Author:
Mark Freed
Subject:
Mathematics
Material Type:
Homework/Assignment
Level:
Middle School
Tags:
  • Applied Mathematics
  • Oregon Math in Real Life
  • STEM Education
    License:
    Creative Commons Attribution Non-Commercial
    Language:
    English
    Media Formats:
    Downloadable docs

    Education Standards

    Should Sugary Drinks be Taxed?

    Should Sugary Drinks be Taxed?

    Overview

    Math in Real Life (MiRL) supports the expansion of regional networks to create an environment of innovation in math teaching and learning.  The focus on applied mathematics supports the natural interconnectedness of math to other disciplines while infusing relevance for students.  MiRL supports a limited number of networked math learning communities that focus on developing and testing applied problems in mathematics.  The networks help math teachers refine innovative teaching strategies with the guidance of regional partners and the Oregon Department of Education.

    Lesson Overview

    Introduction

    Students propose tax plans for sugary beverages. They will tax based on three tax plans: $0.01-$0.02 per fluid ounce, a percent of the total cost, and $0.0025- $0.01 per gram of sugar. They will determine how much various drinks will cost under the tax plan. Then they will determine how much total revenue each plan will generate and figure out the percent that will be sent to each state program.

    Core Math Concepts

    • Percent means out of 100, which can be written as a fraction or a decimal.
    • There is a relationship between the percent equation and solving a percent problem using a proportion.
    • Converting a fraction to a decimal is the same process as computing a unit rate.

    Student Objectives

    • I can use an equation or proportion to find percent increase in real-world problems involving taxes.
    • I can use rational numbers and percentages to develop and compare tax proposals.
    • I understand that percent means out of 100, which can be written as a fraction or a decimal.

    Essential Questions

    • How are percents related to proportions, equivalent fractions,and unit rates?
    • How can a percent be found using a proportion? Equivalent fractions? A unit rate?

    Materials

    • Sweet Drink Tax: Student Worksheet (1 per student),
    • Philadelphia Council Passes Sweet Drink Tax ,
    • Optional hook: PodCast, Should Sugar Be Regulated Like Alcohol? (18 mins)

    Or…

    Time Required

    One or two 45-minute lessons or one 80-minute lesson.

    Authors

    Participants in the Oregon Math in Real Life Grant

    Standards

    7.RP.3  Use proportional relationships to solve multistep ratio and percent problems.

    Practice Standards

    MP.3 Construct viable arguments and critique the reasoning of others.
    MP.7 Look for and make use of structure.

    LAUNCH - SET UP

    Anticipated Time:

    10-15 minutes

    Suggested Grouping:

    Suggested Grouping: Individual, Pairs, Groups, Class Discussion

    Teacher Questions and Actions:

    Pass out Student Intro Page:

    1. Private reasoning time/Partner share
    2. Prompt students to make a list of information they need to solve the problem.
      • Private reasoning time/Partner share
      • Make a public record of the ideas/questions that students came up with.
    3. Propose question: What are some different ways you could tax sugary drinks?
    4. Reasonable amounts/percents:
      • Plan 1 (taxing fluid ounces): Philadelphia, San Francisco, Boulder and Berkeley are currently proposing 1-2 cent tax per fluid ounce. (NOTE: Researched April, 2017. Update if necessary).
      • Plan 2 (taxing a percent of the total cost): Could range from 5%-45%. Look at prepared food tax in Ashland, OR (5%) Alcohol/marijuana taxes- (25%-45%) Or look at sales taxes in various states 5-15%.
      • Plan 3 (taxing based on grams of sugar):  $0.0025 - $0.01 per gram of sugar. (Between 0.25 cent and 1 cent per gram of sugar.) OR you some students may want to look at a varying rate depending on sugar per fluid ounce. (This might be a good extension).

    Student Moves:

    • Watch video/Read premise Students answer Intro Question #A.
      • Students generate a list of questions for #B.
      • How would sugary beverages be taxed?
      • What would be considered a sugary beverage?
      • What would the tax be used for?
      • Why would the state want to tax sugary beverages?
      • How much more would it cost to buy a soda?
      • How much would the tax be?
      • Would all sugary beverages be taxed the same?
      • Share ideas with the class.
    • Fill in ideas on Sweet Drink Tax Intro #C.
    • Fill in ideas on Sweet Drink Tax Intro #D.  Ways we want them to explore:
      • Tax 1-2 cents per fluid ounce.
      • Tax 5% - 30% on dollar price.
      • Tax 0.5-2 cent per gram of sugar.
    • Decide as a class how much extra they’d be willing to pay for each drink. (Optional Survey) Determine a range that would give a fair added amount. For example: grams of sugar range from 14-214 grams. So a tax of more than 1 cent per gram seems an unreasonable additional cost for the 214 gram item.

     

      EXPLORE - INVESTIGATE

      Anticipated Time:

      20-30 minutes for each part. If you are short on time, consider doing Part 1 only OR Parts 1 & 2 OR Parts 1 & 3.

      Suggested Grouping:

      Suggested Grouping: Pairs or Groups. Summarize each part as a class.

      Teacher Questions and Actions:

      Part 1 (Teacher)

      This would be a good time for a public record of how to do the math for each plan.
      Anticipate student struggle with finding the tax using percent of dollar amount.

      Misconceptions:

      • May forget to add the original.
      • May set up the proportion wrong
      • May forget to change the percent to a decimal.
      • May change the percent to a decimal incorrectly.

      This would be a great time for a public record so students have an example of each tax plan to
      reference when completing their work on Part 2.
      There is room in Part 1 for students to copy other groups’ methods.

      Part 2 (Teacher)

      Pass out the table for Part 2.

      • Monitor students to be sure they are computing correctly. See excel spreadsheets for various tax amounts.

      Discuss questions as a class.

      • No, the only way to double in price on plan 2 is to have a 100% tax.
      • For the Plan 3 Tax, the only beverage that would likely double in price is a 2-Liter bottle of Sprite.

      Part 3 (Teacher)

      If students have difficulty getting started, you may want to point out which information they should use to solve each plan.

      Select 2 or 3 students to show their math explaining how they found the total revenue for Plans 1 and 2.

      Misconception:

      • Anticipate difficulty changing 65% to a decimal so being off on the answer by a factor of 100.
      • Students may multiply 118% of $326.90 to get the new total annual cost. In order to determine the potential tax revenue, students will need to determine the amount of tax only.

      (Plan 3 might be too complicated and require making some assumptions, but could be solved with proportions. There is a table on the student worksheet to help.) If you are short on time, definitely skip this one.

      Student Moves:

      Part 1 (Student)

      Students should decide with their group what their tax level is going to be for each plan.

      Then they compute the tax rate for each plan for one beverage, showing all steps.

      Plan 1 Student Examples:

      24𝑜𝑧 ⋅ $.01 𝑝𝑒𝑟 𝑜𝑧 = $0.24
      $2.99 + $0.24 = $3.23
      OR
      4oz 1.5 cents 2 · per oz = 36 cents
      $2.99 + $0.36 = $3.35

      Plan 2 Student Examples:

      \(\frac{5}{100}=\frac{x}{2.99}\)

      x = $0.15
      $2.99 + $0.15 = $3.14

      Plan 3 Student Examples:

      $0.005 per gram of sugar · 93 grams = $0.47
      $2.99 + $0.47 = $3.46

      OR

      \(\frac{$0.005}{1 g}=\frac{x}{93 g}\)

      $0.47 = x

      Part 2 (Student)

      After seeing an example of one of each plan, students begin to fill in their tables with their partner or group exploring each of the types of taxes and the effect on the overall price of the item.

      After completing the tables- students will share their favorite plan and answer the questions.

      Part 3 (Student)

      Students begin finding the total revenue for a 1, 1.5, or 2 cent tax on fluid ounces (Plan 1) using the population of Oregon.

      Plan 1: (at 1.5 cents per fluid oz)

      \(56 gal\times\frac{128oz}{1gal}=7168oz\)

       7,168 oz · $0.015 = $107.52 (money raised in taxes per person each year)

      $107.52 per person · 4,093, 465 people = $440,129, 356.80 (total yearly revenue)

      Money to education ~ Method 1:

      • $440,129, 356.80 · 0.65 = $286,084,081.9

      Method 2:

      \(\frac{65}{100}=\frac{x}{$440,129,356.80}\)

       100x = 440,129, 356.80 · 65

      x = $286,084,081.92

      Plan 2: (at 18% of retail cost)

      • Step 1: The average household (2.6 people) spend $850.26 a year on sugary beverages.
      • Find the per person average expenditure ($326.92).
      • Unit rate to per person expenditure.

      \(\frac{$850.26}{2.6}=$326.92\)

      • Step 2: Use the per person expenditure to determine the annual per person tax. For example, 18% of the beverage costs.
      • Proportion:

      \(\frac{18}{100}=\frac{x}{$326.90}\)

      • Multiplication:
      • 18% of $326.90 = (18/100) (326.90)
      • Step 3: At 18%, each person is going to spend an additional $58.85 a year. The population of Oregon is 4,093,465. To determine the potential tax revenue, multiple the per person revenue by the state  population.
      • The potential revenue is $240,900,415.30

       

        SUMMARIZE - CLOSE

        Suggested Grouping:

        Class Discussion

        Teacher Summary:

        • Based on your data, which tax option would you propose and why?
        • Discuss the benefits and drawbacks of each method.

        Student Moves:

        • Share ideas with partner, group, or as a class.

        Exit Task:

        Show and explain your mathematical reasoning on the following problems.

        Starbucks Frappuccino is 13.7 fluid ounces, has 46 grams of sugar, and costs $2.99.

        1. How much would the drink cost if you added a 2-cent per fluid ounce tax?

        Answer: $3.26

        2. How much would the drink cost if you added a 15% tax to the cost?

        Answer: $3.44

        3. How much would the drink cost if you added a tax of 0.75 cents per gram of sugar?

        Answer $3.34

        Extensions:

        1) Find the total revenue for Plan 3. See KEY for method of determining potential revenue.

        2) Have students determine and explore an additional tax option. Assess the reasonableness of the impact of the tax on the beverage cost and the potential revenue for the plan.

        3) Have students conduct a survey on the prices they would pay for each beverage in the provided sample. Have students examine the range, determine the outliers, and find the mean, median, and mode of the data. This data can be used to examine the various tax options.

        Notes/Reflections/Suggestions:

        Teachers could choose to do just Part 1 OR Part 1 & 2 OR Part 1 & 3.
        Part 2 could be given as homework if students had good examples written down in Part 1.

        References:

        NPR article:
        http://www.npr.org/sections/health-shots/2011/01/10/132814924/for-teens-too-much-sugar-can-be-a-heartbreaker

        Fructose content in popular beverages made with and without high-fructose corn syrup
        https://www.sciencedirect.com/science/article/pii/S0899900714001920

        Breaking Down the Chain: A Guide to the Soft Drink Industry
        http://www.changelabsolutions.org/sites/default/files/ChangeLab-Beverage_Industry_Report-FINAL_(CLS-20120530)_201109.pdf

        Oregon census information
        https://www.census.gov/quickfacts/fact/table/OR/PST045219

        Averages of beverage consumption
        https://adage.com/article/news/consumers-drink-soft-drinks-water-beer/228422

        News Clip: Philadelphia Council Passes Sweet Drink Tax

        Optional hook: PodCast: Should Sugar Be Regulated Like Alcohol? (18 mins)

        Australia – sugar tax: https://www.abc.net.au/btn/classroom/sugar-tax/10524986

        Slideshow- how much sugar in each drink?
        https://www.cnn.com/2016/11/01/health/soda-tax-benefits-mexico/