Bianca visits a bike shop and learns how bicycle gears work in this Cyberchase video segment.

The CyberSquad tests which broom can travel the furthest in five seconds in this video from Cyberchase.

In this video segment from Cyberchase, the CyberSquad and Digit construct a physical profile of the person who kidnapped Choocroca, a giant cybercrocodile.

How many calories are in your favorite foods? How much exercise would you have to do to burn off these calories? What is the relationship between calories and weight? Explore these issues by choosing diet and exercise and keeping an eye on your weight.

This lesson unit is intended to help teachers assess how well students are able to visualize two-dimensional cross-sections of representations of three-dimensional objects. In particular, the lesson will help you identify and help students who have difficulties recognizing and drawing two-dimensional cross-sections at different points along a plane of a representation of a three-dimensional object.

Students will analyze ratios and use proportions to solve problems using a cooperative, kinesthetic activity in which they will create “human ratios.” Students will use ratios to compare two quantities, then solve problems cooperatively by demonstrating how proportions are written to show equivalent ratios.

In this activity, students determine their own eyesight and calculate what a good average eyesight value for the class would be. Students learn about technologies to enhance eyesight and how engineers play an important role in the development of these technologies.

This lesson unit is intended to help sixth grade teachers assess how well students are able to: Analyze a realistic situation mathematically; construct sight lines to decide which areas of a room are visible or hidden from a camera; find and compare areas of triangles and quadrilaterals; and calculate and compare percentages and/or fractions of areas.

Students should have prior knowledge of rates and solving proportions. Students will be introduced to a problem that launches the lesson. By the end of the lesson, students should be able to answer the launch question. During the lesson, students will explore finding the unit rate, watch a video demonstration, and practice via whiteboards and interactively.

During this two-day lesson, students work with a partner to create and implement a problem-solving plan based on the mathematical concepts of rates, ratios, and proportionality. Students analyze the relationship between different-sized gummy bears to solve problems involving size and price.Key ConceptsThroughout this unit, students are encouraged to apply the mathematical concepts they have learned over the course of this year to new settings. Helping students develop and refine these problem solving skills:Creating a problem solving plan and implementing their plan systematicallyPersevering through challenging problems to find solutionsRecalling prior knowledge and applying that knowledge to new situationsMaking connections between previous learning and real-world problemsCommunicating their approaches with precision and articulating why their strategies and solutions are reasonableCreating efficacy and confidence in solving challenging problems in a real worldGoals and Learning ObjectivesCreate and implement a problem-solving plan.Organize and interpret data presented in a problem situation.Analyze the relationship between two variables.Use ratios.Write and solve proportions.Create rate tables to organize data and make predictionsUse multiple representations—including tables, graphs, and equations—to organize and communicate data.Articulate strategies, thought processes, and approaches to solving a problem and defend why the solution is reasonable.

Math in Real Life (MiRL) supports the expansion of regional networks to create an environment of innovation in math teaching and learning.  The focus on applied mathematics supports the natural interconnectedness of math to other disciplines while infusing relevance for students.  MiRL supports a limited number of networked math learning communities that focus on developing and testing applied problems in mathematics.  The networks help math teachers refine innovative teaching strategies with the guidance of regional partners and the Oregon Department of Education.

This problem, the third in a series of tasks set in the context of a class election, is more than just a problem of computing the number of votes each person receives. In fact, that isnŐt enough information to solve the problem. One must know how many votes it takes to make one half of the total number of votes. Although the numbers are easy to work with, there are enough steps and enough things to keep track of to lift the problem above routine.

In this task students use ratio and rate reasoning to solve the real-world problem of a runners rate and distance.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Lin rode a bike 20 miles in 150 minutes. If she rode at a constant speed, How far did she ride in 15 minutes? How long did it take her to ride 6 miles?...

This series of 5 word problems lead up to the final problem. Most students should be able to answer the first two questions without too much difficulty. The decimal numbers may cause some students trouble, but if they make a drawing of the road that the girls are riding on, and their positions at the different times, it may help. The third question has a bit of a challenge in that students won't land on the exact meeting time by making a table with distance values every hour. The fourth question addresses a useful concept for problems involving objects moving at different speeds which may be new to sixth grade students.

This is the last problem of seven in a series about ratios set in the context of a classroom election. Since the number of voters is not known, the problem is quite abstract and requires a deep understanding of ratios and their relationship to fractions.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: A penny is about $\frac{1}{16}$ of an inch thick. In 2011 there were approximately 5 billion pennies minted. If all of these pennies were placed in a s...

Students are presented with a guide to rain garden construction in an activity that culminates the unit and pulls together what they have learned and prepared in materials during the three previous associated activities. They learn about the four vertical zones that make up a typical rain garden with the purpose to cultivate natural infiltration of stormwater. Student groups create personal rain gardens planted with native species that can be installed on the school campus, within the surrounding community, or at students' homes to provide a green infrastructure and low-impact development technology solution for areas with poor drainage that often flood during storm events.

Students focus on interpreting, creating, and using ratio tables to solve problems. They also relate ratio tables to graphs as two ways of representing a relationship between quantities.Key ConceptsRatio tables and graphs are two ways of representing relationships between variable quantities. The values shown in a ratio table give possible pairs of values for the quantities represented and define ordered pairs of coordinates of points on the graph representing the relationship. The additive and multiplicative structure of each representation can be connected, as shown: Goals and Learning ObjectivesComplete ratio tables.Use ratio tables to compare ratios and solve problems.Plot values from a ratio table on a graph.Understand the connection between the structure of ratio tables and graphs.