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Instructions: Solve the following problems. Please refer to Task Characteristic #3 (Lester 2003, p. 69 of Teaching Mathematics through Problem Solving, see last page) and Polya’s How to Solve Itsteps (see Problem Solving Process Infogram link on the next page) when explaining and justifying your solution paths. Show your work or offer clear explanation of the solution process you used. Please do not discuss problems with other members of the class until the homework has been assessed. See assessment rubric to be used for your solution process for each problem. Provide evidence of all problem solving steps (see Problem Solving Process Infogram). (10 points each)

1. Patio Problem: A landscaper wants to make a brown tile border around the entire perimeter of a green tile patio. Both the brown and green tiles are squares of the same size. The landscaper has not decided what size to make the patio, but is thinking that it will be a square.

a. Provide a solution to this problem using problem-solving strategies. Hint: Provide an equation for the number of brown tiles needed for any patio size. Show your work. (8 points)b. What grade level is most appropriate for this problem? See the Common Core State Mathematics Standards (content and process standards) and/or Florida B.E.S.T. Mathematics Standards. How would you present this problem to these students? How can you adapt this problem for other grade levels? Explainc. What mathematics (and/or science) skills and concepts are involved in this problem? What possible misconceptions could these students have? How would they approach this problem? Be specific.

2. Band Around the EPCOT Center’s Geodesic Sphere: Imagine a steel band that is wrapped around the EPCOT Center’s geodesic sphere at its widest point. (Part a and b are 8 points)

a. Would you be able to crawl under the band if you added 10 feet to the length of the steel band, and evenly spaced it above the sphere surface? Explain your solution to this problem. Show your work.

b. Assume that you do the same around the Earth’s widest point using a steel band and adding 10 feet, evenly spaced, to the length of new steel band, would you be able to crawl under this steel band (at any given point between the Earth and the steel band)? Explain. Provide evidence of all problem solving steps (see Problem Solving Process Infogram).

c. What grade level is most appropriate for this problem? See the Common Core State Mathematics Standards (content and process standards) and/or Florida B.E.S.T. Mathematics Standards. How would you present this problem to these students? How can you adapt this problem for other grade levels? Explain.

d. What mathematics (and/or science) skills and concepts are involved in this problem? What possible misconceptions could these students have? How would they approach this problem? Be specific.

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