Ratios and Proportional Relationships

Understand ratio concepts and use ratio reasoning to solve problems.

3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

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Resource | Resource Type Grade Level | Rating |
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This series of brief videos (1-10 min. each) demonstrates how a three-part lesson in a classroom focused on accountable talk empowers and engages students to learn through collaborative problem solving in a technology-rich environment. While solving a problem involving rates and proportional reasoning students exemplify shared criteria for successful group work. The teacher explains her strategies for planning, grouping, and peer evaluation. Print resources (pdf) include a Viewer's Guide, organizers, and supporting monographs. | Instructional Strategy, Lesson Plans, Video Grade Level: 4, 5, 6+ | |

In this lesson plan students develop an understanding of early proportionality by helping the Cyberchase kids save money to bid at an auction. Students use line graphs and tables to track their totals and discover the overall relationship between the amount of money needed and the number of days to earn the money. This lesson plan contains two student worksheets, two short video clips, two assessment options, and an answer key. | Assessment, Lesson Plans, Video Grade Level: 4, 5, 6+ | |

This 88-page document addresses the meaning of the Common Core State Standards for teaching fractions in grades 3-7. For each grade level the specific standards that are addressed are listed, followed by a detailed explanation of what the standards mean, including visual models, and any misconceptions teachers or students might have about how specific standards apply to fractions in the CCSS. | Instructional Strategy, Reference Materials, Article Grade Level: 3, 4, 5, 6+ | |

In this 7-minute video grade 4 teacher Todd Hausman explains and demonstrates how his students apply their understanding of elapsed time and the time/rate/distance relationship to follow the progress of mushers in the Iditarod sled dog race in Alaska. Using real-time tracking data, students collaborate to find the mean (average) traveling speed of their chosen Iditarod musher, and predict their arrival time at checkpoints. This resource includes a lesson plan and transcript of the video (downloadable .doc files) and a link to the teacher page of the official Iditarod website. | Activity, Instructional Strategy, Lesson Plans, Video Grade Level: 4, 5, 6+ | |

This Technology Problem of the Week (tPoW) challenges students to use proportional reasoning to determine the speed of a train that two children in a tunnel evade by running in opposite directions, given only the kids' relative starting position and speed as they run out of the tunnel. It links to the Geometer's Sketchpad sketch "Train Tunnel." Solve and explain your solution; download hints and answer checks. Free registration is required. | Problem Set, Interactive Media Grade Level: 6+ |