Gallery Problems Exercise

Gallery Problems Exercise

Create Your Own Rate

Work Time

Create Your Own Rate

  1. Create a problem using two of these quantities. The answer must be the third quantity.
    • 40 pounds
    • $0.80 per pound
    • $32.00
  2. Work individually to write new problems using each set of three quantities. Use the quantities to create realistic problems. Do not include the answer when you write your problems.
    • 40 bags, $32.00, $0.80 per bag
    • 0.15 gallon, 10.5 miles, 70 miles per gallon
    • 25 feet per second, 0.4 second, 10 feet
    • 2.25 miles, 1.8 miles, 4.05 miles
    • 3.4 minutes, 0.4 minute per gallon, 8.5 gallons
  3. Do any of the sets of numbers not describe a rate? If not, explain why.

Paper Clip Challenge

Work Time

Paper Clip Challenge: Part 1

Do you have what it takes to set a record? In 2004, a record was set for chaining 54,030 paper clips in 24 hours! Watch this video to see the 2004 record.

  1. Express the rate in paper clips per second.
  2. Express the rate in seconds per paper clip.
  3. Which unit is more useful? Explain your choice.

VIDEO: Paper Clips

Paper Clip Challenge: Part 2

See what you can do.

  1. Chain together paper clips for 60 seconds.
  • Count the number of paper clips in your chain. What is your rate expressed in paper clips per second?
  • If you could maintain that speed for 24 hours, how many paper clips would be in your chain after 24 hours?

2.  Chain together paper clips for 120 seconds.

  • Count the paper clips in your chain.
  • What is your rate?
  • Did your rate expressed in paper clips per second change, or did it remain the same?

The Speed of Light

Work Time

The Speed of Light

  • Watch the first video. Whose estimate of the time it takes light to reach the moon do you think is closer to reality, Carlos’s or Emma’s?
     
  • Make your own estimate of how long you think it takes light to get from Earth to the moon. Demonstrate your estimate to your partner by moving your finger across the screen.
     
  • What information do you need to have in order to determine how long it takes light to get from Earth to the moon?
     
  • Create a double number line to show how far light travels each second. The speed of light is approximately 300,000kmsec.
     
  • The moon is approximately 384,400 km from Earth. How many seconds does it take light from Earth to reach the moon? Calculate your answer, and then watch the second video to check your answer.
     
  • Why might your calculation be a little different from the actual travel time to the moon?
     
  • Pluto is 7.5 billion km away at its farthest from Earth and billion 4.3 km away at its closest.
    If the beam of a flashlight were bright enough to be seen from outer space, how long would it take a beam of light from Earth to reach Pluto when it’s farthest? When it’s closest?
     
  • Choose an object in the universe and determine how long it would take the light from Carlos’s flashlight on Earth to reach it.
     
  • If the light from Earth (the flashlight) takes 30 days to reach a certain point in space, how far away is that point?

VIDEO: To the Moon Estimates
VIDEO: Actual Travel Time

Tire Weight

Work Time

Tire Weight: Part 1

By measuring the amount of surface area each tire presses into the ground and the pressure inside each tire, you can calculate the weight of a car.

You need to measure the surface area of the bottom of each tire. Make sure you get permission from the car’s owner before you take any measurements, and take measurements only when there is an adult supervising you.

  1. Most tire “footprints” will be roughly rectangular in shape. To find the length and the width of this footprint, use a piece of cardboard, a piece of string, or a yardstick to measure each tire’s footprint boundary. Measure the two sides that are easiest for you to reach.
  2. Record your measurements in inches.
  3. Ask an adult to use a tire gauge to measure the internal air pressure of the tire, or use the average tire pressure of most tires: 35.
  4. Find the amount of tire surface area touching the ground. To find this, multiply the length and width of the footprint. Your answer should be in square inches.
  5. To find the amount of weight the tire is holding, multiply the surface area by the pressure (in PSI) of that tire. For example:

    28sq. in.30lbssq. in.=840lbs
  6. Repeat these steps for each of the other three tires if you have time. If you do not have time, use the same measurement you took for the first tire to represent all 4 tires.

Tire Weight: Part 2

  1. Add the weights together for all four tires to get the total weight of the car.
  2. To see how close you came to the real weight of the car, ask an adult to check the owner’s manual or look at the specification plate on the inside of the driver’s side door.

If you do not have access to an owners manual here are some sample weights of typical cars:

  • A small car weighs about 3,000 lb. 
  • A medium car weighs about 4,000 lb.
  • A small truck or SUV weighs about 4,500 lb.
  • A large truck or SUV weighs about 5,500 lb. 

Planting Wildflowers

Work Time

Planting Wildflowers

Highway workers are going to plant wildflowers on the median strip of a length of highway. Your job is to figure out how many pounds of wildflower seeds are needed for each mile of this highway. Watch the video in order to understand the situation.

  1. What do you need to know to answer this problem?
  2. Solve the problem using the following information:

    • 200 pounds of seeds are needed to plant 1 acre of wildflowers.
    • The median strip is 33 feet wide.
    • 1 mile is 5,280 feet.
    • 1 acre is 43,560 square feet.
  3. Show each step of your solution.
     

VIDEO: Wildflowers

Train Track

Work Time

Train Track

Read this quote about the Union Pacific Railroad from 1867.

“Thirty seconds to a rail for each gang, so four rails go down a minute. There are ten spikes to a rail, 400 rails to a mile.”

A gang is a work crew who lays down the track for the train. The track consists of rails and spikes that hold the rails in place.

  1. List the different rates described in the quote.
  2. How many gangs are at work in the scene described in the quotation? Show your work.
  3. How long does it take 2 gangs to lay down 1 mile of railroad track? Show your work.
  4. How many spikes are needed to lay down 1 mile of railroad track? Show your work.

Heartbeats

Work Time

Heartbeats

  1. Predict what you would hear if you listened to the heartbeats of an elephant and a mouse. Follow the instructions in the interactive to hear the heartbeats of the elephant and the mouse.
  2. Predict what your heartbeat would sound like compared with the mouse’s and the elephant’s heartbeats. Do you think your heartbeat is faster or slower?
  3. Find your pulse. Follow the instructions in the Heartbeats interactive to record your pulse and heart rate.
  4. Compare the graph with the double number line. How are they alike? How are they different?
  5. Pick a point on the graph. Explain what it means.
  6. How does your heart rate compare with a mouse’s heart rate? How does it compare with an elephant’s heart rate?
  7. Choose an animal and research its heart rate. Predict what the graph of its heart rate would look like. How would the graph compare with your heart rate graph?

INTERACTIVE: Mouse and Elephant Heartbeats

Foghorn

Work Time

Foghorn

A foghorn is a device that uses sound to warn vehicles of hazards in foggy conditions. Many lighthouses have foghorns that blast at periodic intervals. Watch the video to learn about foghorns.

  1. The Beavertail Lighthouse in Rhode Island blasts its foghorn once every 30 seconds.

    • What is the rate expressed in blasts per minute?
    • How many times will the foghorn blast in 1 hour?
  2. Before electronic foghorns were invented, the lighthouse keeper periodically fired a cannon. If the lighthouse keeper fired the cannon 20 times per hour, what is the rate in blasts per minute?

  3. Foghorns are checked after 10,000 blasts.

    • How often is the Beavertail Lighthouse foghorn checked?
    • If the cannon was also checked at the same rate, how often would that be?
  4. Research the foghorns at the Golden Gate Bridge in San Francisco. The foghorns are located in two locations: at the middle of the bridge (midspan) and at the south (San Francisco) tower pier. The foghorns have different sounds. Create a problem about their rates.

VIDEO: Foghorns