Ratio Machine I




Overview

The Ratio Machine is a pegboard device students use to experiment with ratios and find proportions.  Students see ratios in a concrete form that they can manipulate. In Lesson 6 Students made qualitative generalizations about the movements of inputs and outputs. In Lessons 7 and 8 these generalizations become quantitative. Students move the input 1”, 2” and 3” and measure how far the output moves. They find the ratio of the distance moved by input to output. They compare this ratio to the ratio of the length of input arm to output arm.


Materials

  • Large data sheets to record class data for Experiments A and B – two for each.
  • Pegboard base, 3 numbered links, 1 link without numbers, 3 pivots per pair.
  • Post-its ™ or masking tape to mark the output starting point.
  • Student data sheet for Experiments A and B: two for each student.

Procedure

Introduce and demonstrate the Ratio Machine.

The Ratio Machine tells students how to make an output move more or less. Demonstrate how the Ratio Machine works.  Identify the input link and output link, and how to measure their movement. Here is further information.

Make the Ratio Machines

Distribute the materials to each pair of students. Demonstrate how to assemble the Ratio Machine as students follow each step.  Here are a video and illustrated instructions.

Use the Ratio Machines

Students follow the teacher’s instructions to make the first two measurements of Experiment A. This video shows how to do Experiments A and B. Here are instructions for getting started on Experiment A. 

Do Experiment A

  1. After students moved the input 1” and 2” and measured the output movement, distribute the Experiment A and B data sheet. Review the data sheet with the class. 

There are two terms that are new:  “input arm” and “output arm.”

The input arm is the distance from the fixed pivot to the input (i.e., where the input link is attached to the lever).

The output arm is the distance from the fixed pivot to the output (i.e. to where the output link is attached to the lever). 

Show students where to record data on the data sheet.

Although students have already done the first two measures of Experiment A, They should begin at the beginning and do all three measures.

  1. Use a large chart to record the Experiment A data from all students. There will be differences among the students' data.

Discuss how they made measurements and why they think they got different results. 

This is troubleshooting. See the Troubleshooting section at the bottom for possible sources of error.

Do Experiment B

  1. Demonstrate how to change the output position on the lever from 6” to 9” for Experiment B   Note: It is easiest to remove the mechanism from the base, take the pivot from the 6” hole of the lever and move it up to the 9” hole.  Then replace the output link.
  2. Review the data sheet, then let students do Experiment B. 
  3. Record the class data on a large chart and discuss reasons for differences in results. 

When discussing the data, don't try to find patterns for either Experiment A or B data. Rather, these discussions are aimed at improving measurements and understanding of the experiment.

Repeat Experiments A and B

  1. Collect the Experiment A and B data sheets and distribute new data sheets for Experiments A and B. The students repeat Experiments A and B, trying to be more careful in their measurements.
  2. After Experiments A and B are completed for the second time, repeat the collection of class data for Experiments A and B on a large chart.
  3. If there is time, look at the data with the class. This video shows one way to analyze data. Look at Lesson 8 for more ideas on analyzing data.
  4. Look for patterns in the data if there is time.  Otherwise, make this a home work assignment and the opening activity of Lesson 8.

Science Notebook

  1. Put Experiment sheet A and B in your Science Notebook.
  2. Look for patterns in the numbers on your experiment sheets.
  3. Describe any patterns that you see.

Outcomes

Students should be able to

  1. set up Experiments A and B, adjusting the input arm and output arm as needed,
  2. correctly measure the distances moved by the input and the output, .and
  3. use the data sheet correctly as they record the data.

Troubleshooting

Here are some things to try when students just don't understand the experiment.
There are several reasons for inconsistencies in students’ data for Experiment A.  Here are four reasons:

  1. The input link or the output link is not connected at the specified place on the lever.
  2. The starting and ending points of the input link or the output link are carelessly marked.
  3. Measurements are made incorrectly.
  4. The input link and output link are not horizontal.


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