cylinders. Volume of Cones. Example Find the volume of the cylinder. Round to the nearest tenth. Volume of Cylinders As with prisms, the area of the base of a cylinder tells the number of cubic units in one layer. The height tells how many layers there are in the cylinder. The volume V of a cylinder