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Line of Best Fit with Scratch

  • 8-8 grade

Lesson Description:

In this lesson, students will use collected data from the autonomous car to predict how much energy to use to complete a task by choosing the best fitting line. 


 

Standards Covered

CCSS.MATH.CONTENT.8.G.A.4

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

CCSS.MATH.CONTENT.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

CCSS.MATH.CONTENT.HSG.SRT.A.3

Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

CCSS.MATH.CONTENT.HSG.SRT.B.5

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

CCSS.MATH.PRACTICE.MP1

Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP2

Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP3

Construct viable arguments and critique the reasoning of others.

CCSS.MATH.PRACTICE.MP4

Model with mathematics.

CCSS.MATH.PRACTICE.MP5

Use appropriate tools strategically.

CCSS.MATH.PRACTICE.MP6

Attend to precision.

CCSS.MATH.PRACTICE.MP7

Look for and make use of structure.

CCSS.MATH.PRACTICE.MP8

Look for and express regularity in repeated reasoning.

image description

Lesson Modules


Teaching Tips:

1. Show the simulation of the car on the icy road and demonstrate how to collect the data. 

  • Try first with the power of 300 and run the car for 1 second. Mark how many centimeters the car drove. 
  • Run the car with 400 power for 1 second for the next interval. Mark how many centimeters the car drove for that interval.
  • Repeat with the energy power of 500 and 600. Mark the distance that the car drove for each interval. 
  • Refer to the image below to enter the correct input:

  • Once you click on the START button, the simulation shows the Distance of each interval. 

2. Complete the table in the Class View. 

3. Plot the data in the graphing calculator. Ask the student if they see any patterns. If they can find the pattern, ask if they can predict how many centimeters the car would drive with 1000 energy power. 

Watch this quick video to learn how to plot a point on the interactive tool. 

You've probably heard of the fuel efficiency of cars described as MPG (Miles Per Gallon). Some hybrid cars can run more than 130 miles with one gallon of gasoline and some cars only can run 13 miles with one gallon of gasoline. When it comes to electric cars, we also need to think about how much the car can run with limited energy because the car cannot have unlimited battery power to carry with it. 

Pop question: What MPG (miles per gallon) do you think this car has? 

You will run the autonomous car with different energy power in the simulation below. Measure how far the car moved with the given power. 

  • Use a table to collect the data.
  2. powerdistance the car drove for one second
      
      
      
      
      
      
      

      

 

 

 


 

 

 

 

Time Interval

 
Power
Time

Step 1

Step 2

Step 3

Step 4

 

Speed :

0.0cm/s

Time Interval :

0.0s

Total Time :

0.0s

Distance :

0.0cm

Total Distance :

0.0cm

 
 
 

 

 


Answer the following question.



If you need to make the car run 120 cm for 1 second, how much energy power does the car need? Estimate the number and type your answer using only the number.


Teaching Tips:

Explore

Have students explore how to find the expected value (energy power for wheels) by using the best fitting line. The following interactive tool can be used to teach the line of best fit concept.


Drive!!

Have students check their answer by running the car. The students might have to move to a hallway. The answer should be around 1000 (depending on the floor material). 

Next, have students answer the questions about whether or not the car moves as they expected, and what they need to change to make it better. 

Use this Scratch file for this activity.

Collecting Data

You will run the autonomous car with different energy power. You will measure how far the car moved with the given power. 


  1. Find an open space with a flat surface to run the autonomous car.
  2. Connect 
    1. Bluetooth2. Orchestra3. Scratch
     

    Connect your autonomous car to your dedicated computer via Bluetooth.

    Open Orchestra and connect your robot to the program.

    If you don't have the program on your computer, use this link to download. 

    Open Scratch from Orchestra

  3. Open Scratch from Orchestra program
  4. Refer the blocks below to program the car


  5. Change the power to both the right and left wheels. Try different power between 300 and 600. You can run the experiment with the same energy power multiple times.
  6. Note that the car will move with at least 300 power to both left and right wheels. If the car is on the carpet, you should provide more power. 
  7. Use a table to collect the data.

    2. powerdistance the car drove for one second














        


Data Analysis

Now you collected the data but how do you comprehend the data? Can you find the patterns? What does each pattern do? 

To explore, follow the direction.

  1. Define the x-axis for energy power for each wheel and y-axis for the distance the car drove for one second.
  2. Graph points of your collected data from the experiment by moving the blue points on the x-y plane. If you have extra points, place them along the line of the pattern. 
  3. Click on "Fit your line". Drag the line or the "x" to change the line. Try to find the "line of best fit".
  4. Compare your line to the "Line of Best Fit". What happens to the line of best fit when you move a point?




Use the scatter plot and the best fit line to answer the following question. Write your answer using only the number. 



If the car has to drive for 130 cm, how many energy power do you need for the car? Use the pattern you found and predict the number. Type your answer using only the number.

 

 

Drive Autonomous Car!!

Now use the energy power to check if the car can drive 130 cm with the power. 

Did the car move as you expected?
  • Not at all
  • Not really
  • Kind of
  • Pretty much
  • Totally

What do you need to change if the car didn't move as you expected? Write your response in a sentence.


Teaching Tips:

Have students mark the self-reporting scores and write the in-depth question.  You have access to the student's responses from the dashboard. 

If time is allowed, have a quick discussion with the class to reflect on what went well and what could be done differently to have a better learning experience. 

Have quite time to answer the following questions individually. Your answer will NOT be graded but only used for the next lesson. So be honest!

 

I understand the concept: Data collection
  • Not at all
  • Not really
  • Kind of understood
  • Pretty much understood
  • Totally got it

Explain how you collected data for this lesson and why that was useful.

I understand the concept of Scatterplots.
  • Not at all
  • Not really
  • Kind of understood
  • Pretty much understood
  • Totally got it

Explain what scatterplots are and when it is useful to use a scatterplot to display data

I understand the concept of Line of Best Fit.
  • Not at all
  • Not really
  • Kind of understood
  • Pretty much understood
  • Totally got it

Explain what a line of best fit is and when you can use it.