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MapStudy · Student worksheet · 10–15 minutes

Same Earth. Different sizes.

Distinguish preserving relative area from preserving local angles and shapes.

Name: Date:

1. Predict

Will circles enclosing equal areas on Earth still have equal areas on every flat map?

2. Explore

Open the experiment in another tab ↗

Start at mapstudy.com/learn/compare-equal-areas and choose “Open experiment.”

  1. Open the experiment to see Mercator and Mollweide together. The pale circles enclose equal areas on Earth.
  2. Unfold Earth. Within each map, compare circles near the equator with circles farther north or south.
  3. Below the maps, move the orange sample’s latitude slider from 0° to 60°. Read the local area scale for each projection.
  4. Change the second map from Mollweide to Gall–Peters. Compare the areas and shapes of the circles again.

3. Notice & explain

What happens to the pale circles’ areas in Mercator? What happens in Mollweide?

At 60° latitude, record the local area scale for Mercator and Mollweide. What does that comparison tell you?

Mollweide and Gall–Peters both preserve relative area. Do they preserve every shape too? Use an observation as evidence.

MapStudy · Original activity · You may print and share this worksheet for teaching with credit to MapStudy.

MapStudy · Teacher notes

Compare equal areas

Learning goal: Distinguish preserving relative area from preserving local angles and shapes.

Preparation: Internet access and the projection explorer on one shared screen or student devices. Suggested ages 10+, with adult guidance as needed. Allow 10–15 minutes.

Discussion & expected observations

  1. Mercator enlarges circles toward the poles. Mollweide changes their shapes while preserving equal areas within that map.
  2. Mercator: 4.0×. Mollweide: 1.0×. These are local area scales relative to the equator, not whole-country size measurements.
  3. No. Both keep relative areas, but circles become different shapes. Equal area does not mean no distortion.

Keep the explanation precise

Compare proportions within each map, not pixel sizes between panels: the explorer fits projections independently. The finite circles are visual samples; the numerical readout describes local area scale. Neither equal-area projection is the only correct world map.

Extend the activity

Ask students to choose a projection for comparing forest coverage, then explain which property supports their choice.

Sources & further reading

Original MapStudy activities, informed by these projection references. Country boundaries in the explorer come from Natural Earth. The animation illustrates a transition; its intermediate shapes are not separate named projections.

mapstudy.com/classroom/compare-equal-areas · Classroom printing and sharing permitted with credit to MapStudy.