 ## 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.
1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."

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In this problem students explore the concept of proportion by comparing the relative strengths of different mixes of juice flavor and water in a visual context. Given four mixtures represented by purple and white rectangles, students order the drinks from strongest to weakest flavor and explain their reasoning. The Teachers' Notes page offers suggestions for implementation, discussion questions, and ideas for extension and support.
Activity
Grade Level: 3, 4, 5, 6+
This interactive Flash applet provides a tool for exploring how gears mesh and turn relative to each other as well as the relationship between the number of teeth on a set of cogs and the number of turns they make. Users place cogs with a chosen number of teeth onto a workspace and hold down the arrow keys to see them rotate. Placing dots on teeth or gaps helps users keep track of numbers of rotations and to investigate factors and multiples.
Activity, Interactive Media
Grade Level: 3, 4, 5, 6+
In this investigation students explore the concept of ratios and their relationship with factors and multiples. Given an assortment of cogs (gears) with different numbers of teeth, solvers are asked to find which pairs allow for each tooth of one to fit into every gap of the other, and to form conjectures regarding which pairs would work generally. The problem is well-suited for group work. The Teachers' Notes page offers suggestions for implementation, key questions, student sheets, and links to articles, videos, and an interactive Cog Environment (cataloged separately).
Activity, Interactive Media, Video
Grade Level: 3, 4, 5, 6+
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+
Students can use this Shockwave applet to learn basic probability concepts and to apply fraction and decimal skills. In Level 1 a number of fish are seen in a tank and users express the probability of catching a red fish as a fraction. In Level 2 the required probability is given as a fraction, and users move more fish into the tank to produce this probability. Level 3 is similar to level 2 but involves a wider range of fractions and some decimals. The Key Ideas page provides background in basic probability concepts. A set of student activity printouts (Probability) is available for further practice.
Activity, Game, Interactive Media
Grade Level: 4, 5, 6+
This interactive Flash applet can be used to compare and explore equivalence among fractions, decimals and percentages. It allows a child or teacher to represent fractions on one or more fraction strips, and to color individual parts. Each displayed strip can be labelled as a fraction, a decimal (to three decimal places) or a percentage; the ratio of yellow to green parts of each strip can also be displayed. It lends itself well to use with an interactive white board. A pdf guide to this collection of teaching applets is cataloged separately.
Activity, Interactive Media
Grade Level: 2, 3, 4, 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+ Resource is part of a PD collection