The Global Village Investigation
In this investigation, students explore the world's populations to analyze and understand the people in the world, access to and allocation of resources, and the local and global questions raised by their new learning. The Global Village builds on students' prior knowledge about global demographics such as age structure, religion, and geography to support their work with real-world data as they solve daily "demographic puzzles." These ratio puzzles engage students in proportional thinking, equivalent ratios, elimination, percents, and solving for variables.
Through collaborative work and discussions, students make mathematical and social meaning of their work in the context of answering the larger, driving questions:
Who in the world are we?
Who makes up our global community and
why should we care?
How do we represent global demographics?
6.RP.A.1, 6.RP.A.3, 6.EE.A.2
6.EE.C.6, 6.NS.1
MP.1 MP.3 MP.4
Key Mathematical Ideas
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Ratios and percent
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Division and Multiplications of fractions
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One-step, one-variable equations
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Data distribution
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Visualizing data
Measuring Diversity Investigation
In this investigation, students explore different ways to measure the diversity of a population. Students learn about the religious diversity Index (RDI) developed by the Pew Research Center to rank countries and populations by their level of religious diversity. Using datasets that contain the religious makeup of countries around the world, students match various countries with mathematical representations (e.g., histograms, pie charts) and further analyze the religious diversity in the countries of their choice.
Afterward, small groups analyze the religious diversity of one state in the USA and visually represent this diversity by proportionally coloring the state according to the different religious representations in their state. At the end of this project, students compile their states and create a complete map of the United States that visually represents the country's religious diversity. Students learn about scale, proportions, composing and decomposing shapes, and mathematical modeling in this process.
Throughout this process, students compare and discuss their findings with peers and draw conclusions about the advantages and disadvantages of living in areas with low or high religious diversity levels.
What is diversity?
How can we visualize diversity in a geographic map?
How can we use math to measure and better understand diversity in a population?
What are the advantages and disadvantages of living in areas with low or high levels of religious diversity?
6.SP.A.1-3, 6.SP.B, 4, 6.RP.A.3, 6.G.A.1
MP.1, MP.2, MP.4
Key Mathematical Ideas
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Data & Measurement
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Ratio and rate reasoning and Percent
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Area and Surface Area
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Geometric Shapes (composing and decomposing)
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Visualizing data
Microlending Investigation
In this investigation, students explore concepts relating to poverty in developing and developed nations and are introduced to the notion of microfinance, the practice of lending small sums of money at a low interest rate to allow financially marginalized people to start businesses. Students analyze several of such loans using loan applications from Kiva.org and create a visualization of Kiva’s loan cycle. In small groups, students explore Kiva’s loan applicants and choose a person or group to whom they would like to provide a loan. Students use various indicators that help them provide mathematical reasoning to support their choice of the applicant(s). At the end of this investigation, students create a proposal to their school and community, demonstrating the impact of collective lending power.
How can we provide loans so they have the most impact on people’s lives?
How can mathematical analysis help us decide to whom we give the loans?
How can we use mathematical reasoning and evaluate whether a loan is a high or low risk for both the borrower and lender?
7.RP.A.1-3, 7.SP.B, 4, 6.RP.A.3, 6.G.A.1
MP.1, MP.2, MP.4
Key Mathematical Ideas
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One variable equation and inequalities
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Ratios, unit rates, and percent
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Simple interest rate
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Expected value
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Positive and negative numbers
Forced Away From Home
Investigation
Forced Away From Home taps students' curiosity and empathy, and links math to the real-world challenge of the millions of people who have been displaced from their homes due to war, political unrest, climate change, economic trouble, or religious persecutions. This investigation focuses on designing refugee camps in various host communities and pays specific attention to the refugees' water and community needs living in these camps. Students have the opportunity to build on their own experiences of community, daily water use, and cultural needs.
Forced Away From Home focuses on three mathematical areas: modeling with mathematics, ratio and proportional reasoning, and making informal inferences about populations. Through collaborative work and discussions, students make mathematical and social meaning of their work in the context of answering the larger, driving questions:
What conditions force people from their homes?
How do we design communities for displaced people?
What does it mean to be "forced from home?"
What people in the world have been forced from home?
7.RP.1, 7.RP.2, 7.G.A.1-2, 7.G.B.3, 7.G.B.6,
Key Mathematical Ideas
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Proportional reasoning,
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Constant of proportionality and, unit rates
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Converting units
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Scale drawing & scale factor
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Area, volume, and surface area
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Comparing two populations
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Positive and negative numbers
8
Population Dynamics
Investigation
Students explore mathematical models that illuminate human population dynamics across the globe. Students examine patterns of change in specific regions and use models such as doubling rates and half-time rates to make predictions about population growth and decline. The investigation culminates with a debate on whether or not countries should create policies that regulate the population. A series of sequenced mathematical explorations prepare students to make informed positions for this debate.
Through collaborative work and discussions, students make mathematical and social meaning of their work in the context of answering the larger, driving questions:
What is the world’s population? How do we know?
How can we predict the human population in the future?
Is there a maximum carrying capacity for the earth?
How will population dynamics impact the environment?
Should countries enforce policies that regulate population growth?
8.SP.A.1-4, 8.F.A, 8.F.B, F.BF.1, F.IF.
MP.1, MP.2, MP.4, MP.8
Key Mathematical Ideas
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Associations in bivariate data
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Dependent and independent variables
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Modeling relationships with functions
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Lines of best fit
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Linear equations, graphs, and slopes
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Exponential functions/growth
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Population change
Measuring Human Rights
Investigation
In this investigation, we focus on the human right to adequate food. Investigators unpack the complexities of using quantitative indicators to measure the degree to which this human right is attained.
Students begin by developing their indicators to measure the right to adequate food. After discussing the merits and drawbacks of the class-generated indicators, students examine, evaluate, and use the United Nations (UN) indicators : (1) the prevalence (in %) of children < 5 who are underweight and, (2) the percent of adults with body mass index (BMI) < 18.5.
Mathematical modeling and descriptive statistics are at the core of this investigation. As investigators unpack these indicators, they are confronted with challenging notions. For example:
How can we use math to measure human rights?
What are indicators to measure the right to adequate food?
How do we use children's weight and adults' BMI to determine the wellbeing of a population?
What is normal weight? How do we know? Who decides?
How can we apply our learning to local food security?
S.ID.1, S.ID.2, S.ID.4, S.ID.4, S.ID.5, S.ID.6, S.CP.4, S.CP.5
MP.3, MP.4, MP.5
Key Mathematical Ideas
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Analyzing and representing univariate data
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Dependent and independent variables
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Categorical and quantitative data
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Two ways frequency table
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Measurement of center and distribution
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Conditional probability
