• ## Recognize and Represent Proportional Relationships Between Quantities: Ratio, Proportion, Cross Multiply, and Divide

In this Cyberchase media gallery, learn about ratio and proportion and how to use an algebraic shortcut to solve proportion problems. In the accompanying classroom activity, students play a game called the "Pom-Pom Nose Push," in which they collect data and determine the ratio of time to distance. This resource is part of the Math at the Core: Middle School Collection.

• ## Scale City | Proportional Relationships Among Time, Distance, and Speed

In this interactive, students compare the speed of the racehorse Man o’ War to other famous racehorses, a cheetah, a track star, and a middle school student. Students discover the direct proportional relationship between distance traveled in a set time and speed, and the inverse proportional relationship between speed and the time it takes to travel a set distance. In the accompanying activity, students complete a chart based on data from the interactive and make observations about the relationships that the data represent. This resource is part of the Math at the Core: Middle School Collection.

• ## Scale City | Proportional Relationships in the Real World

In this video, students visit the Kentucky Horse Park where they are introduced to the question How are speed, time, and distance interrelated? The accompanying activity builds on a demonstration from the video of the length of Man o’ War’s stride versus the length of a person’s stride by allowing students to measure their own strides versus that of the great racehorse. This resource is part of the Math at the Core: Middle School Collection.

• ## Scale City | Inverse Proportions and Shadows in the Real World

In this video, students take a quick trip through the history of drive-in theaters and are then asked to consider the question, "What is the relationship between the size of an object’s shadow and the object’s distance from a light source?" In the accompanying classroom activity, students do a hands-on experiment about the size of their own shadows at different distances from a projector or other light source. This resource is part of the Math at the Core: Middle School Collection.

• ## Scale City | Inverse Proportions and Shadows in Practice

In this interactive, students explore what happens to a figure’s shadow on a movie screen as the figure moves away from the projector. They also use approximate measurements to complete a chart of distance from light source versus height of shadow on the screen. As the chart is completed, students see how the relationships are represented graphically. The accompanying activity provides discussion questions for students to consider as they work through the interactive, as well as a chart for them to complete as they measure and compute values based on the interactive. This resource is part of the Math at the Core: Middle School Collection.

• ## Variation About the Mean: The Boston Harbor Project

Investigate how the Massachusetts Water Resources Authority has determined that their water treatment facility has had a positive impact on Boston Harbor. This video focuses on how mean, standard deviation, and confidence intervals are used to demonstrate measureable improvements in the water quality, taking math out of the classroom and into real world problem solving. This resource is part of the Math at the Core: Middle School Collection.

• ## Real-World Proportional Relationships: Gender Wage Gap

Using this infographic, learn how wage equity today compares with data from 50 years ago, at the dawn of the equal pay movement. The accompanying classroom activity invites students to explore the change in the gender wage gap from 1965 to 2010. First, students will learn how the wage gap can be calculated from different median salaries for men and women. Then, students will consider the real monetary impact of increasing equity in wages—and will look to the graph for clues about when the wage gap will be eliminated, if at all. This resource is part of the Math at the Core: Middle School Collection.

• ## Comparing Volumes of Cylinders, Spheres, and Cones

Squash cones and spheres to compare their volumes to similar cylinders and look for patterns. This interactive exercise focuses on comparing volumes between figures that have the same height and diameter and drawing conclusions based on the ratios of the sizes. This resource is part of the Math at the Core: Middle School collection.

• ## The Largest Container: Problems Using Volume and Shape

Maximize the volume of each solid if it is to be constructed from a single sheet of paper. This interactive exercise focuses on volume equations, measurement, and problem solving skills to compare the volume of 3D figures constructed from similar amounts of construction materials.

This resource is part of the Math at the Core: Middle School collection.

• ## Line Plot Representation of Deviation from the Mean

See what happens when you drag data points to different locations on a line plot. This interactive exercise focuses on attempting to manipulate a set of data on a line plot while keeping the mean constant and exploring the data set's deviation from the mean. This resource is part of the Math at the Core: Middle School Collection.

• ## Horsepower

In this video, a young man talks about buying a new car and tries to understand what horsepower really means. With some help from a young woman who explains where the term comes from, he sets out to look for more information to find his perfect car. In the accompanying classroom activity, students conduct an experiment to calculate how much horsepower they can produce. This resource is part of the Math at the Core: Middle School Collection.

• ## Comparing Slopes

Recognize the part rise and run play on the composition of a linear equation and graph. This interactive exercise focuses on linear equations and how a positive or negative slope effects the graphical representation.

• ## 2D Nets for 3D Decorative Boxes

Figure out how to make the most of your materials and budget when buying decorative paper to cover a given box. This interactive exercise focuses on surface area, measurement, and problem solving skills to compare alternate solutions to the same problem, taking math out of the classroom and into the real world.

• ## Scale City | Proportions and Music in the Real World

In this video—through footage of the calliope aboard the Belle of Louisville, a church pipe organ, and various instruments at a recording studio—students are introduced to the mathematical concept that the length of a musical pipe or a string has a proportional relationship with the sound it produces.  In the accompanying activity, stringed instruments are used to demonstrate the concept presented in the video. This resource is part of the Math at the Core: Middle School Collection.

• ## Determining Surface Area with Unit Blocks

Use your spatial reasoning skills to calculate the surface area when given a 3D figure. This video focuses on a right rectangular prism and shows you how unit blocks can help you visualize, then calculate the surface area. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers. This resource is part of the Math at the Core: Middle School collection.

• ## Scale City | Proportions and Music in Practice

In this interactive, students explore the relationship between sound frequencies and the length of pipes on a pan flute. By answering questions about the values of ratios and completing a chart, students are introduced to the concept of an inverse proportional relationship. The accompanying activity helps students explore the mathematical relationships that exist among musical notes and their frequencies. This resource is part of the Math at the Core: Middle School Collection.

• ## Formulas for a Circle

This media gallery uses video from Cyberchase to teach students how to determine the diameter, radius, and circumference of circle, including how to use pi to find the circumference. In the accompanying classroom activity, students test the theories presented in the videos and record their findings. This resource is part of the Math at the Core: Middle School Collection.

• ## Random Sampling: How Many Fish?

Experiment with random sampling methodology using goldfish crackers. This video focuses on making inferences based on a set of data, finding averages, and using a ratio table to demonstrate statistical procedures used by scientists when estimating populations in the real world. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers. This resource is part of the Math at the Core: Middle School Collection.

• ## Addition of Positive and Negative Integers

Introducing a card game that your students can play in small groups to develop their addition skills. This video focuses on addition of positive and negative numbers and briefly touches on subtraction of integers.

This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers and is part of the Math at the Core: Middle School collection.