Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
- Students will use line of best fit to make predictions.
- Students will analyze a line of best fit to interpret the slope and y-intercept.
- Students will use the slope and y-intercept to write an equation for a line of best fit.
- Students will use the equation for a line of best fit to make predictions.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should be able to:
- Identify the slope and y-intercept given a table, graph or equation.
- Graph a linear equation in slope-intercept form.
- Write a linear equation in slope-intercept form.
- Use a point and the slope to write an equation in point-slope form.
- Use the point-slope form of an equation to rewrite the equation in slope intercept form.
- Construct a scatterplot.
- Recognize whether a graph shows a positive, negative or no correlation.
Guiding Questions: What are the guiding questions for this lesson?
- What does the slope of a line tell us about the relationship between two variables?
- What does the y-intercept for a line of best fit represent?
- How can we use a line of best fit to make predictions?
Teaching Phase: How will the teacher present the concept or skill to students?
The teacher will begin class with the Discovery and Exploration Activity that is attached. Students will determine if there is a relationship between fat grams and the total calories in fast food. Students will be paired in groups of two.
Display the instructions for the students and distribute graph paper and a strand of spaghetti to each pair of students.
- Given a data set, students will create a scatterplot using graph paper and pencil. Students should include a title for the graph and label all axes.
- Students will position a piece of spaghetti so that the plotted points are as close to the spaghetti as possible. This will accurately reflect the line of best fit for the data set.
- Students will find two points that lie on their line of best fit that most accurately reflect the data. Students may choose different points.
- Students will calculate the slope of their two points, rounding to the nearest hundredths place.
- Students will use the slope and choose a point from the data. They will then use point-slope form to find the equation of the line in slope intercept-form. Some students may choose to use a point and the slope to find the y-intercept and then rewrite the equation in slope-intercept form.
- Students will compare their equation with other groups and answer the following questions.
- Did you obtain similar results?
- Is there a correlation between fat grams and number of calories? If so, what is the correlation?
- What does the slope of your line represent in terms of the relationship between fat grams and calories?
(Each student's results should be similar. The students should also state the positive correlation and mention that the slope is representative of the fact that as fat grams increase, calories also increase)
When students are finished comparing, ask students the following questions:
- What general shape did your scatterplots make? (In general, the data points were linear and showed a positive correlation.)
- Is there a constant rate of change? (No.)
- How do you know? (Calculating different pairs of points would produce different slopes.)
- How did you determine one slope that best described the data? (Answers will vary but students should mention that they chose points based on how closely they fell to the spaghetti line of best fit.)
- What is the independent variable? Dependent variable? How do you know? (Fat grams and calories, respectively. The number of calories in a sandwich depends on the number of fat grams.)
- Use the graph and the equation to make a prediction about how many calories sandwiches with 7 and 40 fat grams would have. (Answers will vary. Ask students to share their answers. Write them on the board discuss as a class whether or not the answers are reasonable.)
Explain to students that different people may choose different points and arrive at different equations. All of these equations are correct, but in order to arrive at the best answer a graphing calculator would be a better tool.
The student and teacher instructions are attached. The teacher attachment includes a graph of what student models should look like, as well as slope and equation calculations. The attachments also include extension activities using TI graphing calculators to determine the line of best fit. Students have essentially covered every objective in the lesson with this activity.
Teacher Discovery and Exploration Activity with Answer Key
Guided Practice: What activities or exercises will the students complete with teacher guidance?
During guided practice the teacher will introduce new vocabulary and have students copy the definitions into their notes. Next, they will display Example One in the Guided Practice attachment. Students will use the data in the examples to create a scatterplot. The teacher will then instruct students to use a straight edge to draw a line of best fit. The class will choose two points to calculate the slope and use point-slope form to write an equation for the line of best fit in slope-intercept form. Students may also choose to use the slope and a point to find the y-intercept and then rewrite the equation in slope intercept form. This will be a teacher led follow up to the discovery and exploration activity. At this point, students have covered the objectives of the lesson. However, new vocabulary (interpolation and extrapolation) is introduced during this guided practice. The guided practice shows an example of each, as well as an example involving a negative correlation in which the y-intercept is more meaningful with respect to the data. The real world examples include a connection to Biology (giraffe growth), gasoline prices and the relationship between the temperature and an airplane's altitude.
Guided practice attachment with answers: Line of Best Fit Guided Practice
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
During independent practice, students will take out their individual whiteboards and dry erase markers to complete the attached practice problems.
See the Formative Assessment box for the Independent Practice Problems.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher will assign a project. Students will be told to collect their own data for two related variables and compare the relationship. They must have at least 20 pairs of numbers. Students may use a almanac, newspaper, magazine, the internet or conduct a survey of people they know to collect the data.
Once the data has been collected, students will graph the data and draw a line of best fit. Students will then calculate the slope and write an equation for the line of best fit.
Students will then write a paragraph about what they found that describes the relationship between the two variables.
The teacher will give students the following suggestions and ask the class to add to the list. However, students may choose whatever they wish, provided that the two variables show a correlation.
- Height vs. shoe size
- Highway vs. city mileage
- Points scored vs. time on court
- Hits vs. times at bat
- Sunlight exposure vs. plant growth
Student instructions and rubric are attached.
Project for Line of Best Fit
Rubric for Line of Best Fit Project.docx
The attached Summative Assessment will test students ability to analyze a line of best fit and interpret the slope and y-intercept. Students will use the slope and y-intercept to write an equation for a line of best fit and will use the graph to make predictions about the data.
The assessment will be distributed at the end of class and each student will complete the assessment independently. The answer key is also attached.
Line of Best Fit Summative
Line of Best Fit Summative Answer Key
Individual whiteboards may be used to answer the formative assessment questions. After the gradual release problem, during guided practice, students will be given the attached problems to complete on their whiteboards.
Students will copy a table and create a scatterplot. Then students will draw a line of best fit and write an equation for the line. Students will interpret the slope and y-intercept and make inferences about the data based on the graph and equation.
After completing each problem on their own, students will compare their answers to others at their table group and justify their answers to each other. The teacher will walk around the room observing student work to determine understanding and adjust instruction as needed. The teacher also will use this time to provide one on one instruction to students that need help while other students compare their answers.
Finally, the teacher will ask students to share their answers with the rest of the class. If the students demonstrate a clear understanding of the material, the teacher will move on to the summative evaluation for students to complete on their own. If the students are struggling, more practice problems will be required.
Formative Assessment: Line of Best Fit Independent Practice
Feedback to Students
As students work, the teacher will circulate around the room to ensure that the students are creating their scatterplots correctly. During the Discovery and Exploration Activity, teachers may need to guide students who are unsure of where to place their line of best fit. Students may also need to be reminded of the slope formula. The teacher should also circulate during whiteboard practice in order to assist students with corrections and misconceptions as they work practice problems on whiteboards. Students may need to be reminded to label their graphs. Students may also need to be led by guided questions to help them to interpret the slope and y-intercept.