6RP-Understand+ratio+concepts+and+use+ratio+reasoning+to+solve+problems

6.RP.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.”// 6.RP.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. //For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” *// 6.RP.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. 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. b. Solve unit rate problems including those involving unit pricing and constant speed. //For 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 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. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)**=== ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Learning Target/Task Analysis**===
 * ===**Common Core Standards**===
 * Reason abstractly and quantitatively.
 * Attend to precision.
 * Make sense of problems and persevere in solving them.
 * Model with mathematics.
 * Use appropriate tools strategically.
 * Look for and make use of structure. ||
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**=== || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking: Remembering, Applying**=== ||

Students should be able to identify and describe any ratio using “For every _ ,there are _” In the example above, the ratio could be expressed saying, “For every 2 goldfish, there are 3 guppies”.

Students are able to name the amount of either quantity in terms of the other quantity. Students will begin to notice that related unit rates (i.e. miles / hour and hours / mile) are reciprocals as in the second example below. At this level, students should use reasoning to find these unit rates instead of an algorithm or rule.

Students use tables to compare ratios.

Students are able to plot ratios as ordered pairs

Students use ratios to identify percents.

Students use percentages to find the part when given the percent, by recognizing that the whole is being divided into 100 parts and then taking a part of them (the percent).

Students also determine the whole amount, given a part and the percent.

Students use ratios as conversion factors and the identity property for multiplication to convert ratio units.

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**I can...**** Understand ratio concepts and use ratio reasoning to solve problems. **===


 * I can determine if a ratio represents part to whole or part to part.
 * I can identify and calculate a unit rate.
 * I can create, use, and plot the ordered pairs from tables of equivalent ratios using whole numbers.
 * I can find the percent of a number.

ratio, equivalent ratios, tape diagram, unit rate, part-to-part, part-to whole,percent

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Sample Assessments**
Daily Spiral Review Signaling Questioning Teacher Observation Thinkgate

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Differentiation:**
Teaching the Common Core Math Standards with Hands-On Activities: p. 2 Ratios All Around Us Teaching the Common Core Math Standards with Hands-On Activities: p. 4 Unit Rate Tic-Tac-Toe Teaching the Common Core Math Standards with Hands-On Activities: p. 7 The Faster Rate Quantiles Quantiles 2 Quantiles 3 Quantiles 4

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Intervention:**
Proportional Reasoning AIMS: p. 62 Dominoes percent, fraction, decimal

Walking Rates p.82: Navigating Through Algebra Ratios p.95: Navigating Through Probability Proportional Reasoning AIMS: p.57 Cents of Percents Proportional Reasoning AIMS: p.158 Reading Rates Proportional Reasoning AIMS: p.172 Drop It

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Instructional Resources:**===

Mathematics Station Activities for Common Core State Standards Grade 6 (pages 1, 8 and 15) Carnegie Learning: Chapter 5, Chapter 12, Lesson 6.1, Lesson 6.2 DPI Indicators: Pages 54-56 Proportional Reasoning AIMS: p.37, 39 (Could also be used for intervention) Proportional Reasoning AIMS: p.44 Paper Clip Chains Proportional Reasoning AIMS: p.48 Percent Bands Proportional Reasoning AIMS: p.153 Pulse Rates ===Identifying Ratios Worksheet=== ===Examples of Problems for Solving Unit Rates=== ===Rates and Ratios Venn Diagram and Definitions=== Unit Notes Ratios PowerPoint Practice 1 Practice 2 Practice 3 Interactive Games

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Notes and Additional Information**===