Recognize Proportional Relationships
Harbor Rate Lab
Run cargo trials in a harbor and watch each result appear in a table and on a graph. Compare crates per trip and check the origin, then send proportional routes to Dispatch and other routes to Inspect.
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How to Play Harbor Rate Lab
- 1
Test a trip count
Select one of the available numbers in the Trips column. Watch the tugboat move and find the new result in the log and graph.
- 2
Compare the results
Test the remaining positive trip counts. Compare the values under Crates per trip and look at the shape made by the plotted points.
- 3
Test zero trips
Select 0 when it becomes available. Check whether the graph reaches (0, 0). The rate is undefined at zero trips, so use the point itself.
- 4
Choose a dock
Choose Dispatch if the rates match and the points form a straight line through the origin. Choose Inspect if the route fails a check. Use Next route to continue or Play again after six routes.
Key Features
Run the cargo trials
Choose a trip count to move the tugboat and reveal how many crates the route carries. The result fills the log and plots a matching point.
Read the rate in each row
The log shows crates divided by trips as a fraction and its value. Use several rows to see whether the rate holds steady.
Check the origin
Run the zero-trip trial after the other trials. A straight graph with crates already counted at zero trips belongs at Inspect.
Route the tugboat
Use Dispatch for a proportional route or Inspect for a route that fails a check. Feedback explains what the measured points show, and a wrong choice leaves the route open for a retry.
What is Harbor Rate Lab?
Harbor Rate Lab is a seventh-grade math game about recognizing proportional relationships. Each route gives you a table and a coordinate graph of the same cargo trials. Trips are the input on the horizontal axis, and crates are the output on the vertical axis. You use the evidence to decide where the tugboat goes. In the opening route, 1 trip carries 3 crates, 2 trips carry 5, and 4 trips carry 9. The rates are 3, 2.5, and 2.25 crates per trip. The points form a straight line, but at 0 trips the log still counts 1 crate. Choose Inspect. A route with 3, 6, and 12 crates at the same positive trip counts and 0 crates at 0 trips has a constant rate of 3 and goes to Dispatch.
Why Play Harbor Rate Lab?
- 1
Check more than one pair
Some routes look proportional at the first trip count or even the first two. A later trial can reveal a changing rate.
- 2
Connect the table to the graph
Each trial shows how one row of quantities becomes one point with trips first and crates second.
- 3
Use the origin as its own check
Zero trips should give zero crates in a proportional route. This test uses a coordinate pair without dividing by zero.
- 4
Distinguish two kinds of counterexample
Some routes form a straight line that misses the origin. Others include the origin but change direction.
Frequently Asked Questions
How do I tell whether a route is proportional?
The positive rows must have the same crates-per-trip value. The graph of the route must be a straight line through (0, 0).
Why is there a dash for crates per trip at zero trips?
Dividing by zero is undefined. Check the plotted point for zero trips to see whether it is at the origin.
What if I choose the wrong dock?
The route stays open and the feedback points to its defining evidence. Your streak resets, and you can send the tugboat to the other dock.
How do points and replay work?
A correct first choice earns 100 points. A correct retry earns 60. After six routes, Play again starts a fresh set. Best score and the sound preference are saved in your browser.
Can I play with a keyboard?
Yes. Tab to a trip count or a dock button and activate it with Enter or Space. The table gives the measured values even if you are using a screen reader.