Integrated Algebra 1 Course Framework Appendix A.pdf

Integrated Algebra 1 Course Framework

Draft For Development Purposes

July 2026

Maryland State Department of Education | 1

Integrated Algebra 1 Framework July 2026

Purpose of This Document

This framework is intended to communicate the vision and conceptual organization of Integrated

Algebra 1. It describes the major learning arcs, mathematical progressions, and design priorities that should guide curriculum development.

The Maryland College and Career Ready Standards for Mathematics remain the primary source for the specific mathematical expectations of the course and should be used alongside this framework.

While the standards define what students are expected to know and be able to do, this framework illustrates how those expectations can be organized into a coherent and connected course experience.

The learning arcs described in this document are intended to support the development of curriculum that reflects the integrated nature of the course and advances students' understanding of relationships, change, structure, reasoning, and mathematical modeling.

https://marylandpublicschools.org/about/pages/dcaa/math/revised-standards.aspx

Maryland State Department of Education | 2

Conceptualization of Integrated Algebra

Integrated Algebra should be intentionally designed around the idea that algebra, geometry, statistics, and probability are complementary ways of describing, analyzing, and making sense of mathematical situations. Rather than organizing learning as isolated strands, curriculum should create purposeful opportunities for students to draw on ideas from multiple domains to investigate a common concept, phenomenon, or problem.

This integration is not simply a matter of including content from different domains within the same unit. It requires identifying the mathematical connections that allow students to deepen and extend their understanding. For example, students might explore quadratic relationships by analyzing patterns of change, interpreting graphical representations, examining geometric structures that exhibit quadratic behavior, and using mathematical models to describe and predict real-world phenomena.

Through these experiences, students develop a more robust understanding of the underlying mathematics and recognize how different representations and perspectives reveal different aspects of the same idea.

Curriculum should regularly engage students in tasks that require them to connect representations, reason across mathematical domains, and apply mathematics to meaningful contexts. Learning experiences should be designed so that concepts introduced in one domain strengthen and are strengthened by concepts encountered in another. This coherence helps students build durable understanding, transfer learning across contexts, and develop increasing sophistication in their reasoning, problem solving, and mathematical communication.

An effective Integrated Algebra curriculum therefore treats mathematical connections as a central design principle.

Maryland State Department of Education | 3

The Progression of Learning Across Integrated Algebra 1

Integrated Algebra 1 is organized around the development of ways of understanding and using mathematical relationships. Across the course, students move from investigating relationships, to understanding patterns of change, to justifying relationships, and ultimately to using relationships to make decisions and solve problems.

Each learning arc contributes a distinct perspective while building toward a coherent understanding of mathematics as a connected discipline.

Learning Arc Central Focus Role in Student Learning

Using Data to Investigate

Relationships

Investigating

Relationships

Students use data to identify patterns, examine associations, evaluate claims, and recognize that mathematical relationships can be used to describe real-world phenomena.

Comparing & Modeling Patterns of Change

Understanding Change

Students use linear, exponential, and other functions to analyze, compare, and model patterns of change.

They develop a deeper understanding of how relationships behave over time.

Structure, Geometry, &

Mathematical Justification

Justifying Relationships

Students use transformations, symmetry, congruence, and coordinate geometry to analyze relationships, explain patterns, and justify mathematical conclusions.

Applications of Equations, Inequalities, &

Systems

Using Relationships to

Make Decisions

Students apply equations, inequalities, systems, and mathematical models to analyze constraints, evaluate options, and identify viable solutions.

Maryland State Department of Education | 4

Learning Arc 1: Using Data to Investigate Relationships

APPROXIMATE COURSE EMPHASIS: 15%

Role in the Course

This arc serves as students' entry point into the study of relationships. Rather than beginning with symbolic procedures, students begin by investigating questions, examining evidence, and making sense of patterns that emerge from data. The purpose of this arc goes beyond teaching statistics and establishes modeling, interpretation, and evidence-based reasoning as central purposes of mathematics. Many of the ideas that become central throughout the remainder of the course (e.g., rate of change, functional relationships, prediction, model fit, and interpretation) are first encountered through the analysis of data.

Mathematical Story

Students investigate statistical questions and analyze how data are collected, represented, and interpreted. The arc progresses from describing individual variables, to examining associations between categorical variables, to modeling relationships between quantitative variables. Students use one-variable data displays to describe distributions and interpret measures of center, spread, and shape.

They then use two-way tables to investigate associations between categorical variables and scatterplots to examine relationships between quantitative variables. As students analyze bivariate data, they use regression models to describe relationships, make predictions, and evaluate the appropriateness of linear and exponential models. Throughout the arc, students examine the distinction between correlation and causation and recognize the importance of study design and data collection methods in supporting valid conclusions. By the end of the arc, students understand mathematics as a tool for investigating, modeling, and interpreting relationships using data.

Design Priorities for Curriculum Students Should Leave This Arc Understanding That…

Position statistical inquiry around meaningful questions and investigations.

Emphasize interpretation, critique, and communication over procedural computation.

Develop a progression from one-variable data, to categorical associations, to quantitative relationships and modeling.

Use technology as the primary tool for creating and analyzing data representations.

Treat regression models as opportunities to introduce mathematical modeling.

Provide opportunities for students to evaluate claims, assess evidence, and communicate conclusions.

Connect statistical relationships to future study of functions and patterns of change.

Statistical investigations depend on the quality of data collection methods and study design.

Different representations reveal different aspects of a data set and may support different types of conclusions.

Measures of center, spread, and shape provide complementary ways to describe and compare distributions.

Associations between categorical variables can be investigated using two-way tables and interpreted through relative frequencies and probabilities.

Relationships between quantitative variables can be described, analyzed, and modeled using scatterplots and regression models.

Mathematical models can be used to describe, explain, and predict patterns in data.

Correlation describes the strength and direction of an association but does not establish causation.

Maryland State Department of Education | 5

Learning Arc 2: Comparing & Modeling Patterns of Change

APPROXIMATE COURSE EMPHASIS: 35%

Role in the Course

This arc develops students' understanding of how mathematical relationships behave and change.

Building on prior experiences with functions, students investigate and compare linear and exponential patterns and use multiple representations to analyze how quantities vary together. Through modeling, interpretation, and comparison, students develop increasingly sophisticated ways of describing change and predicting future behavior. The arc establishes foundational understandings about rates of change, growth, and mathematical modeling that support later work throughout the secondary mathematics program.

Mathematical Story

Students investigate situations involving change and compare how quantities grow, decay, and vary over time. Building on prior understandings of functions, they analyze linear and exponential relationships through graphs, tables, equations, sequences, and contexts, and through this develop a deeper understanding of additive and multiplicative patterns of change. Students examine key features such as intercepts, rates of change, growth factors, domain, range, and end behavior and interpret the meaning of those features in context. Arithmetic and geometric sequences provide a bridge between recursive reasoning, explicit rules, and functional thinking. Students also investigate absolute value, piecewise-defined functions, transformations, and inverse linear functions, which extends their understanding of how relationships can be represented, interpreted, and compared.

Design Priorities for Curriculum Students Should Leave This Arc Understanding That…

Position functions as tools for describing and analyzing relationships.

Develop linear and exponential reasoning through continuous comparison rather than teaching each type of function in isolation.

Consistently connect representations so students experience them as complementary views of the same relationship.

Emphasize interpretation of parameters, features, and patterns in context

Use technology strategically to explore behavior, compare models, investigate transformations, and analyze data.

Engage students in creating, comparing, refining, and evaluating mathematical models.

Linear functions are characterized by constant additive change, while exponential functions are characterized by constant multiplicative change.

Arithmetic and geometric sequences can be represented recursively and explicitly and serve as important examples of linear and exponential relationships.

Features such as intercepts, rates of change, growth factors, domain, range, and end behavior have meaning within the situations being modeled.

The appropriateness of a model depends on how well it represents the underlying relationship and context.

Transformations produce predictable changes in the graphs and interpretations of functions, while inverses reverse the roles of inputs and outputs.

Maryland State Department of Education | 6

Learning Arc 3: Structure, Geometry, & Mathematical Justification

APPROXIMATE COURSE EMPHASIS: 20%

Role in the Course

This arc develops students' ability to explain and justify mathematical relationships. Through transformations, symmetry, congruence, and coordinate geometry, students learn how mathematical claims can be supported using definitions, properties, structure, and logical reasoning. The arc strengthens connections between algebraic and geometric thinking while helping students understand that mathematical relationships can be analyzed, generalized, and justified through multiple representations and perspectives.

Mathematical Story

Students begin investigating transformations by exploring rigid motions and examining how transformations preserve distance, angle measure, and other geometric properties. Through these experiences, students develop an understanding of congruence as a consequence of transformations rather than simply a collection of criteria. Students then use transformations, symmetry, and geometric structure to reason about properties of figures and justify conclusions. Coordinate methods extend this reasoning by connecting geometric relationships to algebraic concepts such as slope and equations of lines. Parallel and perpendicular lines, angle relationships, triangle congruence, and properties of parallelograms provide opportunities for students to construct arguments, test conjectures, and use established relationships to support claims. Throughout the arc, students also connect transformations of geometric figures to transformations of function graphs, which reinforces the idea that transformations are a unifying mathematical concept that extends across domains.

Design Priorities for Curriculum Students Should leave This Arc Understanding That…

Use transformations as the primary lens through which students investigate congruence, geometric structure, and relationships among figures.

Treat geometric properties and theorems as outcomes of reasoning rather than facts to be memorized.

Explicitly connect transformations of geometric figures to transformations of function graphs developed in Arc 2.

Position slope as both an algebraic and geometric concept that helps explain relationships among lines and figures.

Leverage symmetry, transformations, and coordinate methods to investigate properties of quadrilaterals and other figures.

Rigid transformations preserve distance, angle measure, and parallelism, so they are useful tools for defining and verifying congruence.

Geometric conclusions can be justified using definitions, transformations, previously established results, and logical reasoning.

Coordinate representations provide a way to analyze and verify geometric relationships using algebraic methods.

Equal slopes indicate parallel lines, while negative reciprocal slopes indicate perpendicular lines.

Triangle congruence criteria, angle relationships, and properties of figures can be used to establish and justify geometric relationships.

Properties of polygons and quadrilaterals can be explained and verified through symmetry, congruence, angle relationships, and slope criteria.

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Learning Arc 4: Applications of Equations, Inequalities, & Systems

APPROXIMATE COURSE EMPHASIS: 30%

Role in the Course

This arc serves as the culmination and synthesis of Integrated Algebra 1. Students bring together ideas from functions, equations, inequalities, graphing, modeling, and reasoning to analyze situations involving multiple relationships and constraints. While earlier arcs focus on describing and understanding relationships, this arc emphasizes using mathematics to make decisions, evaluate possibilities, and identify solutions that satisfy given conditions. It provides students with powerful tools for representing complex situations and reinforces the idea that mathematics is a means of solving problems and supporting decision-making.

Mathematical Story

Students begin by representing conditions and constraints using equations and inequalities and interpreting what solutions mean within a given context. As students move from single equations and inequalities to systems, they learn to analyze multiple relationships simultaneously. They interpret intersections, solution sets, and feasible regions as meaningful representations of possible outcomes.

Graphical, numerical, and algebraic approaches are used together to build understanding of why solution methods work and what solutions represent. Students then extend this reasoning to systems of inequalities, where they analyze regions that satisfy multiple constraints and determine viable solutions. The arc culminates in optimization problems that require students to identify solutions that satisfy all constraints while maximizing or minimizing a particular quantity. Technology is used strategically to investigate more complex systems, including situations involving both linear and exponential relationships.

Design Priorities for Curriculum Students Should leave This Arc Understanding That…

Introduce equations, inequalities, and systems through meaningful situations involving conditions and constraints.

Develop systems conceptually as interacting relationships.

Use graphing as a tool for developing understanding of intersections, solution sets, and feasible regions.

Use optimization as a natural culmination of work with inequalities and systems.

Leverage technology to investigate systems that extend beyond what can be efficiently solved by hand, including systems involving linear and exponential relationships.

Solutions have meaning within the situation being modeled and must be interpreted in context.

A system represents two or more relationships that must be satisfied simultaneously.

Different solution methods reveal different aspects of a system while producing the same solution set.

Systems of inequalities define regions that represent all solutions satisfying multiple constraints simultaneously.

Optimization problems require balancing constraints and objectives to identify the most effective solution.

Technology can be used strategically to explore, analyze, and interpret more complex mathematical models and systems.