Innovative Math Lesson on Fighting Hunger in the Community

1. Food For Thought A NSF SPONSORED MSP PROFESSIONAL DEVELOPMENT OPPORTUNITY THROUGH GEORGE MASON UNIVERSITY Michele Panczyszyn Becky Pierce Willow Springs Elementary Willow Springs Elementary Fairfax County Public Schools Fairfax County Public Schools Mary Anne Rossbach Cortney Barnes Sunrise Valley Elementary Halley Elementary Fairfax County Public Schools Fairfax County Public Schools

2. Introducing the Mathematical Modeling Task Setting the Stage: Sixth graders brainstormed for ways that they could ‘give back’ to their communities. All students felt strongly about helping fight hunger. In fact, many of them have had experience already helping those in need through scouting organizations and faith communities. So, this problem-based unit capitalized on their interest in making a difference in the community by providing food for those in need.   Although we anticipated several directions our students would go, we knew that this journey would take on the life that our students breathed into it.

3. “I used to think...but now I think…”

4. “1 out of 5 children don’t know where their next meal will come from.”

5. “1 out of 5 children don’t know where their next meal will come from.” How can we use MATH, as we work together to help solve this community problem?

6. The Essential Mathematics • Students, in the process of problem solving, will draw upon several mathematical standards. Some such standards may include proportional reasoning, computation of rational numbers, data and statistics and measures of central tendency.   • SOLs • Number and Number Sense: • 6.1 The student will describe and compare data, using ratios, and will use appropriate notations. • 6.2  The student will • investigate and describe fractions, decimals, and percents as ratios; • identify a given fraction, decimal, or percent from a representation; • demonstrate equivalent relationship among fractions, decimals, and percents; and • compare and order fractions, decimals, and percents. • Computation and Estimation: • 6.6  The student will • multiply and divide fractions and mixed numbers; • estimate solutions and then solve single-step and multi-step practical problems involving addition, subtraction, multiplication, and division of decimals. • 6.7  The student will solve single-step and multi-step practical problems involving addition, subtraction, multiplication, and division of decimals. • 7.4  The student will solve single-step and multistep practical problems, using proportional reasoning. • Probability and Statistics: • 6.15  The student will • describe mean as a balance point; and • decide which measure of center is appropriate for a given purpose. GMU COMPLETE Center

7. The Research Lesson Engage: Posing a mathematical task How can you, as sixth graders, help eliminate hunger in our local community? GMU COMPLETE Center

8. EXPLORE: Information Gathering Variables we considered Variables the students considered • Community size • Community needs • Food pantries in the area • Possible initiatives that students might propose to support the community • Possible ways students might present their project • Size and need of the community at the local, state, and national levels • Ways to get food to the needy • Fundraising ideas • Food delivery ideas • Ways to raise awareness • Presentation formats to serve as proposals for implementation of one or more of the projects GMU COMPLETE Center

9. EXPLAIN: Assumptions and Constraints • Anticipated Assumptions/Givens • There are several food pantries in a given area in Fairfax County. • Food pantries provide food items and other services to those in need. • People in need go to the food pantry; not just the homeless. • Kids’ Assumptions • Not only people in shelters need food • There is lots of food waste, which could possibly be donated • Food production could fill the deficit of lacking food • Commercial restaurants could donate food • This is a community problem that could/should be solved collaboratively • There are single parent households • Households are on fixed budgets • There are people with jobs and homes who are hungry • There are many ways to help, including: volunteering, cleaning, fundraising, donating and holding service days GMU COMPLETE Center

10. ELABORATE: Build Solutions • The problem was posed: • “How can you, as sixth graders, help eliminate hunger in our local community?” • Then the students were given a 35-40 minute work period to brainstorm possible solutions, and use research, as needed. GMU COMPLETE Center

11. GROUP IDEAS Group One Group Two Explored how many hamburgers McDonalds makes per second, so if, for every 10 hamburgers sold, they gave one to someone in need, how many hamburgers would that be per day? • Explored how many pounds of food are wasted. Once they had the number of pounds, they divided it to find out how many pounds for Fairfax County. • Explored if they could divide the number of pounds by the number of food pantries to find out how many pounds each would get, if it was distributed to them. • Explored if there could be more farms to grow food/raise cattle to help feed, if there is still a deficit, after all of the wasted food is distributed. GMU COMPLETE Center

12. GROUP IDEAS Group Three Group Four Explored about family income, particularly for a single mom, and how that would allow her to purchase food for her family.  After researching and computing, they calculated how much in debt she would be, even before all of the components of a monthly budget were factored in. • Explored how many people of need are in Fairfax County. • Explored, if 1 out of every 3 families is in need, and if it costs $175/month to feed a family, how much would it cost to feed everyone in Fairfax County who is hungry. GMU COMPLETE Center

13. GROUP IDEAS Group Five Group Six Explored what the population in Fairfax County is. Explored what the average family pays for food each day. • Explored what the average sized family is, and when they found out it was 4, how much money would be left over each month to buy food. • Explored how many people actually go hungry. GMU COMPLETE Center

14. EVALUATION: Validate Conclusions • How did students justify their solutions for the mathematical modeling task? • Michele and Becky’s Classes • Students created PowerPoint presentations including their research and proposals for how to solve the problem of hunger in their community. These presentations included their mathematizing processes for solving the problem of hunger in their communities. • Mary Anne’s Class • Students created electronic proposals, including their solution/goals, their research findings, mathematizing, and processes for solving the problem of hunger in the Reston community, that are going to be presented, and voted on so that the class can take action, as soon as possible! • Cortney’s Class • In groups, students researched the population of the Lorton community and by using proportional reasoning based on statistics from the “No Kid Hungry” national campaign, extrapolated the number of hungry children in their community. They then developed plans on how to support the need in their area. They are continuing to develop the logistics of their plans and vote on the most feasible plan for implementation. GMU COMPLETE Center

15. Sharing the outcomes: Ideas: How did your task engage students in doing mathematics? Wow! Here’s some of what the students said… “It made me think about all that I have at home and how much I don’t really need” “I used to think only a few people were hungry, now I know that a lot of people are hungry” “People that are hungry look like us, they just do not have food” “People that are hungry are not just the ones who live in shelters” GMU COMPLETE Center

16. Sharing the outcomes: Ideas: How did your task engage students in doing mathematics? Math Talk! “We have to find a way to help the 20%” “So, for every 100 people, there are 20 that are hungry!” “Look up the population, we can figure out 20%” “Look up how many restaurants are in Virginia, see if you can find out how many people eat at those restaurants a day. We can pick a restaurant and see if people donated $1 from every meal how much money we can make.” “It costs $31.70 per day to feed a family. What food would be the healthiest to buy for that amount?” “How much does it cost to feed the 930 kids in Lorton for a month?” GMU COMPLETE Center

17. Students engaged in processing the problem of hunger in our community. GMU COMPLETE Center

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20. What’s out there? What’s sustainable? GMU COMPLETE Center

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22. Student demonstration of new understandings and skills. Students were able to use ratios and proportional reasoning to estimate the population of hungry children both in a classroom of 30 students, a school, and their home communities. They used multiple strategies and processes while reasoning proportionally in an authentic setting. Students used research skills to gather data from multiple sources. In making sense of their research, they interpreted graphs, charts and tables to gather information about the hungry children in their communities. A powerful goal leads to a powerful product! The learning goal for this lesson is to use math to solve the authentic problem of hunger in their communities. The learning product is the implantation of a feasible, well-planned service project. GMU COMPLETE Center

23. REFLECTING on our role, as teachers, in the process

24. We learned how compassionate and dedicated our children are. The problem took on a life of its own in each of the four classrooms. Students reveled in the open-endedness of the problem and were empowered by the opportunity to make a difference. There were numerous opportunities for mathematizing and subsequent direct math instruction to support their planning and solution posing, which varied within the four classrooms. All four teachers continually assessed math understandings, misconceptions and applications of the content in order to meet individual, group, and whole class needs(anticipating, enacting, monitoring, and revisiting cycle). When students are given rich problems, their engagement is over the top! REFLECTING on our role, as teachers, in the process GMU COMPLETE Center

25. Next Steps • Becky and Michele’s students will be collecting food items for a local agency and making backpack lunches starting the week of Thanksgiving. • Mary Anne and Cortney’s classes are still developing their proposals which will result in determining the solutions that they will have the opportunity to implement. GMU COMPLETE Center

26. “I used to think...but now I think…”