(Illustrative Mathematics) (Mathematics Assessment Project – FAL) Back to: Algebra – Seeing Structure in Expressions NC.M1.A-SSE.1b Interpret the structure of expressions. Interpret expressions that represent a quantity in terms of its context. Interpret a linear, exponential, or quadratic expression made of multiple parts as a combination of entities to give meaning to an expression. Concepts and Skills The Standards for Mathematical Practices Pre-requisite Connections Interpret a sum, difference, product, and quotient as a both a whole and as a composition of parts (6.EE.2b) Understand that rewriting expressions into equivalent forms can reveal other relationships between quantities (7.EE.2) Interpret numerical expressions written in scientific notation (8.EE.4) Generally, all SMPs can be applied in every standard. The following SMPs can be highlighted for this standard. 2 – Reason abstractly and quantitatively. 4 – with mathematics 7 – Look for and make use of structure. Connections Disciplinary Literacy Factor to reveal the zeros of functions and solutions to quadratic equations (NC.M1.A.SSE.3) Creating one and two variable equations (NC.M1.A-CED.1, NC.M1.A-CED.3) Interpreting part of a function to a context (NC.M1.F-IF.2, NC.M1.F-IF.4, NC.M1.F-IF5, NC.M1.F-IF.7, NC.M1.F-IF.9) Interpreting changes in the parameters of a linear and exponential function in context (NC.M1.F-LE.5) As stated in SMP 6, the precise use of mathematical vocabulary is the expectation in all oral and written communication. New Vocabulary: exponential expression, quadratic expression Mastering the Standard Comprehending the Standard Assessing for Understanding The set of A-SSE standards requires students: to write expressions in equivalent Students should understand that working with unsimplified expressions often reveals key information from a context.
In 8th students created scatter plots and described patterns of association between two quantities. They also informally fit a straight line to data based on how closely the data points resembled a line. That knowledge is extended to fitting a linear regression equation to a set of data using technology. Technology includes graphing calculators, computer software/programs and web-based applets and tools. The initial exploration with technology should include a discussion of domain and range and their relationship to the graphing window. Most technology tools include an automatic feature that graphs data within a window representative of the data, however understanding of the graphing window can lead to further discussions about domain, range, interpolation and extrapolation. Students can represent data on a scatter plot using an appropriate scale and describe the relationship between two quantitative variables. Example: Represent the data from the table below in a scatter plot. Determine if and what the relationship is between the population of each high school and the number of active band members. Example: The data gives the number of miles driven and advertised price for 11 used models of a particular car. Use a calculator or graphing technology to make a scatter plot of the data. Find the correlation coefficient for the data above. Describe what the correlation coefficient means in regards to the data. Fit a linear function to model the relationship between miles driven and the price of these cars. How do you know that this is the best-fit model? If a used car is driven 98,000 miles, what will the price be (to the nearest dollar)? If the price of the car is $12,540, how many miles could have been driven (to the nearest thousand)? Instructional Resources Tasks Additional Resources (Illustrative Mathematics) (Illustrative Mathematics) (DESMOS) Back to: Interpreting Categorical and Quantitative Data NC.M1.S-ID.6b Summarize, represent, and interpret data on two categorical and quantitative variables. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.