Task 1, Part 1

Given: You drive from Albuquerque, NM, to Rock Springs, WY, at an average speed of 55 miles per hour. Your route is along Interstate 25 to Cheyenne, WY, then Interstate 80 to Rock Springs.

1a) What would be your total driving time (to the nearest half hour)?

Use an atlas or road map to solve the problem.

1b) Write a brief description of the problem-solving process including steps, calculations, and tools used. Use actual road distances in miles.

Task 1, Part 2

2a) Write a problem using the following elements.

• Travel by air from Memphis, TN, to Las Vegas, NV, with stops in Oklahoma City, OK, and El Paso, TX, en route.
• Students have a map of the United States that shows cities and a distance scale in kilometers.
• Require use of straight-line distance in kilometers for each leg of the trip.
• Average aircraft groundspeed is 380 km/hour from Memphis to Oklahoma City and 310 km/hour from Oklahoma City to Las Vegas.

2b) Write a brief description of the process you used to construct the problem.

2c) Write the steps you expect students to follow to solve the problem.

2d) Write a scoring key with directions for its use and application.

Task 2:

Figure A)

Use the given information and the diagram in Figure A to complete Task A and Task B.

Keep in mind:

1. The diagram is NOT drawn to SCALE.
2. There may be multiple ways to show your solution.

Task A : For each statement listed in Table A, provide a reason to justify why each statement is true.

TASK B : Prove that triangle AGC is isosceles. Insert answers in table contained in Table B.

Table A)

STATEMENTS	REASONS
\(\overline{GB}\cong \overline{GD}\)
2. \(\angle BGE\cong \angle DGE\)
3. \(\overline{GE}\cong \overline{GE}\)
4. \[\Delta BGE\cong \Delta DGE\]
5. .

Table B)

Task 3:

Prove: If the base angles of a triangle are congruent, then the triangle is isosceles.

4a) Draw and label a diagram that includes:

1. A triangle with each vertex and the given information labeled.
2. All other information needed to present the proof.

\(\begin{aligned}

& \Delta ABC \\

& \measuredangle CAB\cong \measuredangle ABC \\

& \text{Prove: The triangle is isosceles} \\

\end{aligned}\)

4b) Construct a formal proof of the theorem including:

1. Given statement(s)
2. Other statements
3. A reason for each step.
4. A conclusion that restates the theorem.

Therefore, if the base angles of a triangle are congruent, the triangle is isosceles.

Task 4 :

A person is planning to buy some storage units. The storage units are in the shape of a rectangular solid (See above).

The person needs to compare the dimensions of the storage units before choosing which storage units to buy.

The dimensions are given in the table in below.

Use the table to investigate how changes in dimensions affect the perimeter, area, and volume of the rectangular solid.

1. Determine the perimeters of the base of the rectangular solids. Record your answers in the table in the column labeled "Perimeter."
2. Determine the volumes of the rectangular solids. Record your answers in the table in the column labeled "Volume."
3. Determine the surface areas of the rectangular solids. Record your answers in the table in the column labeled "Surface Area."
4. Explain the relationship between changes in dimensions and perimeter of the base of rectangular solids. Use ratios in your explanation.
5. Explain the relationship between changes in dimension and volume of rectangular solids. Use ratios in your explanation.

Price: $19.26

Solution: The downloadable solution consists of 9 pages, 1026 words and 4 charts.
Deliverable: Word Document