Academic skills & content: Writing and Evaluating Algebraic Expressions, Making predictions based on statistical data. The statistics from the previous week’s games such as offensive yards and turnovers.
Final Product(s): The final product was the victory of two groups who tied or did better than the professionals. Two seventh grade students stood up at the podium in front of over 350 guest and explained the process that professionals used to make predictions and set odds for NFL games. Then they explained their own process to the audience and how they beat “Vegas”. After they spoke, it was cool to watch grown men walk up to my female students to ask them for their formulas. One of whom asked me “What does the quarterback do?” at the start of the project.
This is how we Create the Expression
This is how we Gather the data
Suggested Duration: The project should run in two stages. Four weeks collecting data, and four weeks to make predictions (8 weeks total).This project could run for the entire NFL season if students wanted to continue independently or as a whole class.
This project was created with the generous support of the Avalon Foundation.
The students brainstormed ideas for the exhibit. They voted on their top three favorite ideas. One class period went out to the exhibit space to informally map out the amount of space to determine the maximum number of exhibits possible. They narrowed down the ideas to the top 13 (a feasible amount with space and group size). The students self-selected an exhibit of their interest to work on.
Created with the support of the California Department of Education California Career Pathways Trust
]]>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
]]>- Calculate the cheapest location for an airport,
- Find the center of a circular garden when they only know the location of 3 trees,
- Craft an evidence based argument for where a cell tower should be placed to restore service,
- Determine the likelihood of landing in different regions on a dart board and come up with a sequence of throws to earn a specified number of points,
- Locate the center of a fountain inside a koi pond AND find out how long each option really is at baseball conditioning practice
Item #6 is a chance for students to be creative and design their own scenario which includes a map, storyline, and construction. This piece encourages creativity! To round it out, they are also asked to complete an overarching reflection piece to help them practice an analysis of their experience and practices they engaged in.
Academic Skills and Content:
- Triangle center constructions,
- creating and solving linear equations,
- applying properties of midsegments,
- calculating and comparing: costs, distances, areas;
- reading comprehension and interpretation,
- written communication of student ideas with mathematical vocabulary
Final Product: Students submit all six parts as a portfolio demonstrating their learning in these topics. The last item has the option of being hard-copy, electronic, or a hybrid.
Suggested Duration: 2 weeks
Created with the support of the California Department of Education California Career Pathways Trust
]]>- How might we use mathematics to solve real problems in our communities?
- How can we inspire students to solve problems and bring change to their community?
- How can we make our voices heard to spark the change needed?
Academic Skills and Content: Using systems of inequalities, students bring awareness to local issues by creating a city map with the affected areas shaded. Using geometry and constructions, students design and create decals that bring awareness to the issues they care most about. The project culminates in a community presentation bringing awareness to their concerns through their work.
Final Products: a city map of community problems, and decals designed to raise awareness of specific local issues.
Suggested Duration: one semester
Created with the support of the California Department of Education California Career Pathways Trust
]]>Final Product: a poster displaying your findings.
Suggested Duration: Eight weeks
Created with the support of the California Department of Education California Career Pathways Trust
]]>In the Electioneering Project… students answer the questions “does my vote matter?” and “what is fair?” by analyzing how well their local congressional districts, and voting systems, represent the will of the people.
Academic skills & content: students learned various methods of measuring compactness, applying visual and spatial reasoning, geometric ratios and areas, and optimization to manipulate several variables while meeting real world constraints; voting criteria including Pareto, Monotonicity, and Independence of Irrelevant Alternatives; sequences and series in proportionality and the efficiency gap. Students studied voting theory, group theory, social choice theory, and topology.
Final products: all students create a poster explaining an existing voting system. In addition, students choose whether to develop and test their own new voting system, or to redraw congressional districts in order to make them more compact.
Suggested duration: 12 weeks
Created with the support of the California Department of Education California Career Pathways Trust
]]>You can create the world you want to see and be a part of. You have that power. We’ll paint one happy little tree right here. Here’s another little happy bush We can always carry this a step further. There’s really no end to this. If you don’t like it – change it. It’s your world. We don’t have to be committed. We are just playing here.
Created with the support of the California Department of Education California Career Pathways Trust
]]>Academic skills & content: Bivariate statistics, trend-lines, correlation, r-squared values, and residuals.
Final product: Student groups publish magazines and newspapers with articles, graphs, and infographics derived from data gathered in their original research.
Suggested duration: 2 to 4 weeks.
Created with the support of the California Department of Education California Career Pathways Trust
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