Lesson 9: Spaghetti Line

Lesson 9: The Spaghetti Line

Objective:

Students will estimate the line of best fit for a height and arm span data set using a strand of spaghetti as a modeling tool.

Materials:

  1. The Spaghetti Line (LMR_4.9_The Spaghetti Line)

    Note: Advance preparation is required. Cut out plots prior to beginning the lesson.

  2. What’s the Trend? (LMR_4.7_What’s the Trend) from lesson 8

  3. Arm Span vs. Height Scatterplot (LMR_4.6_Arm Span vs Height) from Lesson 7

  4. 1 lb. of Uncooked Spaghetti

  5. Grid Paper

  6. Tape or Glue

  7. Poster paper

Vocabulary:

line of best fit, regression line

Essential Concepts:

Essential Concepts:

We can often use a straight line to summarize a trend. “Eye balling” a straight line to a scatterplot is one way to do this.

Lesson:

  1. If necessary, begin by sharing out the descriptions for the plots in the Strength of Association (LMR_4.8_Strength of Association) handout from the previous lesson.

  2. Inform students that in this lesson, they will estimate the equation of the line of best fit for a height and arm span data set.

  3. Refer students back to the plots in the What’s the Trend? handout (LMR_4.7_What’s the Trend). The line in each of the plots is known as the line of best fit, or the regression line. This is a trend line that best represents or models the data in each scatterplot. Ask students:

    1. Why do you think this line is called “best fit”? Some possible answers are that it is a line that is closest to all data points or that it “fits” evenly among the data points. This is a good time to refer back to the discussion about height versus arm span in lesson 7.
  4. Distribute The Spaghetti Line (LMR_4.9_The Spaghetti Line) to each student and a couple of spaghetti strands per team. Students will estimate the line of best fit as outlined in the handout. Team solutions should be recorded on poster paper. They will glue their assigned plot on the poster and record their responses to the questions on the poster paper.

    Note to teacher: If necessary, review how to find the slope of a line using two points and how to write an equation using the slope and y-intercept.

  5. Ask teams to post their work around the room. Conduct a Gallery Walk so that teams can see each other’s work.

  6. Lead a discussion about the teams’ lines. Ask: Which team has the best line? Why?

    Note to teacher: Push the students a bit by adding an obviously bad line to the graph and asking why their line is better than this one. Push them to come to an understanding that the “best” line comes close to the most points.

  7. Inform students that data scientists have a way of finding the best line. They choose the line so that the mean squared distances between the points and the line is as small as possible. Discuss with students:

    1. What methods have we used so far? We’ve used Mean Squared Deviations and Mean Absolute Error (Lesson 6).

    2. How did we use these methods? It was best to use Mean Squared Deviations when we are looking at mean and Mean Absolute Error when we are looking at median.

    3. Which method do you think data scientists use most often? Data scientists often use MAE.

  8. [See graphic below] If time permits, ask students to calculate the distances and squares of two different lines so that they can understand what it means. This is the 2D version of the game they played in Lesson 6.

  9. Inform students that they will see the equation of the arm span vs. height data in lesson 10.

Class Scribes:

One team of students will give a brief talk to discuss what they think the 3 most important topics of the day were.

Homework & Next Day

Students will use a straight edge to draw a line of best fit for the scatter plot in the Arm Span vs. Height handout (LMR_4.6_Arm Span vs Height) from lesson 5. They will use their knowledge of slope and y-intercept to determine the equation for the line of best fit that they drew.

LAB 4C: Cross-Validation

Complete Lab 4C prior to Lesson 10.