8.EE.5

Nia and Trey both had a sore throat so their mom told them to gargle with warm salt water.
Nia mixed 1 teaspoon salt with 3 cups water.
Trey mixed 12 teaspoon salt with 112 cups of water.

Nia tasted Trey’s salt water. She said,

“I added more salt so I expected that mine would be more salty, but they taste the same.”

a.  Explain why the salt-water mixtures taste the same.

b.  Find an equation that relates s, the number of teaspoons of salt, with w, the number of cups of water, for both of these mixtures.

c.  Draw the graph of your equation from part b.

d.  Your graph in part c should be a line. Interpret the slope as a unit rate.

Scaffolding questions:

1)  Shelly ran 2 miles in thirty minutes. Which shows how fast Shelly ran in miles per hour?

  1. 1 mile per hour
  2. 4 miles per hour
  3. 8½ miles per hour
  4. 15 miles per hour

2)  A machine can fill 50 bottles per second. Which equation shows this proportional relationship? In the equations, s is the number of seconds and b is the number of bottles.

  1. b = s +50
  2. b = 50 – s
  3. b = 50s
  4. b = 50/s

3)  A bicycle rider travels at a constant rate of 6 meters per second. Complete the table of ordered pairs below to graph the proportional relationship.

Time in seconds (x) / 1 / 2 / 3 / 4 / 5
Distance in meters (y) / 6

Use your table to graph the proportional relationship

4)  The maximum distance traveled by the space shuttle can be determined using the equation d = 4.8s, where d is the distance, in miles, and s is the number of second. The table below shows the distance traveled by the Apollo 10 astronauts returning from the moon.

Distance Traveled by Apollo 10
Number of Seconds / Distance Traveled (in miles)
5 / 23.5
10 / 47
15 / 70.5
20 / 94

Did the space shuttle or Apollo 10 travel at a greater speed. Explain.

8.EE.6

In the diagram below, triangle ABC is similar to triangle ART.

Part A: What is the scale factor from triangle ABC to triangle ART?

Part B: If the slope of AC is -2, what is the value of x for coordinate C?

Part C: Using the information from parts A and B, what is the length of RT?