Algebra: Concepts and Connections (Georgia's K-12 Mathematics Standards)

Mathematical Modeling (MM)

• A.MM.1 Apply mathematics to real situations and build models of real-life phenomena.
  • A.MM.1.1 Explain real problems by using a mathematical model.
  • A.MM.1.2 Create models that explain situations in science, social science, the arts and humanities.
  • A.MM.1.3 Use, convert and keep track of units through a problem and interpret input and output units.
  • A.MM.1.4 Use a range of representations and structures to show and solve real-life problems.
  • A.MM.1.5 Choose suitable quantities when describing and modeling a situation.

Numerical Reasoning (NR)

• A.NR.5 Explore rational and irrational numbers and rewrite expressions with square and cube roots.
  • A.NR.5.1 Rewrite numeric and algebraic expressions that contain radicals.
  • A.NR.5.2 Justify whether sums and products of rational and irrational numbers are rational or irrational.

Patterning & Algebraic Reasoning (PAR)

• A.PAR.4 Write, analyze and solve linear inequalities and systems of inequalities that model situations.
  • A.PAR.4.1 Write and solve two-variable linear inequalities and graph them on labeled, scaled axes.
  • A.PAR.4.2 Use linear inequalities as constraints and decide whether data points are possible.
  • A.PAR.4.3 Solve systems of linear inequalities by graphing, including in applied problems.
• A.PAR.6 Build quadratic expressions and equations that model real situations and solve them in context.
  • A.PAR.6.1 Interpret the parts of a quadratic expression in terms of its context.
  • A.PAR.6.2 Fluently write equivalent forms of a quadratic that reveal its properties.
  • A.PAR.6.3 Write and solve one-variable quadratic equations and explain the solutions in context.
  • A.PAR.6.4 Use quadratic equations as constraints and decide whether data points are possible.
• A.PAR.8 Write and analyze exponential expressions and equations that model real situations.
  • A.PAR.8.1 Interpret the parts of an exponential expression in context.
  • A.PAR.8.2 Write one-variable exponential equations and use them to solve problems.
  • A.PAR.8.3 Write two-variable exponential equations and graph them on labeled, scaled axes.
  • A.PAR.8.4 Use exponential equations as constraints and decide whether data points are possible.

Functional & Graphical Reasoning (FGR)

• A.FGR.2 Build and interpret arithmetic sequences and linear functions and compare them with nonlinear functions.
  • A.FGR.2.1 Build and interpret arithmetic sequences as functions whose domain is a set of integers.
  • A.FGR.2.2 Draw and interpret graphs of linear functions that model situations, using notation for key features.
  • A.FGR.2.3 Relate a linear function's domain and range to its graph and context using interval and set notation.
  • A.FGR.2.4 Write and evaluate linear functions in function notation and interpret them in context.
  • A.FGR.2.5 Compare linear and nonlinear behavior informally using parent graphs (quadratic, exponential, absolute value, root).
• A.FGR.7 Build and interpret quadratic functions from data and describe graph features in context.
  • A.FGR.7.1 Write and evaluate quadratic functions in function notation and interpret them.
  • A.FGR.7.2 Predict how f(x) + k, kf(x), f(kx) and f(x + k) change a graph and find k from graphs.
  • A.FGR.7.3 Graph quadratic functions and analyze their key features, including in context.
  • A.FGR.7.4 Relate a quadratic function's domain and range to its graph and the quantities involved.
  • A.FGR.7.5 Rewrite a quadratic to show its maximum or minimum and explain what it means in context.
  • A.FGR.7.6 Write two-variable quadratic relationships and graph them on labeled, scaled axes.
  • A.FGR.7.7 Estimate and interpret average rates of change of quadratics and compare them with linear rates.
  • A.FGR.7.8 Write a quadratic function in equivalent forms that show different properties.
  • A.FGR.7.9 Compare two functions given in different ways (graphs, tables, equations or words).
• A.FGR.9 Build and analyze exponential graphs that model situations and compare them with linear and quadratic ones.
  • A.FGR.9.1 Write and evaluate exponential functions in function notation and interpret them in context.
  • A.FGR.9.2 Graph simple exponential functions from real situations and analyze key features.
  • A.FGR.9.3 Predict the effects of f(x) + k and kf(x) for positive and negative k and find k from graphs.
  • A.FGR.9.4 Build and interpret geometric sequences as functions whose domain is a set of integers.
  • A.FGR.9.5 Compare two functions given in different ways.

Geometric & Spatial Reasoning (GSR)

• A.GSR.3 Solve problems about distance, midpoint, slope, area and perimeter that model real situations.
  • A.GSR.3.1 Solve real problems with slope, parallel and perpendicular lines, area and perimeter.
  • A.GSR.3.2 Use the distance, midpoint and slope formulas in real-world problems.

Data & Statistical Reasoning (DSR)

• A.DSR.10 Analyze one-variable data to compare groups and show two-variable data on scatter plots with fitted functions.
  • A.DSR.10.1 Compare the centers and spreads of distributions with suitable statistics, by hand and with technology.
  • A.DSR.10.2 Explain differences in shape, center and spread in context, including the effect of outliers.
  • A.DSR.10.3 Make scatter plots of two quantitative variables and describe how they are related.
  • A.DSR.10.4 Interpret the slope of a linear model as a predicted rate of change and the intercept as a constant.
  • A.DSR.10.5 Find a line of best fit with technology, interpret r and judge whether predictions are reasonable.
  • A.DSR.10.6 Choose the best type of function for data by looking at its graph.
  • A.DSR.10.7 Tell the difference between correlation and causation.