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### Oil Oil Everywhere

3-5

Oil spills are in the news. To make real-world connections, this lesson provides hands-on experiences with mixing oil and water, provides surface area information about the 2010 oil spill in the Gulf of Mexico, and gives students opportunities to estimate small oil spills of their own making.### The Venn Factor

3-5, 6-8

In this lesson, students use a Venn diagram to sort prime factors of two or more positive integers. Students calculate the greatest common factor by multiplying common prime factors and develop a definition based on their exploration.### Bears in a Boat

3-5, 6-8

Who can build the best boat? In this lesson, students are challenged to create aluminum foil boats that are then tested by filling them with plastic bears until they sink. The lesson serves as a fun, hands-on way to collect data. The data from two attempts is collected and used to make two class box-and-whisker plots with some surprising results. ### Too Hot To Handle, Too Cold To Enjoy

9-12

Predicting the right time to take that first sip of any hot beverage is difficult. Unfortunately, the temperature of hot coffee does not decrease steadily (linearly) over time. If so, it would be easy to predict when to take that first sip. Which function best represents the rate at which coffee cools: linear, quadratic, square root, absolute value, exponential or logarithmic?### The Line Runner

6-8

Students studying linear equations inevitably explore the concept of slope. Slope is a recurring topic found in algebra when studying linear equations, in trigonometry when studying the tangent ratio, and in calculus when studying the derivative. Lead students to a deeper understanding of slope and linear equations using elevation and distance data from a popular mapping website.### It's Not Heavy, It's Your Grade

6-8

In baseball, a batter's slugging average is weighted according to the number of bases he gets. To calculate the average height of a team, each height must be weighted according to how many players are that tall. This lesson introduces students to weighted averages by looking at their own grades.### Roller Coasting through Functions

6-8

In this lesson, students determine the time it takes for a roller coaster to reach the bottom of its tallest drop. They use tables and graphs to analyze the falls of different roller coasters. Students conclude the study by creating their own roller coaster and providing an analysis of its fall.### Armstrong Numbers

6-8, 9-12

An Armstrong number is an *n*-digit number that is equal to the sum of the

*n*

^{th}powers of its digits. In this lesson, students will explore Armstrong numbers, identify all Armstrong numbers less than 1000, and investigate a recursive sequence that uses a similar process. Throughout the lesson, students will use spreadsheets or other technology.

### Cubed Cans

6-8

In this lesson, students will use formulas they have explored for the volume of a cylinder and convert them into the same volume for rectangular prisms while trying to minimize the surface area. Various real world cylindrical objects will be measured and converted into a prism to hold the same volume. As an extension, students may design and create a rectangular prism container according to their dimensions to compare and contrast with the cylinder.### Feeding Frenzy

6-8

In this activity, students will multiply and divide a recipe to feed groups of various sizes. Students will use unit rates or proportions and think critically about real world applications of a baking problem.