 ## Common Core State Standards for Mathematics

Grade(s) 6 resources related to the following standard:
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.
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

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This tutorial provides students with experience using three types of distance scales on regional maps of North America. An introduction shows how to make use of the bar scale, the statement of equivalence, and the representative fraction (ratio) to determine distance between two locations. Printable instructions and two sets of interactive exercises are provided.
Activity, Interactive Media, Tutorial
Grade Level: 5, 6+
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+
This interactive lesson helps students connect time and longitude on a globe. Learners use the time discrepancy between their location and Greenwich, England, and a conversion factor to determine their longitude. Several exercises of varying difficulty and precision are provided. The historic background and vocabulary definitions of this topic are provided.
Activity, Interactive Media, Lesson Plans
Grade Level: 5, 6+
This brief article describes some methods of indirect measurement that have been applied throughout history to the problem of estimating the height of tall trees. Several methods involving scaling, angles, ratios, and tools are discussed.
Activity, Reference Materials, Article
Grade Level: 5, 6+
This problem from the Figure This! collection of NCTM asks the student to make measurements and consider proportion and scaling to estimate the length of the Statue's nose, given the length of her arm. The activity includes links to a hint, the solution, related math questions, and additional resources.
Activity
Grade Level: 4, 5, 6+
This problem provides an opportunity for students to reason about ratio and proportion in the realistic context of mixing a fruit drink from concentrate. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and links to related problems (Blackcurrantiest is cataloged separately).
Activity
Grade Level: 4, 5, 6+