Ratio+problems

= 6-RP3 = =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.=

a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. [6-RP3a]

b. Solve unit rate problems including those involving unit pricing and constant speed. [6RP3b] Example: If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were the lawns being mowed?

c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. [6-RP3c]

d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [6-RP3d]

Tape diagrams are [|defined] in the Common Core Standards as
 * Drawings that look like a segment of tape, used to illustrate number relationships. Also known as strip diagrams, bar models or graphs, fraction strips, or length models.

For more information, see this [|presentation] by an Australian math specialist and an [|article] about how tape diagrams are used in Japanese schools.

Success with Word Problems Using Singapore Math [|Model Drawing] Wonderful resource with lots of problems.

Double number line diagrams
 * [|Seeing Double] - explanation and blackline master
 * Use with [|fractions]

North Carolina's Lessons for Learning Bake Sale Brownies (p. 3) - 6.RP.3, 6.EE.9
 * I can use knowledge of multiplication and division to scale recipes to make different numbers of servings.
 * I can identify quantitative relationships between scaled recipes.
 * I can represent relationships between quantities by plotting points on the coordinate grid.

Dan Meyer Three Act Tasks
 * Split Time What should his split time on the indoor track be? -6.RP.3, MP.4
 * Leaky Faucet How long will it take the sink to fill up? - 6.RP.3, MP.4
 * Nana's Chocolate Milk How do we fix Nana's chocolate milk? - 6.RP.3, MP.4 - Features a Double Number Line
 * See also Pain Relief, Fort Steuben, Bolt, Coke vs. Sprite, Super Bear, Shower vs. Bath, Print Job, Sugar Packets...


 * Suggested by [|Harding Math Specialist]**
 * **6.RP.1, 2, 3 - Snail Pace -** @http://insidemathematics.org/index.php/tools-for-teachers/6th-grade-math/mars-tasks-scoring-rubrics-a-analysis - The Snail Pace task listed on this page requires students to work with distances, time and speeds in inches and minutes. These tasks also have sample student work, teacher reflections, and other resources.
 * **6.RP.1,2,3 - Measuring Up -** @http://illuminations.nctm.org/LessonDetail.aspx?ID=U148 - unit (7 lessons) on proportional reasoning, ratio and indirect measurement.
 * **6.RP.2,3 - Unit Price and Comparison Shopping** - @http://ethemes.missouri.edu/themes/443 - this site has links to different lessons on finding a unit price (one application of unit rate).
 * **6.RP.3c - Percent Cards -** @http://insidemathematics.org/index.php/tools-for-teachers/6th-grade-math/mars-tasks-scoring-rubrics-a-analysis -The Percent Cards task listed on this page requires students to relate fractions, decimals and percents and place them on a number line. These tasks also have sample student work, teacher reflections, and other resources.
 * **6.EE.2c, 6.EE.4, 6.RP.3a,b - Gym** -- @http://insidemathematics.org/index.php/tools-for-teachers/6th-grade-math/mars-tasks-scoring-rubrics-a-analysis -- The Gym task listed on this page asks students to evaluate different options for a gym membership. These tasks also have sample student work, teacher reflections, and other resources.