Gallery Problems Exercise

Gallery Problems Exercise

Dog and Cat

Work Time

Dog and Cat

Rosa’s dog eats dry dog food. Rosa’s cat eats dry cat food. Each animal started eating from a new bag of food on the same day. Rosa graphed the situation as shown.

  • What information can you conclude from the graph? Be specific.

Faucet Rate Problem

Work Time

Faucet Rate Problem

Research on the Internet the standards for water flow rates for bathroom faucets in the United States. You should find that the maximum rate should be about 0.5 gallon per minute.

  • Test some of the faucets in your school or home.
    1. Turn the fixture to its fully open position.
    2. Place a container under the fixture and collect the flowing water for 10 seconds.
    3. Measure the quantity of water in the container.
    4. Convert the measurement to gallons. Use the conversion factor 1 gallon = 16 cups.
    5. Multiply the measured quantity of water by 6 to calculate the flow rate in gallons per minute (for example, 0.25 gallon × 6 = 1.5 gallons per minute).
  • Do the faucets you tested have standard flow rates?

Shower versus Bath

Work Time

Shower versus Bath

Watch the video Water Efficiency.

  1. Which do you think uses less water, a shower or a bath? Why?
  2. What information do you need to figure out which one uses more water?
  3. Watch the video Flow Rate and use the information in the video to calculate the flow rate of a shower faucet and a bath faucet.
  4. Watch the video Bath versus Shower. Use the information in the video to determine which uses more water, a bath or an average shower.
  5. How would the situation need to change to reverse the answer to problem 4?
  6. Given the information you have, how long a shower can be taken to use the same amount of water as the bath used?

VIDEO: Water Efficiency

VIDEO: Flow Rate

VIDEO: Bath versus Shower

Laps, Miles, Kilometers

Work Time

Laps, Miles, and Kilometers

A runner can measure her progress in terms of laps, miles, or kilometers.

A sign is posted at a track that gives the distances in miles and in kilometers for one-half of a lap.

12 lap = 18 miles, or 0.2 km

Rosa ran 14 laps.

Emma ran 5 km.

Mina ran 3 mi.

  1. Who ran the longest distance? Justify your answer mathematically.
  2. Who ran the shortest distance? Justify your answer mathematically.

Paper Problem

Work Time

Paper Problem

The stack of paper pictured is 100 sheets.

  1. Find the height in centimeters of the following:
    • 600-sheet stack
    • 250-sheet stack
    • 1 sheet of paper
  2. Let n equal the number of sheets of paper, and let h equal the height of the stack in cm. Write a formula for h in terms of n.
  3. Find the number of sheets of paper it takes to make a stack with the given heights:
    • 9 centimeters
    • 6.75 centimeters
    • 1 centimeter
  4. Write a formula for n in terms of h.
  5. What does the constant represent in each of your two formulas?
  6. A 100-sheet stack of a different kind of paper is 1.6 centimeters high. Let t equal the number of sheets of paper, and let h equal the height.

    • Write a formula for h in terms of t.

Three Scales

Work Time

Three Scales

Emma reads this information in a healthclub’s brochure:

“On our track, 1 mi equals 4 laps. On the same track, 1 km equals 2.5 laps.”

  1. Look at the image and use it to help you with the following:
    • Draw three number lines arranged as shown. Work carefully, and use a ruler.
    • Mark the Miles scale and the Kilometers scale so that the two scales show the same distance as the Laps scale.
  2. Use your triple number line to answer these questions:
    • Which is longer, a mile or a kilometer?
    • Approximately how many kilometers equal 1 lap?
    • Approximately how many miles equal 1 lap?
    • Approximately how many kilometers equal 1 mile?

Water Problem

Work Time

Water Problem

Watch the Container video, which shows water filling up a cube container.

  1. What do you need to know about the situation to determine the volume of the water in the cube container at any point in time?
  2. If the width and the length of the cube container are each 3 inches, describe the situation using your knowledge of rates and representations of rates.
    VIDEO: Container