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 EQ3. How can I use models (tape diagrams, A proportion is a relationship of equality double number lines, ratio tables, coordinate between two ratios that can be represented in plane, etc.) to display an understanding of a variety of ways. In a proportion, the ratio of ratios and proportional relationships? 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. *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 Procedural Fluency Application Understandings (Do) (Apply) (Know/Understand) Understand the concept of a Identify the various ratio Identifying the items ratio and use ratio language forms: a:b and a/b representing quantities that to identify the relationship will be compared in real world between two quantities. situations. Understand the concept of a Identify a unit rate as a Solve real-world problems unit rate a/b associated with fraction of a/b, where b = 1 using unit rates. a ratio a:b where b = 1 and a and a = any rational number. represents any rational number. Use rate language in Convert a rate to a unit rate by scaling.
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_unit_guide_final.docx