Algebra Project – Topic 2 Constructed Response



Extra Credit Packet #2: Due January 27th, 2009 Do as much as you can.

Algebra Project – Topic 1 Constructed Response Name __________________

Period ______

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a. Complete the table to show the amount of each ingredient needed to make 1 serving of trail mix.

Show your work.

|Ingredient |Amount for 1 serving (in cups) |

|Raisins |[pic] |

|Peanuts |[pic] |

|Sunflower seeds |[pic] |

|Granola | |

|Dried fruit | |

|Chocolate candies | |

b. For each ingredient, use the amount per serving to write an algebraic expression to determine the amount of cups needed for any number of servings, N. (The expression for the amount of raisins is completed for you.)

Then, use these algebraic expressions to find the amount of each ingredient needed to make 15 servings.

|Ingredient |Amount for N servings (in cups) |Amount for 15 servings (in cups) |

|Raisins |[pic] | |

|Peanuts | | |

|Sunflower seeds | | |

|Granola | | |

|Dried fruit | | |

|Chocolate candies | | |

c. Use the prices shown to complete the table showing the cost per serving for each ingredient.

Round to the next penny. Recall that there are 2 cups in one pound.

[pic]

|Ingredient |Cost per serving |

|Raisins | |

|Peanuts | |

|Sunflower seeds | |

|Granola | |

|Dried fruit | |

|Chocolate candies | |

BONUS

Use the cost per serving of each ingredient to write a cost equation for any number of servings, N, of trail mix. Then use your cost equation to find the cost to make 15 servings of trail mix.

Algebra Project – Topic 2 Constructed Response Name __________________

Period ______

Michael needs to mail some small cube−shaped gift boxes. He goes to Boxes2Go to purchase a large cardboard box in which to ship them. He realizes that he has left the gift boxes at home; fortunately, he had measured them with his hand before he left. Each side of the gift boxes is the length of one of his hands.

The first large cube box he finds at Boxes2Go costs $2.00 and measures 2 of his hand lengths on each side. He needs to decide if this cardboard box will be large enough to mail all the small gift boxes that he has. In case he needs a bigger box, Michael continues looking. He finds an extra−large cardboard cube box that measures 3 of his hand lengths on each side. It costs $3.50.

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Here is one of Michael's gift boxes. What is the volume of this small cube? Explain how you arrived at your answer.

[pic]

How many of Michael's small, cube−shaped gift boxes will fit into this $2.00 large cardboard box? Explain how you arrived at your answer.

[pic]

How many of Michael's small, cube−shaped gift boxes will fit into this $3.50 extra−large cardboard box? Explain how you arrive at your answer.

[pic]BONUS

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Compare the dimensions of the 1h, 2h, and 3h boxes with the volumes you found for them.

Based on the pattern you see, propose a law of exponents that you could use to quickly evaluate [pic]without having to write out the n individual factors. Explain why your law should work.

Topic 3--Constructed Response Project Name ______________________

Period ______

Making Stuffed Animals

It costs a company $20 per box to make pocket−sized stuffed animals. The company also has a fixed manufacturing cost of $2300. The owners are trying to calculate their cost for making boxes of animals.

a) Identify the variables in this relationship and indicate which would be the independent variable and which would be the dependent variable.

b) Complete the table to explore this relationship.

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c) Use the table to write a function rule that describes the relationship between the number of boxes manufactured, b, and the cost of manufacturing those boxes, c.

d) How much does it cost to manufacture 300 boxes of stuffed animals? Show your work.

e) How many boxes of stuffed animals can the company manufacture for $5000? Show your work.

f) Use the table to graph this relationship on graph paper. Don’t forget to label your axes. The independent variable goes on the horizontal axis and the dependent variable goes on the vertical axis.

Topic 4 Constructed Response Project Name __________________

Period ______

Anthony Chen's family operates a full−service pool and landscaping business.

Sometimes their clients want low decorative fences around their flower beds.

Anthony's father wants a quick way to estimate the amount of fencing needed. Mr. Chen asked Anthony to help him. Anthony realizes that this is just a perimeter question. He starts his task by analyzing the relationship between the length of the side of a square flower bed and the perimeter of the flower bed. This will tell him the amount of fence needed to enclose the flower bed. Anthony realizes that lengths of sides of flower beds are not always whole numbers, but he decides to use square tiles to build models of flower beds of various sizes to help him find a pattern. In his models, 1 tile represents 1 square foot.

a. Draw the next two models in Anthony's concrete representation.

b. Make a numerical representation of the relationship between the length of the side of a square flower bed and the perimeter of the flower bed. Explain how the pattern in your numerical representation relates to the concrete models.

|Length of Side (feet) |Perimeter (feet) |

| | |

| | |

| | |

| | |

| | |

c. Write an algebraic representation for the relationship between the length of the side of a square flower bed and the perimeter of the flower bed. Explain how your rule relates to the concrete models.

d. Make a graphical representation of the relationship between the length of the side of a square flower bed and the perimeter of the flower bed. Explain how the graphical representation relates to the concrete model, the numerical representation, and the algebraic representation.

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Algebra – Topic 5 Constructed Response Project Name _________________

Period __________

Reuben learned in art class that a mosaic is made by arranging small pieces of colored material such as glass or tile to create a design. Reuben created a mosaic using tiles. Then he decided on a growing pattern and created the second and third mosaics. He counted the number of tiles in each mosaic and then represented this data in multiple ways. He thinks he sees a relationship between the mosaic number and the total number of tiles in the mosaic.

[pic]

a) Represent Reuben's data from the mosaics problem in at least TWO different ways, including a general function rule, to determine the number of tiles in any mosaic. So I need a table, a graph, or a sentence and I must get a function rule.

b) Write a description of how your rule is related to the tile picture, including a description of what is constant and what changes as tiles are added.

c) How many tiles would be in the tenth mosaic? Use two different representations to show how you determined your answer.

d) Would there be a mosaic in his set that uses exactly 57 tiles? Explain your reasoning using at least one representation.

e) In Reuben's mosaic, there were 2 tiles in the middle. How would the function rule change if the middle of the mosaic contained 4 tiles instead? Explain your reasoning using two different representations.

Algebra – Topic 6 Constructed Response Project Name __________________

Maria folds a sheet of Patty Paper in half. The fold divides the paper into 2 rectangular regions. She then folds the paper in half again. When she opens it, there are 4 rectangular regions formed by the folds.

Take a sheet of Patty Paper and repeat Maria's process. Record your answers in the table. Continue folding until you have made 5 folds.

a) What type of relationship is this data? Linear? Exponential? Quadratic? Explain your answer

b) What is the independent variable? What is the dependent variable?

c) Describe the domain and range for this situation.

d) Write a function rule for the relationship between the number of folds and the number of rectangles.

e) Graph the data. Don’t forget to label your axes.

[pic]

Imagine you are building staircases out of cubes. To make one step, you need only one cube, as you can see. Two steps need 3 cubes, as you see here.

a) What type of relationship is this data? Linear? Exponential? Quadratic? Explain your answer

a) Sketch the first five staircases. Then build a table to reflect the relationship between the number of steps in the staircase and the number of cubes needed to build the staircase.

|Number of Steps |Process |Number of Cubes |

| | | |

| | | |

| | | |

| | | |

| | | |

b) Write a function rule for the relationship between the number of steps in a staircase and the number of cubes in the staircase.

c) Make a graph of the problem situation and the function rule. Don’t forget to label your axes.

How do the two graphs compare?

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Algebra – Topic 7 Project Name __________________

Period ______

1. Ted received a grant from KS Enterprises when he graduated from high school. He was supposed to use the grant to further his education by attending college and getting a well-paying job when he completed the college course work. KS Enterprises is considering awarding Ted an additional grant to continue his education so that he can receive his masters degree, but they will make this new award available only if Ted demonstrates that he has met the requirements of the first grant. Since Ted graduated from college, he has kept a record of his income, and he plans to make a graph of the data. Here are the data that he has recorded:

Annual Income Since College Graduation

|Year |1996 |1997 |

|0 | | |

|1 | | |

|2 | | |

|3 | | |

|4 | | |

|5 | | |

|6 | | |

b. What is the independent variable? What is the dependent variable?

c. What is the domain of the problem situation?

d. What is the range of the problem situation?

e. What is the function rule? What type of function is it?

f.. What is the domain of the function rule?

g. What is the range of the function rule?

h. Create a graph to represent the data accurately.

a. As Sabrina walks in front of a motion detector, the device creates the following graph. It records distance in meters and time in seconds. Based on the graph, write a verbal description (a description in words) of Sabrina's walk.

b. Explain the meaning of the point (0,0.832) in this context.

c. After Sabrina finished her walk, she traced the graph and located the two points shown in the

graphs below. Determine the rate at which Sabrina walks between these two points. Give your

response to the nearest thousandth.

d. You have determined the rate at which Sabrina was walking to create the first section of the

graph. At what rate was she walking in order to create the second section of the graph?

e. Describe how the graph would have been different if Sabrina had stood still first and then

walked away from the motion detector.

Mrs. Cortez has received the following graph and table with the bill for her cell phone. Using them, she can see the amount the phone company charges for monthly service in terms of the number of minutes.

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|a. Determine any rates of change that you see in this graph. |

|b. Write a description of the way a customer such as Mrs. Cortez pays for phone service. |

|c. Mrs. Cortez is looking for a new cell-phone plan. She finds another phone company that charges 10 cents per minute no matter |

|how many minutes you use. Sketch this graph. |

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|d. Mrs. Cortez finds a third phone company, which charges $20 for 0 to 300 minutes, plus 3 cents per minute for minutes over |

|300. Complete the table for this company's rates. |

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