Ratio Machine II

Overview

In Lesson 7 students did Experiments A and B with the Ratio Machine. In Lesson 8 students consider the variables in these experiments: input arm length, output arm length, distance moved by input, and distance moved by output. They analyze the data from Experiments A and B, to find a pattern that relates these four variables. Then they carry out Experiments C and D, analyze these data and generalize the patterns found.


Materials

  • Large data sheets for Experiments A and B, Lesson 7
  • Large data sheets to record class data for Experiments C and D.
  • For each pair: The Ratio Machine from Lesson 7.
  • Data sheet for Experiments C and D for each student.

Procedure

What is an experiment?

Many students have not carried out an experiment where they manipulate variables and collect data. Help students reflect on what an experiment is. Here are some ideas for this discussion. 

Science Notebook

  • List four variables in Experiment A.
  • Which variable did you change?
  • Which variable did you measure?
  • Which two variables did you keep the same?

Analyzing data from Experiment A

Examine the data from Experiment A. If at the end of the last class, the students did not consider reasons for the different results, or which results are probably most accurate, do so now.  Then ask;

  • What pattern do you see in these numbers?

If no one offers a pattern say

  • I think I see a pattern in these data.

Where the input is 1”, circle outputs of 2”; where input is 2”, circle outputs of 4”; where input is 3”, circle outputs of 6”:

  • Does anyone see my pattern?  (The output moves 2 x the input.)

Once everyone sees the pattern, ask:

  • What other numbers do you see where one number is twice as much as the other?

Help them notice that

  1. the output arm is twice as long as the input arm and
  2. the output moves twice as far as the input.

Analyzing data from Experiment B

In Experiment A students found that each output was twice as long as its input. They also found that the output arm was twice as long as the input arm.

  • What pattern do you see in the data from Experiment B?

Help students notice that in Experiment B

  1. the output arm is three times as long as the input arm and
  2. the output moves three times as far as the input.

Experiments C and D

Distribute Experiment C and D. Here are a download of the experiment and ideas for introducing it. citytechnology.org/node/131  Students continue on to Experiment D after completing C.

Analyzing data from Experiments C and D

Record the student data for Experiment C on the class data sheet.  If students got different results, ask:

  • Which of these results do you think is most likely correct?  Why?

Circle the numbers where the output is twice the input.

  • What patterns do you see in Experiment C data?

When students see that output movement is twice the input movement and output arm is twice the input arm, proceed to collect Experiment D data..

Record the student data for Experiment D on the class data sheet. Again, if students got different results, ask:

  • Which of these results do you think is most likely correct?  Why?

Circle the numbers where the output is three times the input.

  • What patterns do you see in Experiment D data?
  • What is the relation between the input arm, 3 ½” and the output arm, 10 ½” ?

Science Notebook

  • Put Experiment Sheets C and D in your Science Notebook
  • What pattern did you see in Experiment C? Compare this to Experiment A.
  • What pattern did you see in Experiment D? Compare this to Experiment B.
  • How can you use these patterns when you design your MechAnimation?

Outcomes

Students should have these understandings about an experiment:

  • They did an experiment when they took measurements on the Ratio Machine, recorded them and analyzed them.
  • The purpose of each experiment was to find out how far the output moved when the input was moved a specified amount.
  • The input and output arm didn’t change during each experiment.
  • Each experiment had four variables:
  1. Input arm length, which didn’t change during an experiment
  2. Output arm length, which didn’t change during an experiment
  3. Distance the input moved, which they changed before each measurement.
  4. Distance the output moved, which they measured after they moved the input.
Students should have these understandings about the results of the experiment:
  • If the output arm length is twice the input arm length, then the output will move twice as far as the input
  • If the output arm length is three times the input arm length, then the output will move three times as far as the input.
  • If I want one of the outputs on my MechAnimation to move twice as far, then I must shorten the input arm by half.

Troubleshooting

Students often do not see the patterns in data that we want them to see.  Here are some suggestions on seeing patterns.


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