Cube3D立方体数理

READY FOR A FIRST CLASSROOM TRY

A small experiment.
A better question.

Three short investigations that turn a simulation into a conversation. Make a prediction, change one thing, then use evidence to explain what happened.

10–15 minutes eachNo student accountPrint or use on screen

Your answers stay in this browser on this device, separately for each language. They are not sent to a teacher or to Cube3D. Avoid entering names or other personal information.

Ready to write

ACTIVITY 01 / GEOMETRY

Unwrap a cylinder

Why does the curved surface become a rectangle?

Open the experiment in a new tab
Time about 12 minSuggested ages 11–14Before you start circumference and rectangle area
Learning goal

Explain why a cylinder’s lateral area is 2πr × h, and predict the effect of changing one dimension.

1

Predict before you drag 2 min

Keep the height fixed. If the radius doubles, will the lateral area double, stay the same, or become four times as large? Explain your prediction.

2

Manipulate one thing at a time 4 min

  1. Start with r = 1.5 cm and h = 3.0 cm. Move Unfolding fully to the right, then choose Front view.
  2. Track which part of the cylinder becomes the rectangle’s length. Does unfolding change its area?
  3. Use the settings in the table below. For the doubling comparison, change r from 1.0 to 2.0 cm while keeping h = 3.0 cm.

The experiment opens in another tab so your worksheet stays here. Use the radius and height readouts to set each value.

3

Record the evidence 3 min

Use the fully unfolded view. Round readings to two decimal places.
Radius r (cm)Height h (cm)Length (cm)Lateral area (cm²)
1.53.0
1.03.0
2.03.0
1.04.0
4

Explain what the evidence means 3 min

Complete the argument: “The rectangle’s length is ___, its width is ___, so its area is ___.” Use two rows to support your answer about doubling the radius. Why are the two circular ends excluded?

Teacher notes & suggested answers

Expected readings (length; lateral area): (1.5, 3): 9.42 cm; 28.27 cm². (1, 3): 6.28 cm; 18.85 cm². (2, 3): 12.57 cm; 37.70 cm². (1, 4): 6.28 cm; 25.13 cm². Values use π before rounding.

The rectangle is one circumference long and one cylinder height wide. At fixed h, area is proportional to r; the r = 1 and r = 2 rows show a factor of two. Doubling both r and h gives a factor of four. The total surface area would additionally include 2πr².

Listen for: confusing the circumference with the diameter, adding the bases to the lateral area, or assuming the side stretches as it unfolds.

ACTIVITY 02 / ELECTRICITY

One path or two?

Find out what an open switch changes in a series or parallel circuit.

Open the experiment in a new tab
Time about 15 minSuggested ages 12–16Before you start complete circuits and I = V/R
Learning goal

Compare current in series and parallel circuits, and explain why opening one parallel branch leaves the other working.

1

Predict before you switch 2 min

Two identical lamps are connected to the same 6 V supply. Will changing from series to parallel change the current through each lamp? What will happen to lamp 1 when switch S2 opens?

2

Build the comparison 5 min

  1. Choose Reset experiment. Keep the supply at 6 V and both lamp resistances at 10 Ω. Both lamps must be installed.
  2. In Series, close both switches and record the currents. Open S2 and record again.
  3. Choose Parallel. Close both switches and record. Open only S2, keeping S1 closed.
  4. Switch to Circuit diagram to trace the complete path for lamp 1 in the final case.

Each parallel switch controls its own branch. These are simulated, ideal low-voltage circuits; this activity does not require building a physical circuit.

3

Record the evidence 4 min

V = 6 V; R₁ = R₂ = 10 Ω; both lamps installed.
Connection / switchesI₁ (A)I₂ (A)Total I (A)
Series / both closed
Series / S2 open
Parallel / both closed
Parallel / S2 open
4

Explain the path, not just the glow 4 min

Use the table to explain the two outcomes when S2 opens. Then use I = V/R to calculate one parallel branch current. How do branch currents relate to the total current?

Teacher notes & suggested answers

Expected readings (I₁, I₂, total): series, both closed: (0.30, 0.30, 0.30) A. Series, S2 open: (0, 0, 0) A. Parallel, both closed: (0.60, 0.60, 1.20) A. Parallel, S2 open: (0.60, 0, 0.60) A.

Series has one path: opening either switch breaks it. In parallel, S1 and lamp 1 still form a complete loop when S2 opens. Each closed parallel branch has 6 V across it, so I = 6/10 = 0.60 A. The total is the sum of the branch currents. For the extension with R₂ = 20 Ω: I₁ = 0.60 A, I₂ = 0.30 A, total = 0.90 A.

Listen for: saying that current is “used up” by lamp 1 or that both parallel lamps must share the supply voltage equally. For these equal fixed resistors, each lamp’s power is 0.90 W in series and 3.60 W in parallel. The visual glow is illustrative.

ACTIVITY 03 / ENERGY

Where did the energy go?

A slowing ball has less mechanical energy. Has the total energy changed?

Open the experiment in a new tab
Time about 12 minSuggested ages 12–16Before you start potential and kinetic energy
Learning goal

Distinguish mechanical energy from total energy, and account for energy transferred to thermal energy by resistance.

1

Predict where to look 2 min

When resistance makes the ball reach a lower height on each pass, what happens to the energy it no longer has as potential or kinetic energy? What do you expect the total-energy reading to do?

2

Compare ideal and resistive motion 4 min

  1. Pause the motion first. Set release height to 3.5 m, mass to 1.0 kg, then choose No resistance. Changing a parameter releases the ball from rest again; it stays paused if you paused first.
  2. Record the release values. Start the motion, observe at least one full return, and pause as close to the lowest point as you can. Record the displayed values.
  3. While paused, choose With resistance (γ = 0.12 s⁻¹). Start again and pause when the thermal-energy share reaches 20% or more. Record the values.

“Release again” starts the motion immediately. Use Pause first, then change a setting to inspect a release at rest. Timing is approximate; your moving-ball readings may differ from a partner’s.

3

Record all three stores 3 min

m = 1.0 kg; release height = 3.5 m. All energy readings are in joules (J).
ObservationPotentialKineticThermal QTotal
No resistance / at release
No resistance / near bottom
With resistance / thermal ≥ 20%
4

Account for the missing mechanical energy 3 min

Add potential, kinetic and thermal energy in the final row. Compare the result with the release total. Explain how the ball can slow down while total energy is conserved.

Teacher notes & suggested answers

Release: potential = 34.30 J; kinetic = 0; thermal = 0; total = 34.30 J. Ideal lowest point: potential ≈ 0; kinetic ≈ 34.30 J; thermal = 0; speed ≈ 8.28 m/s. A pause slightly away from the bottom will retain some potential energy.

With resistance: individual potential and kinetic readings depend on when the learner pauses. At a thermal share of at least 20%, Q ≥ 6.86 J and potential + kinetic ≤ 27.44 J, with a total of about 34.30 J. Accept small rounding differences when adding displayed readings.

Resistance transfers mechanical energy to thermal energy. Including all three in the model keeps the total constant. With the same starting height and no resistance, doubling mass doubles energy to 68.60 J but leaves the bottom speed unchanged, because m cancels in mgh = ½mv².

Listen for: energy being “used up”, confusing heat with temperature, or assuming that conservation means the mechanical energy alone stays constant when resistance acts.

TAKE IT TO CLASS

Your worksheet, your way.

Print only the selected activity. Student copies hide suggested answers; teacher copies include them. Entered answers appear in both.

PASS A GOOD QUESTION ON

Share the activity.

Send the selected activity to a colleague or use its link with a classroom clip. Shared links do not contain your answers.

HELP SHAPE THE NEXT VERSION

What happened in class?

Keep a short, anonymous note after a trial. Download a feedback draft to keep or share yourself. This page does not send it anywhere.

No account or contact details required. Feedback notes are not saved when you leave.

ABOUT CUBE3D

A place to test an idea.

This early classroom version of Cube3D · 立方体数理 offers three guided activities: cylinder area, circuits and energy. Each combines an interactive experiment, a student worksheet and teacher notes.

Simulations simplify the real world. Read each activity’s model notes when explaining your results. Worksheet answers stay in this browser on your device; shared activity links do not include them.

Explore the experiments →