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: Hippos sometimes get to eat pumpkins as a special treat. If 3 hippos eat 5 pumpkins, how many pumpkins per hippo is that? Lindy made 24 jelly-bread san...

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 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: Ty took the escalator to the second floor. The escalator is 12 meters long, and he rode the escalator for 30 seconds. Which statements are true? Select...

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 aspects of the task and its potential use.

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 aspects of the task and its potential use.

Ratio errors confuse a dodgeball coach as two teams face off in an epic tournament. See how mathematical techniques such as tables, graphs, measurements and equations help to find the missing part of a proportion.

True love has the right ratio. In this humorous animation, the number of words spoken by each partner predicts whether a date goes well or horribly. What do you do when someone asks if you listen to country music backwards, but won't let you get a word in edgewise?

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

This Cyberchase video segment features Bianca, who must figure out the fastest route to a movie premiere.

Explore the concept of evaporative cooling through a hands-on experiment. Use a wet cloth and fan to model an air-conditioner and use temperature and relative humidity sensors to collect data. Then digitally plot the data using graphs in the activity. In an optional extension, make your own modifications to improve the cooler's efficiency.

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

Open middle problems require a higher depth of knowledge than most problems that assess procedural and conceptual understanding. They support the Common Core State Standards and provide students with opportunities for discussing their thinking.

The Finding Equivalent Ratios problem asks students to use the digits 1-9 to create 3 equivalent ratios made up of single and double digit numbers.

In this video segment from Cyberchase, Harry decides to train as a firefighter and uses line graphs to chart his physical fitness progress.

Students begin their sixth grade year investigating the concepts of ratio and rate. They use multiple forms of ratio language and ratio notation, and formalize understanding of equivalent ratios. Students apply reasoning when solving collections of ratio problems in real world contexts using various tools (e.g., tape diagrams, double number line diagrams, tables, equations and graphs). Students bridge their understanding of ratios to the value of a ratio, and then to rate and unit rate, discovering that a percent of a quantity is a rate per 100. The 35 day module concludes with students expressing a fraction as a percent and finding a percent of a quantity in real world concepts, supporting their reasoning with familiar representations they used previously in the module.

In this interactive activity adapted from Annenberg Learner's Teaching Math Grades 6–8, explore some of the ways graphs can represent mathematical data contained in a story.

This lesson is regarding the introduction to ratios.  Students will learn what a ratio is, practice finding ratios, and work on making their own ratios. There are YouTube videos, worksheets, and funny images to help students understand ratios.

In this lesson, students learn about sound. Girls and boys are introduced to the concept of frequency and how it applies to musical sounds.

The purpose of this task is to generate a classroom discussion about ratios and unit rates in context.

Students work in a whole-class setting, independently, and with partners to design and implement a problem-solving plan based on the mathematical concepts of rates and multiple representations (e.g., tables, equations, and graphs). They analyze a rule of thumb and use this relationship to calculate the distance in miles from a viewer's vantage point to lightning.Key ConceptsThroughout this unit, students are encouraged to apply the mathematical concepts they have learned over the course of this year to new settings. Help students develop and refine these problem-solving skills:Creating a problem-solving plan and implementing the 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 the 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.Create a rate table to organize data and make predictions.Apply the relationship between the variables to write a mathematical formula and use the formula to solve problems.Create a graph to display proportional relationships, and use this graph to make predictions.Articulate strategies, thought processes, and approaches to solving a problem, and defend why the solution is reasonable.