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# P2 compare proportional relationships represented in

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P.2 Compare proportional relationships represented in different ways. P.3 Apply quantitative reasoning strategies to solve real-world problems with proportional relationships based on an understanding that derived quantities can be described with whole numbers, fractions, or decimals, or in a combination of these, and that to fully explain these relationships, units must be used. Algebraic Reasoning Goal: Students will reason using the language and structure of algebra to investigate, represent, and solve problems. A.1 Understand various uses of variables to represent quantities or attributes. A.2 Describe the effect that a change in the value of one variable has on the value(s) of other variables in the algebraic relationship. A.3 Construct and use equations to represent relationships involving one or more unknown or variable quantities to solve problems. Mathematical Modeling Goal: Students will reason using the language and structure of mathematics to investigate, represent, and solve problems. Students will be able to: M.1 Create models of authentic contextual situations, including: M.1.1 Using multiple representations of mathematical models such as tables, graphs, equations, and words. M.1.2 Using multiple variables to represent quantities or attributes. M.1.3 Describing why these tools are a useful strategy for understanding the world. M.1.4 Describing limitations present in these models. M.2 Demonstrate an extensive understanding of linear models by: M.2.1 Creating and using linear models of real world situations. M.2.2 Describing the behavior of linear models using words, algebraic symbols, graphs, and tables. M.2.3 Identifying when a linear model or trend is reasonable for given data or context. M.2.4 Determining a reasonable domain of the model based on the scenario. M.2.5 Using appropriate terms and units to describe rate of change. (For example: Describe the rate of change using appropriate units: slope for linear relationships or average rate of change over an interval for nonlinear relationships.) M.3 Demonstrate an understanding of exponential models by: M.3.1 Creating and using exponential models of real world situations including growth and decay models beyond financial concepts. M.3.2 Describing the behavior of exponential models using words, algebraic symbols, graphs, and tables. revised 8/18

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M.3.3 Identifying when an exponential model or trend is reasonable for given data or context. M.3.4 Determining a reasonable domain of the model based on the scenario. M.4 Develop mathematical modeling skills in personal finance that move beyond basic exponential models. M.5 Understand and describe models beyond linear and exponential models. Students will be able to: M.5.1 Identify when a linear and/or exponential model is not reasonable.
• Spring '11
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