Skip to Main Content

Share Suggestion

Predictions

Lesson Plan

Predictions

Objectives

In this lesson, students will use the line of best fit to make predictions. Students will:

  • create a scatter plot of time versus distance.
  • draw and write the line of best fit.
  • calculate predictions using the line of best fit by plugging in values for x and y.

Essential Questions

How are relationships represented mathematically?
How can data be organized and represented to provide insight into the relationship between quantities?
How can expressions, equations, and inequalities be used to quantify, solve, model, and/or analyze mathematical situations?
How can mathematics support effective communication?
How can patterns be used to describe relationships in mathematical situations?
How can probability and data analysis be used to make predictions?
How can recognizing repetition or regularity assist in solving problems more efficiently?
How does the type of data influence the choice of display?
How is mathematics used to quantify, compare, represent, and model numbers?
How precise do measurements and calculations need to be?
In what ways are the mathematical attributes of objects or processes measured, calculated and/or interpreted?
  • How can we determine if two variables correlate linearly?
  • How can we use data to make predictions about the future?

Vocabulary

  • Continuous: The representation of data for which no individual values other than a range between intervals can be established. Continuous data is usually associated with physical measurements such as growth. [IS.1 - All Students]
  • Discrete: The representation of data for which one-to-one correspondence is established between individual points of data and the medium of representation.
  • Correlation: A measure of the mutual relationship between two variables.
  • Line of Best Fit: One line that most closely approximates the trend of bivariate data.
  • Patterns: Regularities in situations such as those in nature, events, shapes, designs, and sets of numbers, and that suggest predictability.

  1. Scatter plot: A graph of plotted points that show the relationship between two sets of data.

  2. Slope: The rate of change of the ordinate with respect to the abscissa; the ratio of the change in the vertical dimension to the corresponding change in the horizontal dimension.

Duration

60–90 minutes/1–2 class periods [IS.2 - All Students]

Prerequisite Skills

Prerequisite Skills haven't been entered into the lesson plan.

Materials

Related Unit and Lesson Plans

Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

Formative Assessment

  • View
    • Teacher observations of student performance during the two activities should include an assessment of questions asked of each other and of the teacher. Do the questions reflect a level of understanding of what they are supposed to do? Do any of the questions reflect something they have learned in the activity?
    • Lesson 3 Exit Ticket uses a topic of general interest to high school students and gets them to think qualitatively about the logic of how well a car is maintained and how much it costs to keep it running. Students must use the corresponding pairs of sample data, plot the points to draw the line of best fit, and make interpretations.

Suggested Instructional Supports

  • View
    Active Engagement
    W:

    Students will know that they are going to be collecting data based on their own experiences, and they will know that the reason they are collecting that data is to make predictions.
    H:

    All students like to be active in their own learning. As soon as students hear that they are going to be collecting data about their own walking speed, they are interested to know why they are doing so. They want to know how they can make predictions about their own lives, and this experiment shows them how they will be able to.
    E:

    Students will be actively engaged in a walking activity. Students appreciate experiences in which they are part of their own learning. It gives them intrinsic motivation, which increases their chances of mastering the content.
    R:

    While students are performing their walking lab, the teacher will be walking around, making sure students are on the right track. If they are not, they will be given time to reflect why they did what they did and what they need to do to change their thought processes.
    E:

    Students will have ample time throughout the lesson to express their understandings, especially during the exit ticket.
    T:

    This lesson is tailored to the kinesthetic learner, but all students learn best when they are actively engaged in their learning.
    O:

    This lesson begins with an attention getter that leads to an activity in which students are actively engaged in their learning. This activity should enable students to complete the exit slip individually with timely feedback before any assessments.

     

    IS.1 - All Students
    Consider word walls and different strategies to ensure that the vocabulary is constantly used during the lesson. Refer back to previous lessons and samples in the real world.  
    IS.2 - All Students
    Consider pre-teaching the concepts critical to this lesson, including the use of hands-on materials. Throughout the lesson, based on the results of formative assessment, consider the pacing of the lesson to be flexible based on the needs of the students. Also consider reteaching and/or review both during and after the lesson as necessary.  
    IS.3 - All Students
    Share various ways that predictions are used.  

Instructional Procedures

  • View

    Before class begins, mark off a hallway or sidewalk beginning at 10 feet going to 100 feet by increments of 10.

    “There is data all around us, and it is used to make predictions about the future. Scatter plots are created to determine how variables correlate; [IS.3 - All Students] equations of lines of best fit are used to make predictions about those variables. Today we are going to gather data regarding your walking speed, write a line of best fit, and then use that equation to predict how long it would take you to walk longer distances.”

    Part 1

    “The focus of this lesson is on making predictions using the line of best fit.”

    “Let’s suppose the relationship between interest in mathematics and end-of-year average is modeled by the following equation: y=2.5x+50. Interest in mathematics is measured on a scale of 0 to 20.”

    “Is the relationship positive or negative? How do you know?” Students should state that the relationship is positive because the slope is positive. Thus, for every increase in x-value, there is an increase in y-value.

    “Considering that the x-variable is interest and the y-variable is end-of-year average, what does the slope of 2.5 tell us about the relationship between interest and average?” Students should discover that the slope indicates that for every 1 point increase in mathematics interest, the end-of-year average increases by 2.5 points.

    “What does the y-intercept of 50 indicate?” Students should discover that the y-intercept indicates that at a level of 0 mathematics interest, the end-of-year average is 50.

    “If a student had a mathematics interest level of 15, what would be his/her expected end-of-year average? If we substitute 15 for our x, we will find the solution.”

    y=2.515+50

    y≈87.5

    “The end-of-year average is about 88.”

    “If the end-of-year average is 72, what is the student’s approximate mathematics level?

    We can solve by substituting 72 for our y.”

    72=2.5x+50

    72-50=2.5x

    22=2.5x

    x≈8.8

    “The student’s approximate mathematics interest level is 9.”

    Hand out the Walking Labe (M-A1-6-3_Walking Lab.doc) and divide the class into groups of three. One student will be the walker and the other two will be the timers, and then they will switch. Students will time each other’s walking distances in increments of 10 feet. Each distance will have two times and then students will take the average. They will create a scatter plot of distance versus time, draw and write a line of best fit, and then answer the questions on the walking lab worksheet.

    Part 2

    Hand out the Lesson 3 Exit Ticket (M-A1-6-3_Lesson 3 Exit Ticket and KEY.doc) to evaluate students’ understanding.

Related Instructional Videos

Note: Video playback may not work on all devices.
Instructional videos haven't been assigned to the lesson plan.
DRAFT 11/03/2010
Loading
Please wait...