8th Grade Lesson Plan

Context: Trail Mix

The focus of this context is to have students explore the nutritional content of two different trail mixes. Several important areas within the 8thgrade Idaho Content and Practice Standards can be addressed through this context.

Essential Question: You have two aunts and they love trail mix. Each has a different blend of ingredients and both claim their mix is the most nutritious. Using the fat and calorie content from random samples of each mix, determine which aunt has the most nutritious mix.

Guiding Questions / Prompts

  1. Which mix has more nutritional value? How do you know?

Each aunt keeps their recipe a secret. We have been able to gather 15 random samples of each mix and through an independent lab, determine the fat and calorie content. Can we determine which mix is more nutritious from our sample data? Investigating this question will allow students to represent and analyze the bivariate sample data provided.

  1. From the sample data, can we produce a scatter plot and line of best fit to estimate the nutritional value of each mix?

Students are expected to graph the data for each trail mix and estimate a line of best fit.

  1. Can we use the fat content to predict the calorie content? Why or why not?

From our line of best fit, can we make predictions regarding the relationship between the amount of fat and the number of calories?Investigating this question will cause students to take a deeper look at the data they collect.

Sample Lesson Plan

Mathematical Standards and Practices

Though a full range of 8th grade standards can be targeted through use of this simulator, this sample lesson plan and instructional sequence targets the following:

  • 8.SP Investigate patterns of association in bivariate data.

8.SP.1Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

8.SP.2Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

8.SP.3Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

  • Mathematical practice standards

1.Make sense of problems and persevere in solving them.

2.Reason abstractly and quantitatively.

4.Model with mathematics.

5.Use appropriate tools strategically.

6.Attend to precision.

Material for the Lessons

  1. Printed copies of student handout, URL:
  2. Printed copies of student graphing sheet (each group with need two copies), URL:
  1. Spaghetti noodles to estimate the line of best fit
  2. Scotch tape to attach the noodle to the graph

Instructional Sequence

  1. Break students into groups.
  2. Pose essential question.
  3. Give students the background for the activity.
  4. Distribute student handout, two copies of the graph paper and spaghetti to each group.
  5. Due to the data being clumped together at some points, have students graph each data set on separate graph paper. An alternative would be to massage the data so the points are not clumped together.
  6. Remind students to all use the fat content for the x axis and the number of calories for the y axis.
  7. Remind students to graph each trail mix using a different color.
  8. After they have completed creating the graphs, have each group answer the questions below the raw data on the student handout.
  9. Monitor student work.
  10. Possible press questions.
  11. Why do you feel having more calories makes one mix more nutritional than the other?
  12. Does having more fat make one mix less healthy?
  13. What does the point of intersection represent on your graph?
  14. How would you interpret the slope of your graph?
  15. What does this point (outlier) represent?
  16. How would you interpret your y-intercept?
  17. Have students present their findings to the class.
  18. Note that while the raw data is the same for each group, they should have different lines of best fit. Some of these lines will be drastically different and should provide for interesting questions from their peers.
  19. During the presentations, assess groups based on accuracy of statements and how they answered peer questions.
  20. Have students turn in all work to grade the handout.

Student Examples

The press questions listed in the instructional sequence should be used for each of these sets of student work.