### Top Math Categories

#### Curriculum Titles

OVERVIEW

In this MATH *Expedition*, students analyze data concerning population growth and available resources for a fictional city. They create and graph linear and exponential functions from the data to determine trends.

ESSENTIAL QUESTION

How do population growth, employment growth, and resource availability affect people’s decisions in relocating to an urban setting?

OVERVIEW

In the *Building with Patterns* MATH *Expedition*, students examine patterns used to build and design tetrahedron and box kites. The patterns include both physical and economic models that are associated with building both styles of kites. Students build a base model and then expand the model to more complex arrangements.

ESSENTIAL QUESTION

How can functions help investors make wise decisions?

OVERVIEW

In the *Built to Last* MATH *Expedition*, students work as chief engineers of a high-rise construction project that is having to make adjustments to the project due to earthquake concerns.

ESSENTIAL QUESTION

What ways can math be used to predict how best to maintain safety while minimizing costs in building construction?

OVERVIEW

In this MATH* Expedition*, students compete as designers of bungee cords, using rubber band chains as their bungee cords. The students create three bungee cords: one that will allow for the fewest measurable bounces of a mass, one that will allow for the greatest number of measurable bounces of a mass, and one that will allow for a mass to come closest to the ground without any part of the mass touching the ground. To create the best design in each category, the students conduct a series of tests on several types of rubber bands. Then, they graph and analyze their data to determine any linear or exponential relationships.

ESSENTIAL QUESTION

What can make a regular bungee jump even more exciting?

OVERVIEW

In this MATH *Expedition*, students design a competitive and fair dragster competition. Throughout the *Expedition*, students use measurement and units to guide them as they decide on rules for the competition, what kind of design specifications or constraints to place on the dragsters, how winners will be determined, and how race results will be communicated. Several experiments with the AP Mini Dragster and its launch system are conducted. Students use the data from these experiments to determine appropriate units for measurement and use dimensional analysis to convert units from one measurement system to another. Students also investigate the roles that accuracy and precision play in making the competition fair for all participants.

ESSENTIAL QUESTION

What factors contribute to the design of a competitive, yet fair, competition?

**OVERVIEW **

The 2007 Intergovernmental Panel on Climate Change (IPCC) Report describes causes, effects, and ways of dealing with climate change resulting from global warming. In *Climate Change*, students are introduced to the IPCC Report. They learn the effect of carbon dioxide and other greenhouse gases on global temperature increase. Then, they use graphing, polynomials, and matrices to analyze data from the report and develop possible carbon mitigation strategies.

STUDENT OBJECTIVES

- Learn factors causing climate change.
- Explore effects of climate change on weather, people, and ecosystems.
- Use software to create graphs of temperature and CO2 changes.
- Learn to add, subtract, multiply, and divide polynomials.
- Set up polynomial equations describing factors causing global warming.
- Measure the albedo of different colored surfaces.
- Measure and graph rates of ice melt and water-level rise.
- Learn addition, subtraction, and scalar multiplication of matrices.
- Use matrices and polynomials to describe possible carbon mitigation strategies.

**ACTIVITIES**

*Students complete three performance assessments: 1) Data Analysis – show polynomials describing factors that cause global warming and show and explain graphs of temperature and CO2 changes over time; 2) Rates of Change – calculate rates of change and show graphs of data collected on ice melt and water-level rise; and 3) Polynomials – solve polynomial equations, add and subtract matrices, and explain their own carbon mitigation solution.*

OVERVIEW

In this MATH *Expedition*, students use systems of equations to help them make decisions related to designing, building, and maintaining a roller coaster. Students have the opportunity to design and construct a final roller coaster model based on smaller experiments and energy calculations.

ESSENTIAL QUESTION

What are some important factors roller coaster engineers need to consider when designing a new roller coaster, and why are these factors important?

OVERVIEW

In this MATH *Expedition*, students learn how to rearrange formulas to highlight a quantity of interest and solve the equations, explaining and justifying each step as they solve them. Students use the Ohm’s law formula for resistance, current, and voltage, as well as the distance formula. Students are asked to act as technicians on a racing team that uses electrical motors to power their vehicle. They are asked by members of the racing team to apply mathematical properties to rearrange the formulas that apply to a situation to examine different values of interest.

ESSENTIAL QUESTION

How does rearranging the formulas for electrical properties help to identify which variables improve the performance of an electric vehicle?