We make choices that balance risks and rewards everyday. Some of these choices are small. In a soccer game, you might choose how to wrestle the ball away from your opponent. Other choices are larger and deal with our health, relationships, the environment, and finances. When making these decisions, we weigh the potential risks and rewards and also consider the probability of different outcomes.

In **The Mathematics of Risk** students examined risk though a mathematical lens. First, they considered how slope affects the level of risk in real-life situations, such as on a slide, rollercoaster, or skate ramp. Then, throughout a Socratic Seminar, research, and iterative brainstorming, students identified a real-world decisions that force people to balance risks and rewards and that can be evaluated with probability and other statistical data. The questions at issue ran the gamut from “How do social factors and access to birth control affect teen pregnancy?” to “What should I do after high school?” to “What type of protein should I eat?” Students used the research to design a board game that used probability as well as research about their question at issue. The project culminated in a game day so that students could play their games with their families and students from another campus.

**Academic Skills & Content:**

CCSS.MATH.CONTENT.8.F.A.3: Interpret the equation *y = mx + b* as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. *For example, the function A = s2giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line*.

CCSS.MATH.CONTENT.7.SP.C.8: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

CCSS.MATH.CONTENT.7.SP.C.5: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

CCSS.MATH.CONTENT.7.SP.C.6: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. *For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times*.

**Suggested Duration:** 9 weeks

Created with the support of the California Department of Education California Career Pathways Trust