7th Grade

Context: Trail Mix

Lesson Plan

The focus of this context is to have students use technology to analyze, display, and draw conclusions about trail mix data collected through sampling. In particular, students will compare across data sets by examining the displays and summary statistics for different ingredients. Several important areas within the 7th grade content and practice standards can be addressed through this context.

  1. A dual focus on the Statistics & Probability cluster headings and standards can be developed using the prompt, “How many pieces of each ingredient are in a serving of trail mix?” Answering this question would involve students collecting, representing, and analyzing data collected through repeated sampling of trail mix, generating summary statistics on the counts of each ingredient, and then using their representations and summary statistics to compare ingredients and draw conclusions. Depending on the work they produce and the questions they have, students can be pressed to work with additional cluster headings and standards in the Expressions & Equations and Number System domains.
  1. A focus on both the Statistics & Probability and Ratios and Proportional Reasoning cluster headings and standards can be developed using the prompt, “How many calories are in a serving of trail mix?” Answering this question would involve the provision of nutritional information on trail mix ingredients and then having students collect, represent, and analyze multiple sets of data for comparison purposes. Again, depending on the work they produce and the questions they have about the rational numbers this activity generates, students can be pressed to work with additional cluster headings and standards in the Expressions & Equations and Number System domains.
  1. Yet anotherfocus on Statistics & Probability and the Ratios and Proportional Reasoning cluster headings and standards can be developed using the prompt, “If your class’ samples of trail mix are representative of all samples, how many peanuts would you expect to have in 5, 20, or n servings of trail mix?”Answering this question would involve students using the summary statistics they generate through analysis of their collected data and then applying this analysis in a proportional reasoning setting.
  1. A follow-up focus on the Geometry and the Ratios and Proportional Reasoning cluster headings and standards can be developed using the prompt, “If a serving of trail mix fills a small box with dimensions 1 inch by 1 inch by 3 inches, how many pieces of each ingredient would there be in a party box of trail mix with dimensions 4 inches by 4 inches by 12 inches?” Answering this question would involve students applying what they learned about the ingredients in one serving of trail mix to a proportional reasoning problem involving scaling and volume.

Though a full range of 7th grade standards can be targeted through use of this simulator, this sample lesson plan and instructional sequence targets the following:

7.SP.A Use random sampling to draw inferences about a population.

●7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

●7.SP.A.2Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.

7.SP.B Draw informal comparative inferences about two populations.

●7.SP.B.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.

●7.SP.B.4Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems.

●7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.

●7.RPA.2.ARecognize and represent proportional relationships between quantities.

Given the scope of work involved in answering the Essential Question, it is likely that students will meet all eight of the Standards for Mathematical Practice. However, the bolded practices below are specifically targeted in this sample lesson:

  1. Make sense of problems and persevere in solving them.
  2. Reason abstractly and quantitatively.
  3. Construct viable arguments and critique the reasoning of others.
  4. Model with mathematics.
  5. Use appropriate tools strategically.
  6. Attend to precision.
  7. Look for and make use of structure.
  8. Look for and express regularity in repeated reasoning.

Materials

Trail Mix (enough for each student to have a ¼ cup serving): Ingredients are currently set to mini pretzels, peanuts, M&Ms and raisins. If you elect to make a different recipe of mix, you will need to adjust the slides presentation, student handout, and google form accordingly.

Sample Google Form to copy and customize (**Please do not edit the original form so others have access to the original as well)

Slides Presentation

Student Handout

Before the Lesson

Students can work individually or in groups, but they will need access to an electronic device that has internet access (e.g., smart phone, tablet, computer, etc.).

Instructional Sequence

Time / Activity / Teacher Notes
This lesson will require preparation of a four-ingredient trail mix for students to investigate. Poll ahead of time for peanut, dairy, and gluten allergies before assembling your mix. Be careful adding ingredients that are small (such as pumpkin seeds), as counting them takes a long time. You will need to customize the Slides Presentation, Student Handout, and your individual copy of the Sample Google Form to align with your selected ingredients and the Google Form and Response sheet that you create.
10-15 mins / Before students start using their devices, use your customized version of thisSlides Presentation to introduce the day’s context and essential question.
Distribute “servings” of trail mix and brainstorm how students will use their sample to begin answering the essential question for the day.
Distribute copies of the Student Handout and give students time to count and record ingredient pieces for their sample. / An 1/8 cup scoop makes a good serving size without generating too many pieces for students to count.
Answer any clarifying questions students have about what constitutes a “piece” and how broken or partial pieces will be counted before distributing the handout.
3-5 mins / Address questions 3 and 4 in the Student Handout by having group members discuss the differences between their individual samples. Help facilitate their conversation by providing the prompts:
  • Can you answer today’s question accurately using the data from an individual sample? Why or why not?
  • What’s are potential ways we could improve on our individual answers?
/ Discuss the potential ways that the data from everyone’s sample could be used to answer the day’s question and introduce the benefit of using technology to help process and analyze large data sets or numerous samples.
5-8 mins / Have student collect their devices and navigate to the web address of your customized google form.
Provide the link to the form to each student by pasting it into the PowerPoint, your website, writing it on the board, or emailing it to students.
Have each student enter and submit their individual sample data into your customized form.

/ Make a copy of this Sample Google Form and customize for your trail mix ingredients.
To enable access to your form, click on the Settings gear icon
in the upper right and then designate the settings by un-checking every box and clicking on SAVE.

To create a link to your form, click on the SEND button.

In the dialog box that appears, click on the paperclip link icon, check the “Shorten URL” button, and then copy the link that is generated onto your clipboard.
You can now paste this link into the PPT file, email it to students, write it on the board, etc.
15-20 mins / Provide students with the link to the form responses by pasting it into the PowerPoint, your website, writing it on the board, or emailing it to students.
Once they have located the responses spreadsheet, supervise students as they cut the class data to their clipboard and then follow the Student Handout’sscreenshot tutorial for generating stacked box-and-whisker plots in GeoGebra.
Students should generate stacked Box Plots that are similar to the ones shown below:

… and statistical summaries similar to:

As students work, pose additional questions such as:
  • What might be the source of variability in the number of total (and ingredient) pieces in each sample?
  • Do trail mix servings that are packaged by a company have as much variability as our samples here? Why or why not? What do you think that means about the accuracy of its nutrition label?
  • What do you notice about the stacked box plots that GeoGebra creates for you? What can you say about the trail mix ingredients in terms of their center and variability?
  • Can you say anything different when you look at the ingredient’s summary statistics?
  • Did anything produced by GeoGebra surprise you?
  • What comparison claims can you make about the ingredients in the class’ trail mix?
/ Before class begins, you will need to generate the class’ responses google sheet link by opening your editable copy of the Google form file. The default view is the QUESTIONS view, and you will need to select the RESPONSES view. Once there, click on the green spreadsheet icon.

Accept the default response destination and click on CREATE.

This will generate a blank sheet that will populate as students submit their data. To share the spreadsheet with students, you will need to click on the Share button in the upper right corner:
Click on the “Get shareable link” in the dialog box that appears.

Click on the drop down arrow and then on the More… option at the bottom

Select the radio button for “On – Anyone with the link” and click Save.

Confirm that Anyone with the link can view and click on “Copy link.”

You can now paste this link into the PPT file, email it to students, write it on the board, etc.
10-15 mins / Facilitate a class discussion during which students share and defend their comparison claims. / Prior to sharing out claims, ask probing questions about whether:
(a)Their claims would still hold if the entire school contributed sample data,
(b)They supported their claims by using both the concept of center and of spread to discuss differences
(c)There were two ingredients that were “too close to call” and weren’t different enough to justify a comparison claim.
Press students to justify their claims in ways that use correct academic language and refer to both their displays and the ingredients’ summary statistics.
5-10 mins / If time allows: Use the proportions of each type of ingredient in the trail mix to answer proportional reasoning and probability questions.
You can also consider providing additional nutritional data (grams of protein, fat, and carbohydrate per ingredient piece) and then pose additional questions about the serving of trail mix that involves values other than counts. Students can reason through these types of questions using ratio tables, by solving proportions, by thinking graphically, etc. / Integrate and extend previous learning with proportional reasoning to reinforce fluency and flexibility.
E.g. Use proportional reasoning to make predictions about the number of fat (protein, carbohydrate) grams expected in a representative serving of trail mix.
Assessment / Pose this scenario to students:
“Suppose youstart a company that assembles and mails gourmet trail mixes to athletes around the world. You determine that your customers prefer dried cranberries and almonds to raisins and peanuts. Investigate how the ingredient counts, cost and nutrition of a 1/8 cup serving of trail mix would change if you made this alteration to the recipe used during class.”
Grade-level scaffolding / For 7th grade students needing review of 6th grade concepts, you can spend more time generating the data representations and statistics for the univariate data they collect, as outlined in the 6th grade Statistics & Probability standards.