ratios. Understanding 4 Reasoning with ratios involves attending to and coordinating two quantities. Understanding 5 Forming a ratio as a measure of a real-world attribute involves isolating that attribute from other attributes and understanding the effect of changing each quantity on the attribute of interest Understanding 6 A proportion is a relationship of equality between two ratios that can be represented in a variety of ways. In a proportion, the ratio of two quantities remains constant as the corresponding values of the quantities change. For instance, in a ratio table, both quantities in a ratio must be multiplied or divided by the same factor to maintain the proportional relationship. EQ3. How can I use models (tape diagrams, double number lines, ratio tables, coordinate plane, etc.) to display an understanding of ratios and proportional relationships? *Enduring understandings and essential questions adapted from NCTM Enduring Understandings Source: Lobato, J.E. (2010). Developing Essential Understanding of Ratios, Proportions & Proportional Reasoning for Teaching Mathematics in Grades 6 - 8. Reston, VA: The National Council of Teachers of Mathematics, Inc. Acquisition Conceptual Understandings (Know/Understand) Procedural Fluency (Do) Application (Apply) Understand the concept of a ratio and use ratio language to identify the relationship between two quantities. Identify the various ratio forms: a:b and a/b Identifying the items representing quantities that will be compared in real world situations. Understand the concept of a unit rate a/b associated with a ratio a:b where b = 1 and a represents any rational number. Use rate language in Identify a unit rate as a fraction of a/b, where b = 1 and a = any rational number. Convert a rate to a unit rate by scaling. Solve real-world problems using unit rates.
6.RP.A.3d The Learning Plan: LFS Student Learning Map Unit at a Glance Note: This is a suggested guideline for pacing of this set of standards. Add in days for remediation, extra practice or assessment as needed. - I can define and identify ratios. Standard: 6.RP.A.1 - I can define and identify the different ways to represent a ratio (part to part, part to whole). Standard: 6.RP.A.1 - I can identify multiple ratios that represent the same proportional relationship using multiple representations. Standard: 6.RP.A.3 - I can identify multiple ratios that represent the same proportional relationship using multiple representations Standard: 6.RP.A.3 - I can use ratio reasoning and models to solve real world ratio problems. Standard: 6.RP.A.3a - I can use ratio reasoning and models to solve real world ratio problems. Standard: 6.RP.A.3a - I can use ratio reasoning and models to solve real world ratio problems. Standard: 66.RP.A.3b - I can use ratio reasoning and models to solve real world ratio problems. Standard: 6.RP.A.3a - I can define and model equivalent rates. Standards: 6.RP.A.2 6.RP.A.3b - I can create a unit rate when given a rate. Standards: 6.RP.A.2
Day 1: Defining Ratios Learning Target: I can define and identify ratios. Mathematical Practice Standards MP.4 Model with Mathematics MP.6. Attend to Precision Linked Content Standard: 6.RP.A Understand ratio concepts and use ratio reasoning to solve problems. 6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Instructional Notes: Reach Back Reach Ahead In order for students to succeed with this standard and concepts taught during days students will need to have the prior knowledge of: Converting units of measurement (4.MD.A.1) The four mathematical operations (4.OA.A.2) Multiplication and division of fractions (5.NF.B.3) Write and interpret numerical expressions (5.OA.A.2) Analyze patterns and relationships (5.OA.B.3) Students will use the knowledge gained on day 1 to: Finding unit rates (6.RP.A.2) Solving real world problems using ratios (6.RP.A.3) Write equations to express the independent and dependent variables (6.EE.C.9) Analyze the relationship between the independent and dependent variables using tables, graphs, and equations (6.EE.C.9) Reason about and solve one step equations (6.EE.B.7) Linked Essential Understanding(s): Linked Unit EQ(s): Understanding 2. A ratio is a multiplicative comparison of two quantities, or it is a joining of two quantities in a composed unit. Understanding 4. Reasoning with ratios involves attending to and coordinating two quantities. EQ1. How can rates, ratios, and proportional reasoning help us better understand the use of ratios and rates in the world around us? EQ2: What is a ratio and how do we make sense of whether two or more ratios are proportional? LEQ: How can you represent a relationship between two quantities?
Understanding 3 A rate is a set of infinitely many equivalent ratios. Understanding 6 A proportion is a relationship of equality between two ratios that can be represented in a variety of ways. In a proportion, the ratio of two quantities remains constant as the corresponding values of the quantities change. For instance, in a ratio table, both quantities in a ratio must be multiplied or divided by the same factor to maintain the proportional relationship. EQ1. How can rates, ratios, and proportional reasoning help us better understand the use of ratios and rates in the world around us? EQ3. How can I use models (tape diagrams, double number lines, ratio tables, coordinate plane, etc.) to display an understanding of ratios and proportional relationships? LEQ: How can we transform ratios to define and model equivalent rates? Text Alignment: Text Big Ideas Mathematics (2014) Eureka Math (2015) Glencoe Mathematics (2014) Mathematics in Context (2001) Section(s) 5.3 Module 1 Lesson 16-17 Chapter 1 Lesson 6 Recipe and School Supplies Problem Pgs. #3 p. 11 Strength of Alignment Aligned Aligned Aligned Somewhat Aligned. (#3 more aligned) Sample Lesson Activities/Resources: Diet cola was on sale last week. It cost $10 for every 4 packs of diet cola.(Eureka Module 1 Lesson 16) How much do 2 packs of diet cola cost? How much does 1 pack of diet cola cost? Once a commercial plane reaches the desired altitude, the pilot often travels at a cruising speed. On average, the cruising speed is 570 miles/hour. If a plane travels at this cruising speed for 7 hours, how far does the plane travel while cruising at this speed? This assessment tests students’ understanding of how to use equivalent ratios to solve problems. This game promotes student fluency to recognize equivalent ratios given a time limit.