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7-A-2-2

Page history last edited by Christine Koerner 3 years, 8 months ago

7.A.2.2 Solve multi-step problems involving proportional relationships involving distance-time, percent increase or decrease, discounts, tips, unit pricing, similar figures, and other real-world and mathematical situations.

In a Nutshell

Proportionality is two ratios having equivalency. Many areas in real life are typically proportional such as the distance driven by a car over a period time, prices for goods purchased, money tipped to serving staff, and fencing used for different areas of yards. Problems involving these types of situations can be solved by determining whether the situations are changing at a constant rate.

Student Actions	Teacher Actions
Develop an accurate and appropriate procedural fluency by explaining the solutions/ processes to solving multi-step real world proportional relationship problems. Develop a productive mathematical disposition by finding the importance by relating proportionality to everyday experiences such a tipping, discounts and pricing. Develop strategies for problem solving by solving real world multi-step problems involving proportions. Students will use a variety of methods to verify their answer in context.	Use and connect mathematical representations of proportions to real world situations. Pose purposeful questions about how proportional relationships could be utilized to solve various real world situations. Build procedural fluency by having students discuss and use examples and nonexamples of complex proportional problems.
Key Understandings	Misconceptions
Figures are similar if the ratios of 2 given sides of one object is equivalent to the 2 corresponding sides of the other object. Determine and list corresponding sides and angles of similar figures Contrast properties of figures that are similar and those that are not similar. Unit rates have a constant of proportionality. Unit means one. Use distance/time proportion to solve for distance, rate, and time for real-world problemsIdentify percent change using proportions Solve real-world discount and tip percent problems Identify and compare unit rates of proportions	Students may determine the wrong unit rate by dividing in the wrong order. Students may think the higher rate is the better deal when comparing rates Students may set up their proportion incorrectly, not setting up each ratio to correctly correspond with one another, when working with similar figures. Students may confuse congruence with similarity.