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ALGEBRA 1: NJDOE MODEL CURRICULUM CONTENT AREA: Mathematics STUDENT LEARNING OBJECTIVES # 1 Course: Algebra 1 Write linear and exponential functions (e.g. growth/decay and arithmetic and geometric sequences) from graphs, tables, or a description of the relationship, recursively and with an explicit formula, and describe how quantities increase linearly and exponentially over equal intervals. UNIT #: 5 UNIT NAME: Functions and Descriptive Statistics CCSS NJCCCS F.BF.2 F.LE.1 F.LE.2 Cherry Math: equations of exponential functions http://wcherry.math.unt.edu/math1650/exponential.pdf Regentsprep.org: Equations of Straight Lines Lesson: http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/EqLines.htm Practice: http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/pracEq.htm RegentsPrep: exponential growth and decay http://www.regentsprep.org/Regents/math/ALGEBRA/AE7/ExpDecayL.htm 2 Represent data on the real number line (i.e. dot plots, histograms, and box plots) and use statistics to compare and interpret differences in shape, center, and spread in the context of the data (account for effects of outliers). Page 1 of 4 S.ID.1 S.ID.2 S.ID.3 Laerd Statistics: measures of spread https://statistics.laerd.com/statistical-guides/measures-of-spread-rangequartiles.php Math is Fun: Dot Plots, Histograms http://www.mathsisfun.com/data/dot-plots.html http://www.mathsisfun.com/data/histograms.html Algebra 1: Unit-5 Functions & Descriptive Statistics KK, EE July 2013 ALGEBRA 1: NJDOE MODEL CURRICULUM CONTENT AREA: Mathematics Course: Algebra 1 UNIT #: 5 UNIT NAME: Functions and Descriptive Statistics Shodor: Box Plots (interactive) http://www.shodor.org/interactivate/activities/BoxPlot/ 3 4 Summarize and interpret categorical data for two categories in two-way frequency tables; recognize associations and trends in the data. S.ID.5 Represent and describe data for two variables on a scatter plot, fit a function to the data, analyze residuals (in order to informally assess fit), and use the function to solve problems. S.ID.6 Math is Fun: Frequency Tables http://www.mathsisfun.com/data/mean-frequency-table.html Internet Retailer: Real-World application of data trends http://www.internetretailer.com/trends/ Regentsprep.org: Scatter Plots and Lines of Best Fit (lessons, practice) http://www.regentsprep.org/Regents/math/ALGEBRA/AD4/indexAD4.htm NLVM: Scatter Plot (interactive exploration) Uses a given function or choose a function suggested by the context. Emphasize linear and exponential models. http://nlvm.usu.edu/en/nav/frames_asid_144_g_4_t_5.html?open=activities Fitting Functions to Data http://people.hofstra.edu/stefan_waner/realworld/calctopic1/regression.html 5 Interpret the slope, intercept and correlation coefficient (compute using technology) of a linear model. Page 2 of 4 S.ID.7 S.ID.8 Interpreting Linear Models http://www.math.montana.edu/frankw/ccp/modeling/discrete/linear/learn.htm Algebra 1: Unit-5 Functions & Descriptive Statistics KK, EE July 2013 ALGEBRA 1: NJDOE MODEL CURRICULUM CONTENT AREA: Mathematics 6 Course: Algebra 1 Distinguish between correlation and causation in a data context. UNIT #: 5 S.ID.9 UNIT NAME: Functions and Descriptive Statistics Stats.org: difference between correlation and causation http://www.stats.org/faq_vs.htm Correlation vs Causation in a graph http://chrisblattman.com/2013/05/24/correlation-versus-causation-in-a-singlegraph/ Major Content (identified by PARCC Model Content Frameworks) Code # S.ID.1 S.ID.2 S.ID.3 S.ID.5 S.ID.6 S.ID.7 Page 3 of 4 Common Core State Standards Represent data with plots on the real number line (dot plots, histograms, and box plots). Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models. b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Algebra 1: Unit-5 Functions & Descriptive Statistics KK, EE July 2013 ALGEBRA 1: NJDOE MODEL CURRICULUM CONTENT AREA: Mathematics S.ID.8 S.ID.9 F.BF.2 F.LE.1 F.LE.2 Course: Algebra 1 UNIT #: 5 UNIT NAME: Functions and Descriptive Statistics Compute (using technology) and interpret the correlation coefficient of a linear fit. Distinguish between correlation and causation. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.★ Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals; and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative another. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Major Content (identified by PARCC Model Content Frameworks) Page 4 of 4 Algebra 1: Unit-5 Functions & Descriptive Statistics KK, EE July 2013