Activity 1: Kid Diffusion

Students will:

• construct a spinner to randomize particle movement.
• develop geometric skills with a compass and protractor. 
• demonstrate understanding of congruency, sectors of a circle, and central angle measure through the construction of the spinner.
• understand geometric probability and how it relates to random particle movement. 
• model kinesthetically the movement of particles through a medium (such as air) and will incorporate randomness into the model. 

Overview:  How can we use a spinner to model the movement of a particle? If we quantify and randomize the direction in which a particle can move, can we model the behavior of particles through air?  

Creating the spinner

1. After discussing directions in which the particle could move, determine the number of possible outcomes.
2. Have each student construct a circle on one piece of card stock. Make sure they mark the center of the circle!
3. Cut out the circle and poke a small hole in the center of both the circle and the other piece of card stock.
4. Have students calculate the measure of the central angle of each sector (If 9 sectors, 360° ÷ 9 = 40°)
5. Students will use their protractors to create the sectors with the appropriate central angle measure.
6. Mark each sector with the numbers 1 through 9 (or other)
7. Each number will represent a translation of one step. 
8. To create the spinner: "Unbend" one half of a paper clip. 
9. Push the straight part through both holes with the circular part on top.
10. Bend the straight part of the paper clip so that it is parallel to the card stock but slightly raised.

To spin the spinner:

• The rectangular piece of card stock is your base. The bent portion of the paper clip should be flush to the underside.
• The circular piece of card stock should spin. 
• The straight part of the paper clip indicates the result of the spin.

To play:

1. Have students start clustered together in the center of a large room.
2. At the same time, every student should spin their spinner. Each time step is represented by one spin.
3. The result of the spin indicates the direction each student should move. Example: One student might spin a 1 and another students might spin a 7. They will each take one step in the direction indicated.
4. Repeat the process for several time steps.

Teaching Strategies

• This activity will work best in a large room (such as a gymnasium)

• Students need to come up with the number of directions in which their particle can move along the poster board. 

• Students should be familiar with a compass and how to construct circles. Review this process if necessary.

• Students should be familiar with using a protractor and measuring angles. Review this process if necessary.

• Students should see the necessity of constructing congruent sectors, as opposed to dividing the circle into noncongruent parts. 

• Make sure that the students decide ahead of time what to do in the event that two or more students land in the same spot.

Thought Provoking Questions

Particles have a tendency to move from a higher to a lower concentration and it is impossible to predict exactly which direction they would take.  The spinner is used to add a random factor and increase students' awareness of particle behavior.  Encourage your students to create spinners that are "fair" in outcome.  They should cut the circle as evenly as possible and make sure it spins evenly. 

• In how many directions can a particle move?  Ideally, students should be able to come up with 8 different directions in which to move (forward, back, left, right, and their respective corners) as well as the possibility of no movement at all.

• How can we represent all of those changes in position on a circular spinner? Students should realize that from the center of the circle, one revolution of the spinner is equivalent to 360 degrees. If they choose 9 different outcomes, they should then be able to calculate the central angle measure of 9 congruent sectors (wedges).

• How could we draw each sector? This is an opportunity to introduce the idea of central angle measure, congruent sectors, and the geometric representation of equally likely outcomes having equal areas.

• As they begin to spin and take a step, stop the activity and ask:  "How many of you landed on 1or 2 or 3?"  You may want to record this on a poster chart for each trial.  That allows the opportunity for your students to monitor the probability of landing on a specific number. 

• They will likely see that some numbers are occurring more than others.  Would that occur if a hundred or a thousand trials were run?  You might use a computerized dice throw activity [Project Interactivate] to let them see the results of thousands of truly random throws in a short time fame.

• It is also likely that some may try to move to exactly the same space.  Can two particles or pieces of matter be in exactly the same place?  Why?  Collisions happen in the molecular world too!  That also presents the opportunity for particles to move back towards the source [area of higher concentration]. 

• Are all the students moving at the same pace?  Not all particles move at exactly the same speed either. Does temperature make a difference?  Although because of our need to release heat from our bodies, we might move slower at high temperatures, particles are moving faster!  Ask your students if they can describe examples that provide evidence of this.  They might offer examples that cite hot air balloons or sugar dissolving faster in hot tea than cold tea.  You might offer an analogy of students eating lunch and cookies for energy, and then moving faster on the playground.

• Particles also really do have an attraction for one another.  This is certainly more noticeable with some particles than others.  Water has a much greater attraction for each other than alcohol particles have for each other.  Water takes longer to evaporate and condenses at much higher temperatures than alcohol.  You might observe two student friends moving slightly closer to each other instead of directly towards the number markers at each turn.  Use that as an example of attraction between particles, although particle attractions would only likely occur if the particles were very close to one another.  This is exemplified by shaking a water and oil mixture and then watching them very quickly move to their own layers. 

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