Name: ______

Math 840

Homework 15

Due Tuesday 5/08

For each problem, write your response on the paper provided. On the back of each problem, you will find a self-assessment form with 3 questions. Answer these questions for each problem you work out.

Here are some questions to help you fill out the assessment form. You don’t have to answer all of these questions, but you can use them to guide your responses.

Focusing on the Big Picture…

  • What goals did they have in solving the problem?
  • What assumptions did they make?
  • What was their method for solving the problem?
  • What did the “solution path” look like?

Determining the accuracy of the response…

  • Was the given solution method likely to succeed?
  • Did they justify any assumptions made?
  • Did you notice any errors?
  • Does the answer make sense in reality?
  • Was the solution checked in any way?
  • Was the problem solved in multiple ways?
  • Can you explain why the solution is correct?

Questions you might ask to extend or clarify the response…

About the reasoning involved in solving the problem:
  • Why did you …?
  • How did you know to do …?
  • How does doing … help you?
  • What was the purpose of …?
  • Could you have done things differently?
About the mathematical justification involved in solving the problem:
  • Why can you …?
  • Why does … “work?”
  • How do you know that …?
  • What is the mathematical basis for …?
  • Do things always work this way?
About how to conceptualize the problem:
  • What’s really going on here?
  • How to you visualize, interpret, or think about …?
  • What’s the “big picture” in this problem?
  • How would you describe the main idea of this problem?
  • What other situations might … apply to?

Finally, what can you learn from this problem that will help you solve other problems?

Parabola Plotting

1A. Find the x-intercepts and vertex for the following parabola: y=x2 – 4x + 3.

1B. Use this information to sketch a graph.

Self-Assessment Form

Title of Problem: Parabola Plotting / Your Name: ______
Date: ______
Big Picture:How did you try to solve the problem?
Accuracy:Do you think the problem was solved correctly? How do you know?
Questions:What are you unsure about in the problem or response? How does the math extend beyond this problem?

Table Trouble

For each of the tables below, tell whether the points are on a line, a parabola, neither, or if it’s not possible to determine. Explain how you know.

2A:

x / y
-6 / 12
-4 / 8
2 / -4

2B:

x / y
0 / 0
1 / 1

2C:

x / y
0 / 4
2 / 16
4 / 36
6 / 64

2D:

x / y
-1 / -1
0 / 0
1 / 1
2 / 8

Self-Assessment Form

Title of Problem: Table Trouble / Your Name: ______
Date: ______
Big Picture:How did you try to solve the problem?
Accuracy:Do you think the problem was solved correctly? How do you know?
Questions:What are you unsure about in the problem or response? How does the math extend beyond this problem?

River Fence

You have 120 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed? (hint: start by drawing a diagram and calling one of the unknown lengths x. What will the lengths of the other sides be?)

Self-Assessment Form

Title of Problem: River Fence / Your Name: ______
Date: ______
Big Picture:How did you try to solve the problem?
Accuracy:Do you think the problem was solved correctly? How do you know?
Questions:What are you unsure about in the problem or response? How does the math extend beyond this problem?

Mixed-up Mixtures

To make a perfect-tasting Kool-aid drink, you want to have a 15% concentration of Kool-aid. For your party, you want to make 12 liters of Kool-aid. Unfortunately, you only have pre-made Kool-aid at 10% concentration (too plain), and 30% concentration (too sweet). How much of each of these mixtures do you need to put together to get 12 liters of a 15% concentration?

Self-Assessment Form

Title of Problem: Mixed-up Mixtures / Your Name: ______
Date: ______
Big Picture:How did you try to solve the problem?
Accuracy:Do you think the problem was solved correctly? How do you know?
Questions:What are you unsure about in the problem or response? How does the math extend beyond this problem?