Ratios & Proportional Systems

The Lowdown  Exploring Changing Obesity Rates Through Ratios and Graphs
In these KQED Lowdown infographics, explore how adult obesity rates in the United States, as measured by body mass index (BMI), have dramatically changed in the past halfcentury. A circular graph and a pictograph depict data by decade, indicating which parts of the population were not overweight, overweight, obese, and extremely obese according to BMI. In the accompanying classroom activity, students develop an understanding of the ratios and proportional relationships by examining numerical data found in the graphs and creating their own bar graphs. This resource is part of the Math at the Core: Middle School Collection.
Grades: 6 
Scale City  Scale Models and ThreeDimensional Scaling in Practice
In this interactive, students explore threedimensional scaling—how the volume of an object changes when all three dimensions are increased proportionally. Students determine the measurements of a threedimensional object when it is scaled up by a factor of 10. The accompanying classroom activity invites students to compare the volumes and surface areas of two cubes of different sizes. This resource is part of the Math at the Core: Middle School Collection.
Grades: 67 
Scale City  Scaling Up Rectangles Using Simulations
In this interactive, students explore twodimensional scaling, or how the area of a rectangle changes when both length and width are increased proportionately. By investigating how much paint would be required to create murals in different sizes, students learn that doubling a rectangle’s measurements does not double its area, it quadruples it! In the accompanying classroom activity, students use grid paper to draw a series of squares whose dimensions increase proportionately and record the changing data in a table. This resource is part of the Math at the Core: Middle School Collection.
Grades: 67 
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.
Grades: 68 
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.
Grades: 58,13+ 
RealWorld 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.
Grades: 67 
The Lowdown  Examining California's Prison System: RealWorld Ratio
In this infographic from KQED, examine age, gender, and race in California’s prison population to note the inconsistencies between who is in the general population and who is serving time behind bars. In the accompanying classroom activity, students examine the demographics of California’s prison population. After learning how to find a part given the whole and the percent, students find the size of different populations in the prison system. Students then analyze the data and make recommendations for identifying the communities at which they think crimeprevention efforts should be targeted. This resource is part of the Math at the Core: Middle School Collection.
Grades: 6 
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.
Grades: 67 
Scale City  Inverse Proportions and Shadows in the Real World
In this video, students take a quick trip through the history of drivein 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 handson 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.
Grades: 67 
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.
Grades: 67 
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.
Grades: 67 
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.
Grades: 67 
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.
Grades: 67 
Scale City  Reviewing Ratios, Proportions, and Scale
In this interactive, students put quarters into a virtual vending machine and solve 16 problems involving ratios and proportions in order to receive “treats.” In the accompanying classroom activity, small groups of students take turns solving the problems to see which group is quickest to finish the game. This resource is part of the Math at the Core: Middle School Collection.
Grades: 67 
Scale City  Scale Models in the Real World
This video explores scale models, including 1:12 dollhouse models, 1:24 railroad models, and 1:192 architectural models. It explains what the different ratios represent and asks students to consider how they can use measurement and proportional reasoning to create their own scale models. The accompanying classroom activity gives students handson practice with creating models to scale and with realworld measurement. This resource is part of the Math at the Core: Middle School Collection.
Grades: 67 
Scale City  Scaling Up Recipes and Circles in Practice
In this interactive, students use ratio reasoning to scale up recipes and explore the proportional relationship between the diameter of a circle and its area. The accompanying classroom activity provides students with practice in making unit conversions and guidance in thinking about direct proportions. This resource is part of the Math at the Core: Middle School Collection.
Grades: 67 
Relative Reasoning in Finance
Learn how investment advisors analyze and compare the environmental impact and financial health of companies. This video focuses on the importance of ratios when working with financial data and discusses the idea of relative reasoning, taking math out of the classroom and into real world problem solving.Grades: 68 
Real World Ratio and Rate Problem: Bianca’s Fifty Percent Solution
In this video from Cyberchase, Bianca is lured into a store when she sees a 50% off sale sign in the window. She soon realizes that even when items are 50% off, the final bill can still be a lot of money. In the accompanying classroom activity, students create sales of their own by selecting an item from an advertisement and calculating the savings for 10%, 25%, 50%, and 75% off. This resource is part of the Math at the Core: Middle School Collection.
Grades: 56 
Formulas for Circle Area and Circumference: Simple as Pie
In this video from Cyberchase, Bianca and her friend team up to sell pies. Bianca learns that piepan sizes are the measured diameter of the pan, but that there is a mathematical relationship between the diameter of the pan and the circumference of the pan. In the accompanying classroom activity, students calculate the circumference of a variety of wheels. This resource is part of the Math at the Core: Middle School Collection.
Grades: 67 
The Lowdown  Living Wages in CA: Ratio and Rate in the Real World
In this KQED infographic, find out how much an adult in differentsized households needs to make to pay for basic monthly living expenses. In the accompanying classroom activity, students solve reallife problems involving rate and ratio that involve calculating whether minimum wage in their state is a living wage. They learn whether minimumwage pay can cover expenses such as food, housing, transportation, and medical care. They then compare their findings with data shown on bar graphs representing living wage and minimum wage in California. To get the most out of this activity, students should be comfortable with arithmetic with dollars and cents into the ten thousands. This resource is part of the Math at the Core: Middle School Collection.
Grades: 57