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Shadow Math

Measure the length of shadows to estimate the height of something very tall.

Goal: To explore proportional reasoning in solving a measurement problem.

Time: 45 minutes

Space: Outside on a bright, sunny day


  • tape measure
  • ball of string
  • 2 objects 4 feet and 2 feet tall

For your child:


Time: 30 minutes

  • Find a tall object outside (flagpole, tall pine tree) that casts a shadow whose length can be measured.
  • Select 2 objects about 4 feet and 2 feet tall that can be used to cast shadows outside. (A child can be the 4-foot tall object.)
  • Optional:  Preview the episode or clip, and if using them with your child, cue up the videos via the links above.


TIP: This activity works best mid-morning or mid-afternoon when shadows are longer than the height of the objects casting them.

  1. Start a discussion with your child about shadows. Ask: What can you tell me about your shadow? (Responses might include shadows are attached to feet, resemble body shapes, sometimes are longer and sometimes shorter.)
  2. Optional: Use the episode or clip to further explore this idea.
  3. Outside, stand the 4-foot tall object and the 2-foot tall object side-by-side in direct sunlight. Ask: What can you tell me about these two shadows? (The taller object casts the longer shadow. One shadow looks to be about twice the length of the other shadow.)
  4. Have your child measure the 4-foot and 2-foot tall objects to confirm that one is twice as tall as the other.
  5. Now have your child cut 2 pieces of string to the lengths of the shadows cast by these objects. Use these string lengths to demonstrate that one is twice as long the other. Ask: What can you tell me about the relationship between the two shadows and the two heights? (They are each twice as tall or twice as long as the other. The objects and their shadows share the same relationship.)
  6. Take your child to the tall object you’ve selected. Ask: How could we measure the height of this? Ask: How can we use what we just learned about objects and their shadows to estimate the height of this object?
  7. Give your child a copy of the handout, pencil, tape measure, string and scissors. Review the handout together. Explain that she should measure shadow lengths in as straight a line as possible to keep measurements accurate.
  8. Allow time for your child to do the activity, then discuss the results.

Take It Further

Share this activity’s Science, Technology, Engineering, Math (STEM) connections and invite your child’s comments:

Scientists and engineers often use proportionality — the mathematical relation between two quantities — to figure out unknown measurements. Before more sophisticated tools were invented, early explorers such as Lewis and Clark used proportionality to measure and record the widths of rivers for their maps.

Talk About It

Ask: What did you learn today that you didn’t know before?

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Produced by: Funding is provided by:
WNET logo
Additional funding is provided by Lynne and Marc Benioff, the Tiger Baron Foundation, Shailaja and Umesh Nagarkatte and Ellen Marcus.
The JPB Foundation NSF Heising-Simons Foundation EY

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