Rebecca Davis sets up a coordinate plane on the floor of her classroom. Groups of 3 or 4 students are assigned equations in slope-intercept form and graph them using their bodies on the giant coordinate plane. As extensions, Ms. Davis changes the slope or y-intercept of the original equation and makes the activity into a race.

This lesson teaches about Rates, Ratios, and Unit Rates, using visually appealing art and real-life examples that will engage teenagers.

In this seminar you will have a better understanding of how to identify and write ratios and proportions,understand their relationship to each other, and use them in real-world contexts.StandardsMathematical PracticeCC.2.1.HS.F.2Apply properties of rational and irrational numbers to solve real world or mathematical problems.MP.1. Make sense of problems and persevere in solving them.MP.4. Model with mathematics.MP.5. Use appropriate tools strategically.

Students overlay USGS topographic maps into Google Earth’s satellite imagery. By analyzing Denali, a mountain in Alaska, they discover how to use map scales as ratios to navigate maps, and use rates to make sense of contour lines and elevation changes in an integrated GIS software program. Students also problem solve to find potential pathways up a mountain by calculating gradients.

Planning for the future is a difficult task for most. This lesson ask the learner to participate in role-play and to assume the role of someone who has just graduated and accepted a job and to develop a budget where the goal is to save for a vacation to be taken in a year’s time. The role that the learner is asked to assume is Madison. The name was chosen specifically because it is a unisex name. The character, Madison, has just graduated, but the story intentionally does not reveal the credential that was achieved. The learner is asked to develop a budget with the salary and withheld taxes already established. For learners living in a rural area, the salary may seem high for a recent graduate, but for a learner from an urban area, the salary may seem low. Along with assuming this identity comes the tasks of making decisions for him/her. The actual math problems have definitive answers which are provided for the instructor, but the decisions enable the learner to develop a unique budget. Unit rate is used to help the learner visualize the decisions that are made on a daily basis that may impact savings. Problems included ask the learner to make decisions about housing, transportation, health, and spending. The variety of problems enable the learner to compute unit rates and understand how quantities can be measured in different units. The instructor is a facilitator only, examples of calculations are included in the materials for guidance.

The principal purpose of the task is to explore a real-world application problem with algebra, working with units and maintaining reasonable levels of accuracy throughout.

In this problem-based learning module, students will raise awareness about the amount of excess food wasted each day in America’s schools highlights the consumptive mindset that our county has.  Each day in third world countries, as well as our own, children go without the proper nutrition needed to focus on other activities. This module will raise student awareness about the amount of food taken from the service line and then placed in waste receptacles.  Students will gather and analyze data regarding wasted food in an attempt to design a solution to reduce food waste. Sation rotation will allow to conduct research into the global problems associated with the lack of food and malnutrition. Mathematical skills will be required to calculate rates and percentages of consumption which will be used for analysis.