Integrated Algebra I (from 2027-28) (Maryland MCCRS)

Algebraic Thinking – AT.A: Structure in expressions

• IA1.AT.A.1 Rewrite and interpret linear and exponential expressions, explain their parts in context and compare equivalent forms.
  • a. Treat parts of linear and exponential expressions as single quantities and explain them in context.
  • b. Rewrite the expressions in equivalent forms that show rate of change, initial value or growth or decay rate.
  • c. Compare equivalent forms and choose the one that best helps solve the problem.

Algebraic Thinking – AT.B: Equations, inequalities and systems

• IA1.AT.B.2 Create, solve, justify and interpret one-variable linear, absolute value and exponential equations in context.
  • a. Write one-variable linear and exponential equations for relationships between quantities.
  • b. Solve linear equations efficiently, justify each step and interpret the solution.
  • c. Solve absolute value equations once the absolute value is isolated, and interpret the solutions.
  • d. Solve exponential equations by rewriting both sides with a common base.
• IA1.AT.B.3 Create, solve and interpret one-variable linear and absolute value inequalities and show them on number lines.
  • a. Write one-variable inequalities for constraints or conditions.
  • b. Solve linear inequalities, including variables on both sides; show solutions on a number line and in notation.
  • c. Solve absolute value inequalities as compound inequalities and graph them.
  • d. Explain what the solution set means in context and which values make sense.
• IA1.AT.B.4 Create and graph two-variable linear and exponential equations and use the graphs to solve problems in context.
  • a. Write two-variable linear and exponential equations for relationships and graph them.
  • b. Use the graph as the set of all solutions to find solutions, spot patterns and interpret the relationship.
• IA1.AT.B.5 Create systems of two linear equations, solve them algebraically and graphically, and interpret the solution.
  • a. Write systems of linear equations for relationships.
  • b. Solve systems algebraically by substitution and linear combination (elimination).
  • c. Estimate or check solutions by graphing and finding the intersection.
  • d. Interpret the solution in context.
• IA1.AT.B.6 Write linear inequalities in two variables and graph their solutions as half-planes.
• IA1.AT.B.7 Represent and graph systems of two linear inequalities as overlapping half-planes and interpret them.
  • a. Write systems of two-variable linear inequalities for constraints.
  • b. Graph the solution set as the overlap of half-planes.
  • c. Interpret the solution set and test whether given points satisfy the system.
• IA1.AT.B.8 Model and solve optimization problems with systems of linear inequalities and justify the best solution.
  • a. Represent an optimization situation with constraints and an objective as a system of inequalities.
  • b. Graph the feasible region and find points that meet every constraint.
  • c. Identify and justify the optimal solution and interpret it.
• IA1.AT.B.9 Use technology to solve a system of a linear and an exponential equation and interpret the solution.

Algebraic Thinking – AT.C: Reason about functions

• IA1.AT.C.10 Find domain and range, decide whether a function is one-to-one, and use function notation to evaluate and interpret.
  • a. Decide whether a relation is a function (one output per input) from tables, graphs or equations.
  • b. Decide whether a function is one-to-one and justify.
  • c. Evaluate functions with function notation and interpret values in context.
  • d. See a graph as the ordered pairs (x, f(x)) and explain how it shows domain and range.
• IA1.AT.C.11 Calculate, estimate and interpret average rates of change of linear and exponential functions.
• IA1.AT.C.12 Compare key features of a linear and an exponential function each given in a different form.

Algebraic Thinking – AT.D: Model with functions

• IA1.AT.D.13 Analyze arithmetic and geometric sequences with recursive and explicit rules and use them to model situations.
  • a. Identify sequences as arithmetic or geometric and write an explicit rule.
  • b. Turn a recursive rule into an explicit rule.
  • c. Model situations with arithmetic or geometric patterns using either kind of rule.
• IA1.AT.D.14 Represent functions with tables and graphs and interpret key features in context, including piecewise and absolute value functions.
  • a. Spot patterns in tables and graphs that separate constant (linear) from proportional (exponential) growth.
  • b. Represent piecewise and absolute value functions in tables and graphs, seeing absolute value as a piecewise case.
  • c. Link graph and table features to the context and judge whether the model fits.
• IA1.AT.D.15 Tell linear from exponential situations by whether change is by a constant difference or a constant factor.
  • a. Recognize equal change over equal intervals as linear and build a linear model.
  • b. Recognize a constant percent change per interval as exponential and build an exponential model.
• IA1.AT.D.16 Analyze how changing a function's input or output shifts or stretches its graph and what that means.
  • a. Explain how replacing f(x) with related expressions, using a value k, changes linear, exponential or absolute value graphs.
  • b. Explain how changing inputs or outputs affects the quantities in context, compared with the parent function.
• IA1.AT.D.17 Find and interpret the inverse of a linear function in context.
  • a. Show that a linear function is one-to-one, so its inverse is a function.
  • b. Find the inverse of a linear function given as an equation or a table.
  • c. Interpret the inverse as mapping outputs back to inputs in context.

Geometric Reasoning – GR.A: Transformations and congruence

• IA1.GR.A.1 Treat rotations, reflections and translations as functions on points and use rigid motions to check congruence.
  • a. Describe rotations, reflections and translations as functions on points and use them to transform figures.
  • b. Check experimentally that rigid motions keep distance, angle size and parallel lines, and use this to justify congruence.
• IA1.GR.A.2 Use rigid motions to show that triangles are congruent when corresponding sides and angles match.

Geometric Reasoning – GR.B: Conjecture about and verify geometric relationships

• IA1.GR.B.3 Apply triangle congruence theorems to reason about diagrams and find unknown measures.
• IA1.GR.B.4 Use angle relationships for parallel lines cut by a transversal and slope rules for parallel and perpendicular lines.
  • a. Use theorems about parallel lines and transversals to find and apply angle pair relationships.
  • b. Verify slope rules for parallel and perpendicular lines and use them, including writing equations.
• IA1.GR.B.5 Use angle relationships and slope to verify properties of parallelograms on the coordinate plane.
  • a. Use parallel-line angles and triangle congruence to verify properties of parallelograms.
  • b. Use slope to verify that a quadrilateral on the coordinate plane is a parallelogram.

Reasoning with Data, Statistics and Probability – DS.A: Statistical inquiry

• IA1.DS.A.1 Distinguish between correlation and causation.
• IA1.DS.A.2 Explain how random samples support inferences about populations and judge whether a sample is representative.
  • a. Explain how random selection produces unbiased, representative samples.
  • b. Analyze how representative a sample is and what that means for conclusions about the population.
• IA1.DS.A.3 Analyze how data is used in arguments and evaluate graphs and data collection methods.
  • a. Pick out claims, graphs and statistical language in arguments based on data.
  • b. Judge how accurately graphs show the data and support a conclusion.
  • c. Describe how data were collected and whether the method supports sound conclusions.
• IA1.DS.A.4 Plan a statistical investigation by posing an answerable question and choosing a sound way to collect data.
  • a. Pose statistical questions that data can answer.
  • b. Choose data collection methods that make results more accurate, valid and representative.

Reasoning with Data, Statistics and Probability – DS.B: Describe, analyze and compare data

• IA1.DS.B.5 Compare one-variable data plots on a number line by shape, center, spread and usefulness.
  • a. Compare data displays to see what each one shows best.
  • b. Compare shape, center and spread of data sets with suitable displays.
• IA1.DS.B.6 Build and interpret two-way frequency tables to look for association and find joint and marginal probabilities.
  • a. Use two-way frequency tables to decide whether events are independent.
  • b. Use two-way frequency tables to find joint and marginal probabilities.
• IA1.DS.B.7 Make scatter plots, describe the relationship and fit and assess linear or exponential models.
  • a. Fit linear or exponential functions to scatter plot data and use them to solve problems.
  • b. Judge the fit visually and analytically and decide whether the model suits the data and context.
• IA1.DS.B.8 Interpret the slope and intercept of linear models and the growth factor or rate of exponential models.
  • a. Interpret the slope and intercept of a linear model to describe the data.
  • b. Analyze the growth factor or average rate of change of an exponential model to describe trends and predict.