What do you notice? What do you wonder?

The other day you worked with converting meters, centimeters, and millimeters. Here are some more unit conversions.

1. Use the equation , where represents degrees Fahrenheit and represents degrees Celsius, to complete the table.

   temperature	temperature
   20
   4
   175

2. Use the equation , where represents the length in centimeters and represents the length in inches, to complete the table.

   length (in)	length (cm)
   10
   8

3. Are these proportional relationships? Explain why or why not.

Here are some cubes with different side lengths. Complete each table. Be prepared to explain your reasoning.

1. How long is the total edge length of each cube?

   side length	total edge length
   3
   5

2. What is the surface area of each cube?

   side length	surface area
   3
   5

3. What is the volume of each cube?

   side length	volume
   3
   5

4. Which of these relationships is proportional? Explain how you know.

5. Write equations for the total edge length , total surface area , and volume of a cube with side length .

Here are six different equations.

1. Predict which of these equations represent a proportional relationship.
2. Complete each table using the equation that represents the relationship.

   

   Six identical tables, each with 3 columns and 4 rows of data. All have first rows: x, y, the fraction y over x. All have the same x values: 2, 3, 4 and 5. All have a different equation above it: y = x + 4, y = 4x, y = the fraction 4 over x, y = the fraction x over 4, y = 4^x and y = x^4.

3. Do these results change your answer to the first question? Explain your reasoning.
4. What do the equations of the proportional relationships have in common?