Two clubs used different amounts of water at an event. Club A used 12 liters for 20 people; club B used 15 liters for 30 people. Total use is larger for B, but use per person is smaller: 0.5 rather than 0.6 liters per person. Neither calculation is wrong. They answer different questions, so choose the quantity before choosing the graph.
Predict
Predict whether dividing by the number of people always makes a comparison fair. It adjusts for one difference, but the events may differ in length or activity. Predict whether a graph must always begin its vertical axis at zero. A carefully labeled nonzero origin can reveal small changes in a line graph, while unlabeled truncation or proportional bar comparisons can mislead.
Experiment
Inspect this supplied temperature record; it is a small synthetic example, not a climate dataset.
Time since start, hours
Temperature, °C
0
18
2
19
4
21
6
20
Draw two versions: a vertical range from 0 to 24 °C, and a range from 16 to 22 °C. Use the same horizontal range and explicitly label both vertical origins. Identify which makes the three-degree variation easier to read and why neither changes the numerical differences. The observations alone do not determine the exact temperatures between recorded times.
Understand
A modeled quantity needs a definition: what is counted or measured, over what period, and relative to what denominator. Total liters, liters per person and liters per person-hour are different quantities. The denominator should match the question. A ratio also needs a nonzero denominator; use per person is undefined for an event with no attendees, not automatically zero.
Units provide an arithmetic check. For a wall 2 m by 180 cm, convert 180 cm to 1.8 m before multiplying to get 3.6 m². If paint covers 6 m² per liter, dividing 3.6 m² by 6 m²/L gives 0.6 L. The area units cancel, leaving liters. Squared units matter: one square meter is 10,000 square centimeters, not 100. Tracking dimensions can reveal a plausible-looking numerical error before it reaches a graph.
An axis needs a quantity label, units, a scale and an origin. Equal distances on an ordinary linear axis must represent equal numerical differences. Tick spacing can be 2 hours or 5 liters rather than one unit, but it must be read consistently. The visible coordinate origin need not be the physical beginning of a process; state what time zero means. A truncated vertical axis should display its actual lowest tick and, where appropriate, an axis-break indication.
The purpose of a display affects sensible choices. A line plot of temperatures may emphasize small differences, but a claim about ratios of Celsius readings is physically different from a ratio of absolute temperatures. A bar chart intended to compare amounts usually needs a zero baseline so bar length represents amount. Choosing a scale is part of communicating a claim, not a cosmetic final step.
Apply
Define a quantity for comparing a school activity, then write one sentence describing a different decision it would not answer. Produce a labeled graph specification: horizontal and vertical variables, units, domain, tick increments, origins and whether connecting observations assumes interpolation. Use a multistep unit calculation to check one plotted value.
Continue
A good representation makes its question and assumptions visible. Extra digits cannot repair the wrong denominator, and a dramatic scale cannot replace a numerical comparison. Next, use unequal time intervals to distinguish raw changes from rates of change.
Drafts save locally as you type. Reveal worked solutions when useful; the site remembers that exposure. Automatic matches check the requested answer, while written arguments require review against the rubric.
A club uses 18 liters of water serving 24 people. What is its water use in liters per person?
Integers, fractions and finite decimals are accepted. Expressions such as sqrt(2) are not parsed by this checker.
A rectangular display is 150 cm by 80 cm. What is its area in square meters?
Integers, fractions and finite decimals are accepted. Expressions such as sqrt(2) are not parsed by this checker.
School A recycles 90 kg for 300 students; school B recycles 70 kg for 140 students. Choose a useful quantity for comparing participation scale, compute it and state a limitation.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
For the supplied temperature observations at 0,2,4,6 hours: 18,19,21,20 °C, propose axes for showing small changes. Defend an origin and a scale, and explain how a truncated vertical scale should be labeled.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
A class compares two bus services with different trip lengths and passenger counts. Define a quantity that answers a specific efficiency question and explain the data needed.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
A paint covers 8 m² per liter. A wall is 3 m by 240 cm and needs two coats, with no openings. Compute required liters and distinguish model assumptions from a purchasing decision.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Reflect and continue
Before marking this lesson complete, explain one key idea without the worked solution and identify a condition that matters. Marking complete records participation, not independent mastery.
