Homemade Sciencewith Bruce Yeany

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Lesson plan · Grades 3-8

Can a swinging bottle of sand draw a picture?

Students hang a leaky soda-bottle bob from a Y-shaped string, time its swing in two directions, and discover that one pendulum can have two different periods. They then use the sand traces to see how changing string length changes the pattern, connecting a measurable pattern of motion to the looping designs it draws.

Anchor phenomenon

How can one bottle of sand, given a single push, draw a neat woven pattern that no one is steering?

Learning objectives

  • Students will be able to measure the period of a pendulum by timing 10 full swings and dividing by 10.
  • Students will be able to compare the periods of a Y-string pendulum swinging along and across the line between its two ceiling supports.
  • Students will be able to explain, using string length, why the Y-string pendulum swings faster in one direction than the other.
  • Students will be able to predict how moving the knot of the Y will change the pattern drawn in the sand, and test that prediction.

Lesson flow (5E)

Engage10 min

Day 1. Fill the demonstration bob on the Y-string, pull it toward a corner of the box, peel off the tape and release it with a sideways nudge. Let students watch the first loops form and ask them to sketch what they think the finished picture will look like and to write one question about why it moves the way it does.

Explore25 min

Day 1. Groups tie the short strings to their bob and attach it to their station. With sand in the bottle and the cap hole taped shut, they swing the bob straight along the line between the two hooks and time 10 full swings, then swing it straight across that line and time 10 more. They record both times, divide by 10, and watch which strings move in each direction.

Explain10 min

Day 1. Groups report their two periods. Guide them to the idea that a longer pendulum has a longer period. Swinging across the line between the hooks, the whole Y hinges at the ceiling, so the pendulum is long and slow. Swinging along that line, the top two strings stay still and only the strand below the knot swings, so it acts like a shorter, faster pendulum. Introduce the words period, bob, and Lissajous pattern.

Elaborate35 min

Day 2. Each group fills its bob with sand (layered colors if available), releases it with a sideways nudge, and sketches the pattern. Then each group moves its knot to a new height (higher, lower, or about one quarter of the way up from the bob), predicts how the pattern will change, and runs it again. One station hangs the bob from a single string for comparison. Groups compare patterns on a gallery walk.

Evaluate10 min

Day 2. Students complete the age-appropriate worksheet items about which direction was faster and why, then answer an exit ticket: explain why the loops shrink toward the middle, and predict what shape a single-string pendulum draws.

Discussion questions

  1. What did the sand pattern look like at the start of the swing, and how did it change by the end?
  2. Which direction did the bottle swing faster, and which strings were moving each time?
  3. Why would a shorter pendulum swing back and forth more quickly than a longer one?
  4. Why do the loops get smaller and fill in toward the center instead of repeating forever?
  5. What happened to the pattern when the knot was moved, and why would moving the knot change the two periods?
  6. If the bottle were heavier, would it swing faster or slower? How could we test that fairly?

Common misconceptions

Common ideaA heavier bob swings faster (or slower) than a lighter one.What the demonstration showsA pendulum's period depends on its length, not its mass. Changing the weight of the bob barely changes the timing.
Common ideaSomeone has to steer the bottle to make a neat pattern.What the demonstration showsThe pattern comes from two swings happening at once at two different speeds; the sand simply records the path.
Common ideaA pendulum can only have one period.What the demonstration showsOn a Y-string, the swinging length is different in the two directions, so the same bob has a longer period one way and a shorter period the other way.
Common ideaThe pendulum stops because it runs out of sand.What the demonstration showsIt slows down because friction with the air and the strings takes away its energy; it would slow down even if it were empty.

Assessment

  • Exit ticket: "Which way did your bottle swing faster? Explain why using the word length."
  • Check the timing table on the worksheet for the age group: two directions timed over 10 swings, with one-swing periods calculated.
  • Quick performance task: show the student a knot position and ask them to predict whether the two periods will be closer together or farther apart, then test it.
  • Older students: use the 11-14 worksheet to identify the changed, measured, and controlled variables when moving the knot.

Differentiation

Support: Have younger students focus on watching and drawing the pattern and on noticing which strings move. The teacher can run the stopwatch while students count 10 swings aloud, and the choice items on the 5-7 worksheet can replace written explanations.

Extend: Older students measure the total length (bob to ceiling) and the lower length (bob to knot), then compare their measured period ratio to the square root of the length ratio. They can also hunt for the near 2:1 ratio that gives a figure-eight by making the lower strand about one quarter of the total length.

Classroom safety. The teacher pokes holes and cuts bottles, since sharp points and scissors slip on curved plastic. The teacher hangs ceiling hooks and strings using a step stool or ladder. Keep sand away from eyes and mouths, sweep up spills promptly so floors are not slippery, and keep walkways clear of swinging bottles.