Rates of Change in Pick’s Theorem

Students will use a spreadsheet to investigate rates of change among various figures created on a geoboard. The coefficients of Pick’s Theorem are easily determined from these rates of change.

Hanging Chains

Both ends of a small chain will be attached to a board with a grid on it to (roughly) form a parabola. Students will choose three points along the curve and use them to identify an equation. Repeating the process, students will discover how the equation changes when the chain is shifted.

Movie Lines

This lesson allows students to apply their knowledge of linear equations and graphs in an authentic situation. Students plot data points corresponding to the cost of DVD rentals and interpret the results.

Mix It Up

In this lesson, students will use two colors of beads to form two different percent mixes, and then form a final mix using scoops from the two mixes. From this tactile start, students will develop and use a formula to determine the final percent mix from two source mixtures.

Barbie Bungee

The consideration of cord length is very important in a bungee jump—too short, and the jumper doesn’t get much of a thrill; too long, and ouch! In this lesson, students model a bungee jump using a Barbie^® doll and rubber bands. The distance to which the doll will fall is directly proportional to the number of rubber bands, so this context is used to examine linear functions.

Successive Discounts

In this lesson, students will examine numeric, algebraic, and graphical representations of compositions of function in the context of successive discounts at a retail store.

Growth Rate

Given growth charts for the heights of girls and boys, students will use slope to approximate rates of change in the height of boys and girls at different ages. Students will use these approximations to plot graphs of the rate of change of height vs. age for boys and girls.

National Debt and Wars

Students will collect information about the National debt, plot the data by decade, and determine whether an exponential curve is a good fit for the data. Then student groups will determine and compare common traits and differences in changes in the National debt in three major eras: the Civil War, World War I, and World War II.

Arithme-Tic-Toc

Students will be introduced to modular arithmetic by first examining a five-hour analog clock and its mathematical properties. Then students will investigate patterns and relationships that exist in 12-hour addition and multiplication clock tables.

Walk the Plank

When one end of a wooden board is placed on a bathroom scale and the other end is suspended on a textbook, students can "walk the plank" and record the weight measurement as their distance from the scale changes. The results are unexpected— the relationship between the weight and distance is linear, and all lines have the same x‑intercept. This investigation leads to a real world occurrence of negative slope, examples of which are often hard to find.