mathematical explorations classroom-ready activities rethink your Drink Caroline b. ebby THiNKSTOCK edited by Barbara Zorin, drbzorin@ gmail.com, MATHbonesPro, and carrie Fink, cfink@methow.org, liberty bell Junior-Senior High School, Winthrop, Washington. Submit manuscripts through http://mtms.msubmit.net. a Part Although most students are probably aware that soft drinks are not good for their health, they may not be aware that other drinks, such as fruit juice and flavored milk, often have just as much sugar. The activities in this article give teachers a way to introduce some important nutritional information to students while engaging them in exploring ratio, proportion, data analysis, and measurement important mathematical concepts in the Common Core State Standards for Mathematics (CCSSI 2010). By investigating and representing the sugar content of popular beverages, students can use their developing mathematical skills to investigate a relevant real-world problem while developing critical life skills, such as reading a nutritional label and using data to support an argument. The activity is described in three parts and can typically be completed in two class periods or extended over several lessons and content areas. 1: gathering students initial ideas In the days preceding the activity, students can be asked to bring in empty containers of their favorite beverages. Students are then shown a variety of popular drinks, including sodas, ice teas, sports drinks, energy drinks, juices, and flavored milk, and asked which they think is the healthiest beverage. There is no one right answer to this question; students may focus on calories, sugar content, artificial ingredients, caffeine, vitamins, and so on. Projecting images of popular drinks on a screen is also an effective way to frame the conversation because many labels are designed to make a drink look and sound healthy. At this point, the goal is to collect and record students ideas about what makes a drink healthy and introduce information found on nutritional labels. After the class has had a chance to discuss their initial ideas, the teacher can wrap up the discussion by stating that although many different factors can be considered, the activity will 242 MatheMatics teaching in the Middle school Vol. 19, No. 4, November 2013 Copyright 2013 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved. This material may not be copied or distributed electronically or in any other format without written permission from NCTM.
Fig. 1 Students focus on the sugar content in a container of chocolate milk. Nutrition Facts Serving Size 1 cup (240ml) Servings Per Container 2 Amount Per Serving Calories 170 Calories from Fat 25 % Daily Value (DV)* Total Fat 2.5 g 4% Saturated Fat 1.5 g 8% Trans Fat 0g Cholesterol 10 mg 3% Sodium 160mg 7% Potassium 400mg 11% Total Carbohydrate 29g 10% Dietary Fiber <1g 4% Sugars 28g Protein 8g focus on one in particular: sugar content. This is also good time to introduce some facts about sugar consumption (e.g., Harvard School of Public Health 2013) and ask students to predict which drinks have the most sugar. Part 2: How Much Sugar is That? Students determine how many grams of sugar are in each container and then represent the amounts with sugar cubes. The teacher can work through one example with the class and then distribute the remaining containers among small groups of two to four students. Finding the number of grams of sugar in a beverage container is not as simple as it sounds because most nutritional labels show the grams of sugar in one serving of the drink. Serving sizes may range from 6 ounces to 12 ounces, although most drink containers have between 12 and 20 ounces. For example, the label for a popular brand of chocolate milk (see fig. 1), lists 28 grams of sugar per serving, a serving size of 1 cup, and 2 servings per container. However, the chocolate Fig. 2 A ratio table is one strategy that students can use to find the grams of sugar in a 14 ounce bottle of chocolate milk. milk bottle actually holds 14 ounces, so to calculate how many grams of sugar are in the container, consumers have to use their knowledge of measurement equivalents (1 c. = 8 oz.) as well as proportional reasoning to make that determination. Several methods can be used to find the amount of sugar in the container: 1. Divide the grams of sugar in 1 serving by the serving size to find the grams per ounce, then multiply this number by the number of ounces in the bottle. 2. Divide the number of ounces in 1 serving by the number of ounces in the container, then multiply this number by the grams of sugar listed for one serving. 3. Use a ratio table to work from the ratio of sugar to ounces in 1 serving to an equivalent ratio of sugar to ounces in the container (see fig. 2). Each method leads to the conclusion that 49 grams of sugar are in this container of chocolate milk. It is important to note that there are no standard guidelines for how nutritional information is listed on drink containers. Some containers report the amount of sugar per serving and per container whereas many do not. As the example of the chocolate milk illustrates, the number of servings per container is often an estimate. Likewise, some container 2 2 7 Grams of sugar 28 14 7 49 Ounces 8 4 2 14 2 2 7 sizes are multiples of the serving size; others are not. Therefore, the way in which the teacher assigns the drink containers among the students or small groups can be used to equalize the difficulty level or provide for differentiation. Once students have determined how much sugar is in the container, the next step is to represent that amount concretely with sugar cubes. This part of the lesson was inspired by the SugarStacks website (http:// www.sugarstacks.com). Because each cube is equivalent to 2 grams of sugar, students can use simple division to determine the appropriate number of sugar cubes to use. The chocolate milk s 49 grams of sugar would require 24 1/2, or 25, sugar cubes. When 25 cubes are counted out and placed in a clear plustic cup, students are amazed (see fig. 3). Once the teacher has worked through one example with the class, the remaining containers are distributed. Students work cooperatively to find the number of grams of sugar and represent the amounts with sugar cubes. When they finish, they write that amount on a label (a folded index card or sticky note works well) and place the container, cup, and label on a table or other long surface. As groups finish, they order their beverages from least to greatest in terms of total sugar content (see fig. 4). Each group should also record its data on a class chart that contains columns for drink Vol. 19, No. 4, November 2013 Mathematics Teaching in the Middle School 243
Caroline Ebby Fig. 3 The sugar content in chocolate milk, as represented with sugar cubes, is a stark image. name, total ounces in the container, and ounces of sugar in the container. When students see the containers on display (see fig. 4), they are amazed at how much sugar is in their favorite drinks. Seeing a cup filled with sugar cubes gives students a concrete understanding of how much sugar they are consuming. They also discover that the container sizes differ, sometimes dramatically. This realization can lead to a discussion of why it might be important to have a standard for comparison, which is the next part of the lesson. At this point, the teacher can introduce the American Heart Association s recommendation that adolescents should not consume more than 5 teaspoons, or 20 grams, of sugar per day. This information gives students a new reference point. One student commented, This bottle of Sprite has enough sugar for 3 days! Students will find that few nondiet beverages contain less than 20 grams of sugar in a single bottle or can. (A few options include coconut water, the Honest Tea brand, and vitaminwater.) This is also a good opportunity to discuss the importance of considering container size when selecting beverages. PART 3: EXPLORING UNIT RATE As students are viewing the containers on display, the class can discuss how the amount of sugar can be more accurately compared when the sizes are so different. Students may suggest either using a standard serving size, such as 8 ounces, or finding the amount of sugar in 1 ounce, or a unit rate. Depending on the time available and grade-level goals, the teacher can ask students to go back to their groups to calculate the unit rate for the entire list, dividing the work among the groups or entering the data into a computer program. Students who have not been formally introduced to proportions can reason about unit rate when it is presented concretely. For example, one student used a process of halving to calculate a unit rate: If an 8 ounce container of orange juice has 24 grams of sugar, then 4 ounces has 12 grams, 2 ounces has 6 grams, and 1 ounce has 3 grams. Once students have determined the unit rates, they can reorganize the display of containers (or use a second set) to see how the order changes. See the example shown in figure 5. After students calculated the unit rates, the teacher entered the results into an Excel chart, created a graphical display, and projected the data to begin the second day of the activity. The students could compare this graph with the display from the previous day to see how comparison by unit rate changed the ordering. For example, a 32 ounce bottle of Gatorade had 56 grams of sugar but only 1.8 grams of sugar per ounce; therefore, this drink moved much lower in the list. Students could also see how certain categories were grouped together. For example, fruit juices tended to have around 3 grams of sugar per ounce, and sodas contain between 3.2 and 3.5 grams. Extensions The results that are generated from comparing the amount of sugar in popular beverages are surprising for most students and adults alike. Beverages that we think of as being healthy, such as cranberry cocktail and flavored milk, turn out to have the most sugar per ounce. Even fruit juices with no added sugar have an amount of sugar on par with most sodas. Drinks that tend to be sold in larger sizes, like ice tea and soda, have staggering amounts of sugar (a 20 ounce bottle of grape soda has a whopping 59 grams of sugar). When the results of this lesson Fig. 4 Sorting various beverages from least to greatest on the basis of sugar content provides a healthy dose of not only mathematics but also real-life knowledge about sugar consumption. Caroline Ebby 244 Mathematics Teaching in the Middle School Vol. 19, No. 4, November 2013
Fig. 5 Graphing sugar content provided another mathematical outlet during the exploration of grams of sugar per ounce. to developing healthy citizens and intelligent consumers. are combined with current recommendations and statistics, the lesson can be extended across the curriculum to health, science, language arts, and social studies. Students can use the findings from this activity to practice using mathematics to make and support an argument, which is an important aspect of CCSSM. See the following suggestions for extensions: Should beverage companies list the number of grams of sugar and calories per bottle, per ounce, or per serving? Why? What is the sugar content of the beverage options that are available in the school, cafeteria, or corner store? The Harvard School of Public Health recommends that sugaradded beverages with more than 50 calories in an 8 ounce serving should carry a warning label about obesity and diabetes. Do you agree? Some cities are trying to pass laws that would tax or limit the size of sugary drinks sold. Do you think this a good idea? What is the relationship between sugary drinks and the development of type 2 diabetes? How have statistical arguments been used to expose that link? (See, for example, Schulze et al. 2004.) These activities were created for the Community Based Math Project, a group of university and school-based educators who collaboratively design mathematics curricula to reflect the local community to increase access to important mathematics, institutions, and critical ways of thinking (Ebby et al. 2011). Exploring the context of sugar content in popular beverages elicits critical thought about nutri tion and lifestyle choices while engaging stu dents in real-life mathematical explorations. Although this lesson may not lead directly to a change in patterns of beverage consumption, it allows students to develop a way to make sense of nutritional information, analyze their options, and make more informed choices at the vending machine or corner store. Students also gain an appreciation for the role of mathematics in making sense of and analyzing the world around them. Perhaps most important, teachers note that students are engaged throughout this lesson and that they often go home and talk about the results with their families. Investigating the sugar content of popular beverages is a context that can generate interest, promote an understanding of important mathematics, and provide information that is critical references Common Core State Standards Initiative (CCSSI). 2010. Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/assets/ CCSSI_Math%20Standards.pdf Ebby, Caroline, Vivian Lim, Luke Reinke, Janine Remillard, Emily Magee, Nina Hoe, and Maya Cyrus. 2011. Community Based Mathematics Project: Conceptualizing Access through Locally Relevant Mathematics Curricula. Perspectives on Urban Education 8 (Spring): 11 16. Harvard School of Public Health. The Nutrition Source: Sugary Drinks and Obesity Fact Sheet. http://www.hsph.harvard.edu/nutritionsource /sugary-drinks-fact-sheet/ Schulze, Matthias B., JoAnn E. Manson, David S. Ludwig, Graham A. Colditz, Meir J. Stampfer, Walter C. Willett, and Frank B. Hu. 2004. Sugar-Sweetened Beverages, Weight Gain, and Incidence of Type 2 Diabetes in Young and Middle-Aged Women. Journal of the American Medical Association 292 (8): 927 34. SugarStacks.com. 2009. Sugar Stacks: Would You Eat a Stack of 16 Sugar Cubes? www.sugarstacks.com caroline B. ebby, cbe@gse.upenn.edu, is a lecturer at the Graduate School of education, University of Pennsylvania, and senior researcher at the Consortium for Policy research in education (CPre). She is co-director of the Community based Math Project, a group of university faculty, graduate students, and middle school math teachers who design and adapt locally relevant mathematics curriculum to increase access to math for urban youth. Her research focuses on using formative assessment to improve math instruction. Vol. 19, No. 4, November 2013 MatheMatics teaching in the Middle school 245
activity sheet 1 RETHINK YOUR DRINK: ANALYZING SUGAR CONTENT Materials Drink containers (with nutritional labels) Clear plastic cups 100 sugar cubes Index cards or sticky notes Name Part 1 For each container that you were given, find or calculate the following information. Record your results in the table. Pay attention to the size of the container and the serving size. 1. Size of the container in ounces 2. Serving size listed on the nutritional label 3. Grams of sugar in one serving of the beverage 4. Total grams of sugar in the container 5. A sugar cube is 2 grams of sugar. Determine the number of sugar cubes that you need to equal the amount of sugar in the container. Record your results in the chart below. Drink Name Container Size (oz.) Serving Size (oz.) Sugar in 1 Serving (g) Total Sugar in Bottle (g) Number of Sugar Cubes 6. Explain how you determined the total amount of sugar in each container. 7. For each drink, make a label to show the total grams of sugar (on a folded index card or sticky note). Then fill a clear plastic cup with the appropriate number of sugar cubes. Place the container, cup, and label on the display table. 8. What observations can you make about the information in the class display? Did anything surprise you? from the November 2013 issue of
activity sheet 1 (continued) Name 9. Choose one beverage. How many grams of sugar are in 1 ounce of this drink? Show your calculations. 10. Record the class data in the chart below from least to greatest in terms of grams of sugar per ounce. Drink Name Sugar in Bottle (g) Container Size (oz.) Sugar per Ounce (g/oz.) 11. Use the information in the class chart to create a bar graph below. grams of Sugar per Ounce of Our Favorite Drinks 12. What observations can you make from the graph? 13. How can this information help you make healthy choices about what to drink? from the November 2013 issue of