Increasing Portions, Expanding Waistlines: Exploring the Relationship Between Calories Consumed and Weight

This activity uses a 2009 study based on the book The Joy of Cooking that found portion sizes in the iconic cookbook had expanded 60% since 1936 and 33% since 1996. Students use linear functions to create models of weight as a function of calories and time, then use the models to make projections about what impact increased portion sizes may have on weight.

Ice Cream Puddle

Many problems in mathematics classes are exactly defined and require very specific solutions. This lesson is intended to be an open-ended problem with multiple solutions and multiple entry points. Students use volume formulas and have some decisions to make about how to use them. After making an initial estimate, students will use modeling with more concrete parameters to help them refine their choices.

Gerrymandering: Is It or Isn't It?

Congressional districts are redrawn after a census year (conducted by the federal government every 10 years) to reflect shifting populations. Political scientists say there is a major advantage for whichever political party has control of a state legislature when districts are redrawn. However, during the process, the minority party tends to make accusations that districts are being gerrymandered, or drawn in unnatural ways to manipulate voter populations that would favor the majority. In this lesson, students explore how mathematics can be used to make decisions about whether a given congressional district is or is not being gerrymandered. They also use objective measurements to explore the ambiguity that is inherent in the process.

Trying Out Tangrams: Applying Knowledge of Geometry Vocabulary

In this lesson, students develop their understanding of the terms quadrilateral, parallel, and right angle. They apply that understanding in problem-solving activities with tangrams.

Elapsed Time: Using a Timeline to Determine Elapsed Time

Students learn to calculate elapsed time by using a timeline, and then complete three engaging and fun activities that plan a circus performance, their class schedule, and their day.

Getting to Know the Solids

Students are introduced to some of the basic polyhedra. Students explore the shapes of the faces of these solids.

Extending to Symbols

In Parts I and II of this investigation, students learn about the notion of equivalence in concrete and numerical settings. As students begin to use symbolic representations they use variables as place holders or unknowns. This part of the i-Math investigation illustrates the continued transition from the concrete balance view of equivalence to a more abstract view.

Mars Orbit

Astronomers now know that the planets in our solar system travel around the Sun in roughly circular orbits. However, people used to believe that the Sun and other planets orbited the Earth. If that were the case—if the Earth were the center of our solar system—what would the orbit of the other planets look like relative to Earth? That is the question that students will explore in this lesson. Students will generate parametric equations to describe the position of planets relative to the Sun; then, they will combine the equations to describe the position of Mars relative to Earth.