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 * Unit Title: ** Finding the Surface Areas of Prisms, Cylinders, Cones and Pyramids
 * Grade Level: ** 7th and 8th Grades
 * Subject/Topic Area(s): ** Algebra I
 * Designed By: ** Matt Coulter
 * Time Frame: ** 1 week
 * __Brief Summary of Unit (Including curricular context and unit goals):__**

The unit about Finding the Surface Areas of Prisms, Cylinders, Cones and Pyramids follows a unit in which students learned how to find the areas of circles, triangles and rectangles. This unit explores finding the surface area of shapes using two different methods and proceeds to show how these methods can be used in everyday practical situations. The curricular goals are for the student to learn the necessary skills to find surface areas, to know which method to use in a particular situation, and, most importantly, to be able to interpret real-world situations so as to develop a system of equations that can be used to find a solution to that situation. =Content Standard(s)= 4.2.8 E. Measuring Geometric Objects
 * STAGE 1 – DESIRED RESULTS**

Students will understand that …
· Everyday objects have a variety of attributes, each of which can be measured in many ways. · What we measure affects how we measure it. (4.5A4; 4.5A6)** · Measurements can be used to describe, compare, and make sense of phenomena. = = =Essential Question(s)=
 * How can measurements be used to solve problems?
 * Students will be able to: **
 * Find the surface area of prisms.
 * Find the surface area of cylinders
 * Find the surface area of pyramids
 * Find the surface area of cones
 * Read and interpret a real-world situation and apply and solve formulas or nets to determine the most economic solution.


 * Materials Required **
 * Poster Boards for Final Tables
 * Markers
 * Straight edges for making tables

STAGE 2 – ASSESSMENT EVIDENCE
Two companies have offered to donate their time to build a school playground. Each company had proposed a plan for what they will build on the playground. Company A is proposing a playground with the following play structures:
 * Performance Task **

· (6) 6’ cylindrical towers with a radius of 2’. · (6) cones with a 2’ slant height to place on top of the towers with a 6” overlap around the top of the cylinders. · (4) triangular prisms (base 3’x 3’, sides 2’) to be used as bases for seesaw bases (wood will be donated for seesaws) · (4) pyramids (2 for each entrance) with a 2’x 2’ base and a slant height of 3.5’

Company B is proposing a playground with the following play structures:

· (4) 8’ cylindrical towers with a radius of 1.5’. · (4) cones with a 3’ slant height to place on top of the towers with a 6” overlap around the top of the cylinders. · (6) rectangular prisms (3’x3’x2’) to be used as bases for monkey bars (bars will be donated) · (4) pyramids (2 for each entrance) with a 2.5’x2.5’ base and a slant height of 3’

The school is responsible for buying the material to create these structures and the material costs $30 per square foot. Your assignment is to **apply** surface area formulas to the proposed structures and **evaluate** which plan will cost the school less money. All structures must be closed on all surfaces (you must include top and bottom bases in your calculations). You will present your recommendation to the budget committee. You need to **show** your work (hand in separately) and create a table that displays the surface area of each shape, the cost of each shape, the total cost of the similar shapes and the total cost of the project for each plan.

Ex. Plan A
 * Structure Shape || Surface Area of Shape || Cost of Single Shape || Total Cost for quantity of this type of Shape ||
 * cylindrical towers || 20 sq ft. || $600 || $3600 ||
 * cones ||  ||   ||   ||
 * triangular prisms ||  ||   ||   ||
 * pyramids ||  ||   ||   ||
 * Total Cost for all Structures || xxxxxxxxxxxxxxx || xxxxxxxxxxxxxx ||  ||

There is a separate job to cover the ground of the 30’ x 30’ area with a protective rubber AFTER all the play structures have been built and erected. This material is $20 per square foot. What should be the cost for this job if the school chooses Company A? Company B? How did you come up with your answer? **Explain**.

**Analyze** how much money could you save if the restriction of including the top and bottom bases was changed to say only exposed bases must be included in the structures? **Show** work and **explain** your answer.

Bonus Question for 1 homework pass What would be the change in price if the companies doubled the height of all the cylinders?

· The student is able to determine the surface area of a cylinder. · The student is able to determine the surface area of a cone. · The student is able to determine the surface area of a prism. · The student is able to determine the surface area of a pyramid. · The student is able to understand when to use the surface area and when to use the lateral area · The student is able to interpret the results from a table to determine which playground will cost the school less money. · The student is able to do calculations for a scenario where only part of the surface areas are used in the total amount of material. · The student is able to make necessary changes in plans to account for a change in size of one of the shapes.
 * Key Criteria **
 * Stage 3 – Learning Plan **

= 1) Introduction: = = Review of finding the area of polygons – triangle, circle, rectangle = Introduce new vocabulary – surface area, lateral area, slant height = Discuss the following problem the class. Then try to solve it with them. =  “Your parents ask you to figure out how much paint you need to use to cover the entire garage. Knowing that a quart of paint covers 30 square feet. How would we go about solving this problem?” After discussing the problem and the class’s ideas for solving it, give an overview and put the unit in context. We’ve just learned how to find the area of triangles, circles and rectangles as well as “word” problems that involve those shapes. Now we will move on to more challenging problems that require finding the area of 3 dimensional shapes. This area is called the surface area.  2) Daily lessons on each of the following shapes with corresponding homework: · Surface Areas of Prisms i. Use a net to find the surface area of a rectangular prism – what is the surface area the sum of? ii. Introduce Lateral Area iii. Use a formula to find the surface area – how will the surface area change if the height of the prism is doubled? iv. Solve a real-world prism problem v. Give examples; practice problems in pairs · Surface Areas of Cylinders i. Use a net to find the surface area ii. Use a formula to find the surface area – how would you find the area of a cylinders base if you know the circumference instead of the radius? iii. Solve a real-world cylinder problem iv. Give examples; practice problems in groups · Surface Areas of Pyramids i. Use a net to find the surface area ii. Introduce slant height iii. Use a formula to find the surface area – can you use this formula to find the surface area of a triangular pyramid? Explain iv. Solve a real-world pyramid problem v. Give examples; practice problems in pairs · Surface Areas of Cones i. Use a net to find the surface area ii. Use a formula to find the surface area – is the surface area doubled if the slant height on the cone is doubled? Explain iii. Solve a real-world cone problem iv. Give examples; practice problems in groups 3) Lessons will be interspersed with:  · Periodic short quizzes and a final test   · Periodic opportunities for students’ feedback – What is working? What is not? What can I do to help?   · The final unit test will include:  i. Typical standard end-of-chapter test to see if fundamental skills have been mastered.   ii. The performance task as outlined earlier


 * RUBRIC:**
 * 4 || 3 || 2 || 1 ||
 * The student displayed a strong knowledge of finding the surface area of prisms and how to use the formulas and calculated the correct area in all scenarios. || The student displayed a good knowledge of finding the surface area of prisms and how to use the formulas, but made an addition or multiplication error in one scenario. || The student displayed a good knowledge of finding the surface area of prisms and how to use the formulas, but made an addition or multiplication errors in more than one scenario. || The student was unable to display knowledge of finding the surface area of prisms and did not show any correct answers or formulas. ||
 * The student displayed a strong knowledge of finding the surface area of cylinders and how to use the formulas and calculated the correct area in all scenarios. || The student displayed a good knowledge of finding the surface area of cylinders and how to use the formulas, but made an addition or multiplication error in one scenario. || The student displayed a good knowledge of finding the surface area of cylinders and how to use the formulas, but made an addition or multiplication errors in more than one scenario. || The student was unable to display knowledge of finding the surface area of cylinders and did not show any correct answers or formulas. ||
 * The student displayed a strong knowledge of finding the surface area of cones and how to use the formulas and calculated the correct area in all scenarios. || The student displayed a good knowledge of finding the surface area of cones and how to use the formulas, but made an addition or multiplication error in one scenario. || The student displayed a good knowledge of finding the surface area of cones and how to use the formulas, but made an addition or multiplication errors in more than one scenario. || The student was unable to display knowledge of finding the surface area of cones and did not show any correct answers or formulas. ||
 * The student displayed a strong knowledge of finding the surface area of pyramids and how to use the formulas and calculated the correct area in all scenarios. || The student displayed a good knowledge of finding the surface area of pyramids and how to use the formulas, but made an addition or multiplication error in one scenario. || The student displayed a good knowledge of finding the surface area of pyramids and how to use the formulas, but made an addition or multiplication errors in more than one scenario. || The student was unable to display knowledge of finding the surface area of pyramids and did not show any correct answers or formulas. ||
 * The student presented a comparison of the 2 projects and the cost of materials in an easy to understand table format. The explanation for saving additional money was given and backed up using vocabulary learned in the unit. || The student presented a comparison of the 2 projects and the cost of materials in table format that was correct but hard to follow. The explanation for saving additional money was given and backed up using vocabulary learned in the unit. || The student presented a comparison of the 2 projects and the cost of materials but not in table format or the explanation for saving additional money that was given was not backed up using vocabulary learned in the unit. || The student presented a comparison of the 2 projects and the cost of materials but not in table format and the explanation for saving additional money was not given or was not backed up using vocabulary learned in the unit. ||
 * The student handed in work showing how all the surface areas were found. The work was neat and easy to follow. || The student handed in work showing how all the surface areas were found. The work was neat or easy to follow, but not both. || The student handed in work showing how all the surface areas were found. The work was not neat or easy to follow. || The student handed in work that was incomplete and only showed part of the work or only work for certain shapes. ||