Catch Your Shadow

On the recent winter solstice (Dec 20, 2020) I asked a friend to help me capture my noon shadow.

“How would I do that?” she asked.

I unrolled a length of black felt and gave her a piece of tailor’s chalk. “Follow me outside. But be quick,” I added. “Solar noon is about to happen.”

Shadows are so much fun to have in your drawer. I used to have an entire collection of them, which I would take to elementary schools. Those have been lost during my several home moves, so I decided to start a new collection. Now I asked my friend, “How long do you think my shadow will be?” “Well, it will be short since it’s noon. Maybe you won’t even have one.” She eyed my yardage. Then we went outside. I looked at my watch: 11:59 a.m., exactly solar noon.

I unrolled the fabric and stood so that my shadow fell on it. My friend began tracing it with the chalk. She had to move quickly because the shadow began shifting away from her tracing. Luckily, it was noon, when the shadow moves slowest. If we’d been working at sunset, she wouldn’t have been able to keep up. When I had caught sunset shadows for my previous collection, two of my children would trace frantically to beat the sun as it advanced and my shadow slid out from under me. “Oh, Mom,” they would complain. “Why do we have to do this?” I had interrupted their computer game.

This isn’t my real shadow; it’s a piece of felt fabric

On winter solstice, the sun carves its lowest arc across the sky. A low angle meant shadows would be longer than on any other day of the year. I’d purchased 3 yards of felt at the fabric store the previous night and even that wouldn’t be long enough to capture my shadow. I had to cut off a piece of fabric from the excess folded part and use it to extend the fabric. Even I was surprised at the length of my shadow: it was approximately 10 feet!

I’m lying atop my felt shadow

Now my friend’s husband Mike joined us. “What is the angle of the sun now?” he wondered. “Can you measure it from your shadow?” Yes, you could. My vertical body and the length of the shadow created a right triangle. The angle of the solar height could be computed from this. The angle cast by a stick and its shadow on a summer solstice several thousand years ago is the means used by Eratosthenes to calculate earth’s circumference. That will eventually be another lesson plan!

Mike took out his cellphone and used an app to find true north and we marked its line directly on the shadow for reference. I was surprised, but shouldn’t have been, to find that my shadow was pointing due north, directly toward the north pole. At noon in the northern hemisphere, shadows will always point true north, which is why taking noon sightings were so important for mariners in the days before geo-positioning satellites. (You can have fun confounding people by asking them if they can make their shadow reverse direction, pointing in the opposite direction. Often, they will try repositioning their body before they realize it’s impossible and then they will ask why it’s impossible. We all know that shadows move as the day goes on. Why can’t you get it to point south? North of the tropic of Cancer the sun is always to our south, meaning that shadows will always point northward)

Think of all the ways shadows can be used! Really, the list is endless. Sundials, moondials, Marsdials. Shadows give you an idea of the quality of light in pictures and are used to create realism in cartoons and paintings. As above, shadows can give direction and help determine latitude. Shadows have helped astronomers identify craters on the moon. Over 2000 years ago, Eratosthenes used a noon shadow at summer solstice to determine the circumference of the earth.

What is “solar noon?” That’s when the sun is at its highest point in the sky. It would be easy to say, “when the sun is directly overhead” but that’s not true on most parts of the earth. Where I live at latitude 38 degrees north, the sun will never be directly overhead. And, solar noon is rarely at 12:00 on our watches. Time zones have put our watches out of sync with the sun. To find the “watch time” that corresponds to solar noon, you can look at the NOAA website or merely google solar noon on the date in which you are interested. It was a coincidence of factors that made solar noon nearly the same as clock noon on this latest solstice 11:59 p.m.

What is “true north”? That is the line that runs directly to the north pole, or to the north star at night. It is not the same as magnetic north. because the magnetic north pole is to the east of the true north pole. True north is the one used for navigation. The difference between true north and magnetic north varies from place to place and is computed as an angle. At latitude 38 north, the difference is a whopping 15 degrees. Before cellphone apps, you could use a compass to find magnetic north, look up the angular difference on a table; then use a protractor to redraw the line. Of course, you can still do this. Pay attention to the direction of the angle! Since magnetic north is to the east, the true north line will be rotated to your left.

The best time to take standardized shadows is on the solstices and equinoxes, but any time is fun. Best to take each shadow at solar noon for accurate comparison among them. So much fun! Use felt because it doesn’t ravel when cut. I like to decorate my shadows with embroidery.

Teachers in Ghazni, Afghanistan learn about shadows in a workshop led by Camilla Barry

Chocolate Chip Levers

OK, the title is click-bait. You don’t need to use chocolate chips in this lesson but they sure are fun. I have used pennies or even beans. You simply need small objects that are consistent in weight and don’t roll.

Age level: PreK – third grade
Science Standards: for space considerations, these are addressed at the end
Materials Needed: 12-inch or cm rulers, tape, chocolate chips (or lentils, pennies, metal nuts, beans)

Levers are simple machines. That means they use few or no moving parts and can be the basis of more complex machines. Levers have been used since antiquity to lift or balance objects. In this lesson we will study teeter-totters and their kin to understand how they can be used to lift heavy objects with little effort.

Ancient Assyrians lift a stone colossus using a lever

Introduction

Identify the parts of the lever: lever arms and fulcrum. The position of the fulcrum is crucial. In the following drawing, the fulcrum is in the middle and two children of equal size balance each other. But what if one child is much larger than the other one? Or, a child wants to teeter-totter with her mother who weighs quite a bit more? In those cases, the small child might not be able to lift the larger person and the teeter-totter wouldn’t work. Think: How can this problem be solved? As students provide thoughts, ask them to draw their solutions on the board. Think about this question as you proceed through the lesson. Either the fulcrum must be moved, or the position of the people on the teeter arms must change (effectively changing the fulcrum) The teacher may or may not want to share the correct solution at this point.

One child lifts another

Capturing student interest

Show photos of extraordinary levers at work, or levers that went awry. Or provide a discordant event (see “Fun with Students”, below)

Street scene, Kabul, Afghanistan

The Activity

In this lesson, we will create a teeter-totter from a ruler; then use it to lift objects of unequal weights.

Step 1: Tape a 6-sided pencil firmly to a table.

Step 2: Balance a ruler atop the pencil. You have created a potential lever. Where are the lever arms? Where is the fulcrum? The ruler is 12 inches long. Where should you place the ruler so it is balanced on the pencil?

The ruler is balanced on a pencil fulcrum

Step 3: Only after the pencil is balanced (both ends off the table), give the students two chocolate chips. Place one chip on each end of the ruler-lever and rebalance it. Make sure the two ends are off the table. Ask students to note the length of each lever arm (6 inches and 6 inches)

Success at balancing one against one

Step 4: Only after the two chips are balanced, give the children an extra chip. Ask them how they can change things so that a single chip can balance (or lift) two chips. Tell them they must keep the chips on the end of the ruler (because you want to emphasize the position of the fulcrum and lengths of lever arms). The single chip should be on the “zero” end of the ruler for easier computation. Students should note the lengths of each lever arm.

Step 5: After students have discovered they can change the lengths of the lever arms, give them 3 more chips and ask them to balance a single chip against 5 chips. Remember to leave the single chip on the zero end and keep all chips as close as possible to the end of the rulers.

Working to balance 5 chips against 1

Assessment and Thinking

What did you do, to enable a single chip to lift 5 chips? (made that side longer). Point out that longer levers do more work than shorter levers. Another way of thinking: Pushing on the end of a lever provides more strength than pushing midway on the arm. Some manufactured levers are designed to remind you where to push.

The end of the nail clipper is marked

Who can draw a teeter-totter correctly to enable Jane and her mom to use it?

How could you correct the situation of the poor donkey and his cart (above?) Lengthen the cart arms and put the donkey at the head.

Could an ant conceivably lift an elephant on a teeter-totter? How would you do it and why would it work?

The Elephant and the Ant

Fun with students via a discordant event

Rigging the game. Before asking students to start the lesson, I make one of two rigged rulers:

Rulers painted unevenly, difference magnified for clarity
  • Use red and black poster paint to paint one ruler in two equal 6-inch segments. Paint a second ruler in the same colors but make one end longer – hopefully, not enough for students to notice on casual inspection. The line separating the two colors will be put on the fulcrum. Use the first ruler to demonstrate how to balance one chip against the other. Switch out the second ruler while distracting them. Then use a “super chip” from a special jar to lift more than one chip. Ask students to explain.
  • Use a regular ruler to balance two chips. Then switch that ruler with an identical one that has a penny taped to the bottom. In one case, a chip balances another chip. In the second case, with everything apparently the same, one chip will simply not balance the other chip. Ask students to figure it out. Note that unscrupulous merchants have rigged scales this way in the past. With modern laws and computerized scales this normally wouldn’t be a problem today.
Preschool children share a laugh at rigged ruler

Credits:
Etching of Assyrians and levers; Nineveh and Babylon – a narrative of a second expedition to Assyria during the years 1849, 1850, and 1851 by Sir Austen Henry Layard 1874

Donkey cart in Kabul; photographer known, google photos

Nail Clipper: Amazon.om

All other photos and drawings are owned and copyrighted by Camilla Barry, 2020

This lesson addresses many Next Generation core standards that carry through grade levels PreK – 12. Examples are (but not limited to):
Look for pattern and order in observations
Compare attributes of objects through measurement
Reason abstractly and quantitatively
Model with mathematics, Compare numbers
Use materials and tools to solve a specific problem
Analyze Data
Plan and Conduct an Experiment
Recall and gather information to answer a question
A problem can be solved through engineering
Multiple solutions to a problem are possible and should be compared/analyzed