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Unformatted text preview: PreCalculus Project 1 Optimize our Zoo Using Functions (Revised) Introduction You have been hired by the local community to advise them on how to best design their new zoo. They have limited materials to use and they want to ensure that they get the most out of the materials. You will need to examine their requirements, determine the best way to meet the requirements, and make a scale model or map of your proposed design. Objectives: You will be able to model real situations with functions. You will be able to represent the functions algebraically, numerically (data table), and graphically. You will be able to use proportions to produce a map to scale. Zoo Requirements 1. Gorilla a. We have _________ feet of fence to use for the gorilla cage. b. We want the gorilla to live in a rectangular space with the maximum area possible to swing around. 2. Sheep and Pigs a. We have _____________ feet of fence to use for the sheep and pigs. b. We want the sheep and pigs to live in two adjacent rectangular pens. c. One side of the sheep and pigs area will be bordered by a river for drinking d. We want to give the sheep and pigs the maximum area possible. e. The pig area should be the same size as the sheep area. c. f. 3. Lions, Tigers, and Bears a. We have _____________ feet of fence to use for the lions tigers and bears. b. The animals will live in one rectangular area divided into three equal parts as shown below. c. We want the lions, tigers, and bears to live in the maximum area possible. d. 4. Shark Aquarium a. We want a rectangular aquarium with the left, right, front, back, and bottom is made of clear glass so people can see the sharks b. The top is open (no glass used for top) c. The length should be ______________ times the width. d. The tank should hold a volume of _____________. e. We want to minimize the amount of glass that we use because the material is very expensive. f. Element Labeled picture of description Use Algebra to create the Appropriate Function(s) Numerical Behavior of the function Graphical Behavior of the Function 4 Mastered 3 Proficient You always do these with no You do most of these with few (1 errors: 2) minor errors: draw a clear picture of each Draw a clear picture of each application clearly labeled with application clearly labeled with all known and unknown all known and unknown variables. variables. You do most of these with few (1 You always do these no errors: 2) minor errors: write key equations/ functions write key equations/ functions that show how each of the that show how each of the variables are related to one variables are related to one another . (i.e. V=lwh). another . (i.e. V=lwh). arrange these equations to write arrange these equations to write an appropriate function(s) that an appropriate function(s) that can be used to describe each can be used to describe each problem (i.e. Surface Area function) problem (i.e. Surface Area function) You always do these no errors: You do most of these with few (1 produce a clear table(s) of 2) minor errors: values that show the behavior of produce a clear table(s) of your function(s) values that show the behavior of Use labels, variables, and units your function(s) on your table(s) so it's very easy Use labels, variables, and units to know what the data means. on your table(s) so it's very easy to know what the data means. Highlight any data on the Highlight any data on the table(s) important to your solution and clearly explain why table(s) important to your it helps you solve the problem. solution and clearly explain why it helps you solve the problem. You always do these with no You do most of these with few (1 errors: 2) minor errors: produce a clear graph(s) that produce a clear graph(s) that show the behavior of your show the behavior of your function(s) function(s) Use labels, variables, and units Use labels, variables, and units on your graph(s) so it's very easy on your graph(s) so it's very easy to know what the curve means to know what the curve means Highlight any point(s) on the Highlight any point(s) on the curve that is important to your curve that is important to your solution and clearly explain why solution and clearly explain why it helps you solve the problem. it helps you solve the problem. 2 Developing You do most of these with some (3 6) errors Draw a clear picture of each application clearly labeled with all known and unknown variables. You do most of these with some (3 6) errors write key equations/ functions that show how each of the variables are related to one another . (i.e. V=lwh). arrange these equations to write an appropriate function(s) that can be used to describe each problem (i.e. Surface Area function) You do most of these with some (3 6) errors produce a clear table(s) of values that show the behavior of your function(s) Use labels, variables, and units on your table(s) so it's very easy to know what the data means. Highlight any data on the table(s) important to your solution and clearly explain why it helps you solve the problem. You do most of these with some (3 6) errors produce a clear graph(s) that show the behavior of your function(s) Use labels, variables, and units on your graph(s) so it's very easy to know what the curve means Highlight any point(s) on the curve that is important to your solution and clearly explain why it helps you solve the problem. 1 Emerging You do few or none of these or have major errors. Draw a clear picture of each application clearly labeled with all known and unknown variables. You do few or none of these or have major errors. write key equations/ functions that show how each of the variables are related to one another . (i.e. V=lwh). arrange these equations to write an appropriate function(s) that can be used to describe each problem (i.e. Surface Area function) You do few or none of these or have major errors. produce a clear table(s) of values that show the behavior of your function(s) Use labels, variables, and units on your table(s) so it's very easy to know what the data means. Highlight any data on the table(s) important to your solution and clearly explain why it helps you solve the problem. You do few or none of these or have major errors. produce a clear graph(s) that show the behavior of your function(s) Use labels, variables, and units on your graph(s) so it's very easy to know what the curve means Highlight any point(s) on the curve that is important to your solution and clearly explain why it helps you solve the problem. Element Solve the problem Scale Map On Time 4 Mastered You always do these with no errors: Clearly interpret all the information from your graphs, tables, and algebra to solve the problem. The solution could be one number or a set of numbers so labels and units are used to clarify. If possible, a picture is used to clarify your solution and show that you understand how the numbers solve the original problem. Check to see that your solution makes sense. You always do these with no errors: Make a creative, accurately scaled map that represents your proposal for the configuration of the zoo. Show a legend that indicates the scale of actual lengths to map lengths. Label all required areas and clearly indicate any key measurements You're project is completed and handed in before or at the beginning of class on the due date: 3 Proficient You do most of these with few (1 2) minor errors: Clearly interpret all the information from your graphs, tables, and algebra to solve the problem. The solution could be one number or a set of numbers so labels and units are used to clarify. If possible, a picture is used to clarify your solution and show that you understand how the numbers solve the original problem. Check to see that your solution makes sense. You do most of these with few (1 2) minor errors: Make a creative, accurately scaled map that represents your proposal for the configuration of the zoo. Show a legend that indicates the scale of actual lengths to map lengths. Label all required areas and clearly indicate any key measurements You're project is completed and handed in within 2 days past the due date: 2 Developing You do most of these with some (3 6) errors Clearly interpret all the information from your graphs, tables, and algebra to solve the problem. The solution could be one number or a set of numbers so labels and units are used to clarify. If possible, a picture is used to clarify your solution and show that you understand how the numbers solve the original problem. Check to see that your solution makes sense. You do most of these with some (3 6) errors Make a creative, accurately scaled map that represents your proposal for the configuration of the zoo. Show a legend that indicates the scale of actual lengths to map lengths. Label all required areas and clearly indicate any key measurements You're project is completed and handed in within 4 days past the due date: 1 Emerging You do few or none of these or have major errors. Clearly interpret all the information from your graphs, tables, and algebra to solve the problem. The solution could be one number or a set of numbers so labels and units are used to clarify. If possible, a picture is used to clarify your solution and show that you understand how the numbers solve the original problem. Check to see that your solution makes sense. You do few or none of these or have major errors. Make a creative, accurately scaled map that represents your proposal for the configuration of the zoo. Show a legend that indicates the scale of actual lengths to map lengths. Label all required areas and clearly indicate any key measurements You're project is completed and handed in more than 4 days past the due date: January 14, 2009 January 14, 2009 January 14, 2009 January 14, 2009 Project Assignments
Tuesday, January 06, 2009 3:29 PM Period 2 Period 3 PreCalc (2B) Page 1 ...
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This note was uploaded on 02/03/2012 for the course MATH 101 taught by Professor Lee during the Spring '11 term at International Institute for Higher Education.
 Spring '11
 Lee
 Calculus

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