Arm span scatter plot: a 40-minute data activity for grades 5–8

1. Ask: "Leonardo da Vinci wrote that a person's arm span is about the same as their height. Is that true for us? How could we find out?" Have students write a prediction.
2. Model a careful measurement with a volunteer: arms straight out, fingertip to fingertip, measured along the wall. Height is measured standing against the wall without shoes. Round to the nearest centimeter.
3. Partners measure each other twice and use the closer pair of numbers. Anyone who prefers not to share their own numbers can measure a family member at home or record a data point you provide.
4. While students measure, tape a large grid on the wall: height on the horizontal axis and arm span on the vertical axis, both from 120 to 190 cm in steps of 10.
5. Each student places a sticky note at their point. Ask: "What shape is the cloud of notes making? Do taller people tend to have longer arm spans?"
6. Stretch a piece of string where the notes cluster to show a trend line. Ask: "Where would someone 165 cm tall probably land? How sure are you?"
7. Look for outliers together and talk about why one point might sit far from the line: a measuring mistake or natural variation.

Tip: in my experience, students trust the graph more when they help build it.

Differentiation: for students in grade 5 or new to graphing, use a pre-labeled grid and plot only five class points together first. Advanced students can find how many points fall within 5 cm of the "arm span equals height" line. English learners can use a word bank with axis, point, trend, cluster and outlier. Students who use a wheelchair can measure arm span seated or compare hand span and foot length instead. A student who prefers not to be measured can be the data manager who checks each point.

Quick check: show a new point, (150, 172), and ask: "Does this person fit the pattern? What might explain it?"

If you try it, reply with what your class's scatter plot showed and whether da Vinci was right for your group.