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How Far Will the Finch Turn?
Use math to make your Finch turn to an angle you choose!
This activity was developed in collaboration with Brian Johnson of Lakeside Junior High School in Springdale, AR.
4-5, 6-8, 9-12
This activity is aligned with Common Core elementary math standards for measuring angles (4.MD.C and 4.G.A) and measuring and graphing data (4.MD.B, 5.MD.B, and 5.G.A). For these students, you can eliminate the linear equation portion of the activity. Instead, students can use the graph to estimate the wait time needed for a particular angle. For middle school, this activity is aligned with Common Core math standards that involve the coordinate grid (6.SP.A); proportions (6.RP.A, 6.EE.C, 7.RP.A, and 7.EE.B); and linear equations (8.EE.A, 8.EE.B, 8.EE.C, 8.F.A, and 8.SP.A). At the high school level, this activity is aligned Common Core standards for algebra (HSA.CED.A and HSA.SSE.A) and functions (HSF.IF.B, HSF.BF.A, and HSF.LE.B).
As you have learned to make the Finch move and turn, you have varied the speed of the motors and the wait time. You may have spent some time trying to choose exactly the right wait time to make your Finch turn a particular angle. In this activity, you will use math to find an easier way to make your Finch turn whatever angle you chose!
For this activity, you will need paper, markers (3 different colors), a ruler, and a protractor. You will make the Finch turn around one wheel at speed 30. You will measure how far the Finch turns for different wait times, and they you will use this information to figure out how to calculate the wait time for a particular angle.
You will start with the simple Finch script shown below. This script will make the Finch turn right for 0.5 seconds. The right wheel is stationary, and the left wheel moves at speed 30. This makes the robot turn about the right wheel.
To measure how far the Finch turns, start by making a dot on the right side of a sheet of paper. Tape the sheet of paper to a table so that it doesn’t move. Place the right wheel of the Finch on the dot. Next, use a colored marker to make a dot at the center of the Finch’s tail. This is marked by a small semicircle.
Run your script, and make another dot at the center of the Finch’s tail. Use the ruler to connect the starting and ending dots to the right wheel dot as shown below. Then use the protractor to measure the angle that the Finch turned. Record this angle as “Angle 1” in the data table below.
Repeat this process twice to record two more trials for a wait time of 0.5 s. Use a different color for each trial so that you can tell the angles apart. Your paper may look something like the one shown below.
Next, change the wait time in your script to 1 s. Run this script three times and measure the angle that the robot turns each time. You will probably want to use a new sheet of paper. Remember to record your data in the table. Continue to change the wait time and measure angles to complete the data table.
You will notice that the angle can be slightly different from trial to trial, even when the wait time is the same. This is why you took three trials for each wait time. By averaging the results for these trials, you can get a better estimate of how far the robot will turn for a particular wait time. Complete the data table by finding the mean angle for each wait time.
Open Google Sheets or Excel. Create two columns of data. One should contain the wait times from the data table, and one should contain the corresponding mean angles. Create a scatterplot with wait time on the x-axis and mean angle on the y-axis.
Fit this graph with a linear trendline and record the equation of this line. Your graph should look something like the one shown below, but every robot is a little different!
The linear equation you found has the following form: angle = slope*time + y-intercept.
Think about how you can use this equation. How far will the robot turn for a wait time of 3 s? What wait time should you use to make the robot turn 75°? 120°?
Teacher Note: As an alternative, students can create the scatter plot by hand. Doing this by hand can help students to better form the connection between the different data that they collected.