Fish Tank Feeding Trends

Fit straight lines to feeding data and judge how well they model the points.

1. Model One Tank

Each point represents a separate feeding trial that began with 10 pellets. Use the scatter plot for questions 1–6. Do not connect consecutive data points.

For the fern tank, staff recorded the number of pellets remaining at different times after feeding. A useful line of fit follows the middle of the overall pattern; it does not need to pass through every point.

Which description best summarizes the fern tank's pattern?

A. The points follow a sharply bending pattern.B. The points rise in a roughly straight pattern.C. The points stay near a horizontal pattern.D. The points fall in a roughly straight pattern.

Imagine each straight line described below drawn across the graph. Which is the most reasonable line of fit?

A. A line through (0, 7) and (7, 0).B. A line through (0, 0) and (10, 10).C. A line through (0, 10) and (10, 0).D. A line through (0, 5) and (10, 5).

Draw one straight line of fit for the fern tank. Extend it across most of the graph and keep it near the middle of the points.

Use the proposed line through (0, 10) and (10, 0), not your own drawn line.

How many of the eight data points lie exactly on this proposed line? points

How well does the line through (0, 10) and (10, 0) fit the fern tank's data?

A. It fits poorly because some points are above it.B. It fits perfectly because every point is on it.C. It fits poorly because it slopes downward.D. It fits well because all points are on or near it.

Staff use the line through (0, 10) and (10, 0) to estimate when 2 pellets will remain.

According to this model, about how many minutes after feeding will that happen? minutes

2. Compare the Fit

Compare these scatter plots with the fern tank's plot. Each trial began with 10 pellets, and all three plots use the same scales.

Stone tank

Compare the line through (0, 10) and (10, 0) on the fern and stone tank plots. Which statement is supported?

A. The tanks have equally good fits because their axes use the same scales.B. The stone tank has the better fit because its points spread farther from the line.C. The fern tank has the better fit because its points stay closer to the line.D. The tanks have equally good fits because they contain the same number of points.

For the stone tank, the line through (0, 10) and (10, 0) predicts 6 pellets remaining at 4 minutes. The plotted observation at 4 minutes is 9 pellets.

How far above the prediction is this observation? pellets

Arch tank

Which description best explains why one straight line is not a good model for the arch tank's full pattern?

A. The points include an observation on the vertical axis.B. The points drop quickly at first and then level off.C. The points include repeated counts at different times.D. The points show fewer pellets as more time passes.

10.

Mina joins the arch tank's first point, (0, 10), to its last point, (10, 0). She says, “My line touches both ends of the data, so it must fit well.” Explain why this is not enough evidence. Refer to the other points.

3. Use a Model Carefully

Apply what you know about fitting lines to new feeding observations.

11.

A new tank's points cluster tightly around a downward-sloping straight line. At 5 minutes, the line predicts 4 pellets remaining. How should staff use that prediction?

A. They should expect about 4 pellets, allowing some variation.B. They should connect each point before making an estimate.C. They should reject it unless a point is at (5, 4).D. They should expect exactly 4 pellets in every trial.

12.

For another tank, staff draw a line with all eight observations well above it. The points themselves follow a nearly straight pattern. What is the best first adjustment?

A. Keep the line because it misses every observation.B. Move the line up toward the middle of the observations.C. Move the line farther down from the observations.D. Replace the line with segments joining every observation.

13.

Staff test two feeding schedules using identical graph scales. For each schedule, they draw a reasonable line through the middle of its points. The table summarizes the distances from each line.

Comparing Feeding Schedules
Schedule	Distance from line
Morning	All within 1 pellet
Afternoon	Most 3–4 pellets away

Which conclusion about the straight-line models is supported?

A. The morning model fits better because its observations lie closer to its line.B. Neither model can fit unless every observation lies exactly on its line.C. Both models fit equally well because both lines pass through the middle.D. The afternoon model fits better because larger distances show a clearer trend.