Curriculum Algebra 1 - Second Marking Period - Unit 2: Modeling with Linear Functions, Systems and Inequalities

Sep 30, 2026

Algebra 1 Second Marking Period Unit 2 focuses on modeling real-world situations using linear functions, systems of equations, and inequalities. Students represent functions with words, tables, equations, ordered pairs, and graphs, and interpret slope as the rate of change. The unit emphasizes creating linear models from constraints and relationships, analyzing scatter plots to estimate trends, and solving systems using graphing, substitution, or elimination. Time frame spans one marking period and includes formative and summative assessments.

LanguageEnglish

CategoryExam

FormatPDF

Pages11

Reading Time28 min

AccessFree to download

Overview

Enduring Understandings

Essential Questions

Standards, Topics, Objectives, and Activities

N.Q.A.1-N.Q.A.3

A.SSE.A.1, ASSE.A.2

A.CED.A.2-A.CED.A.3

Objectives: We are learning to/that

Learning Resources and Assessments

Englewood Public School District Algebra 1 Second Marking Period Unit 2: Modeling with Linear Functions, Systems and Inequalities Overview: During this unit, students will investigate functions and their application to the real world using linear equations, scatter plots, and systems of equations. Time Frame: 35 to 45 days (One Marking Period) Enduring Understandings: • A function pairs one input value with exactly one output value. Functions are represented using words, tables, equations, sets of ordered pairs, and graphs. • Functions can be used to model real-world situations. • In the graph of a line, the ratio for the slope indicates the rate of change. • There are several forms for the equation of a line; each form communicates different information. • A scatter plot with an equation of a line models the trend of real-world data; the equation can be used to estimate and make predictions. • Systems of equations of equations and inequalities can be solved using the graphing method, substitution method, or elimination method. • Real world mathematical problems that include two unknowns can be modeled using systems of equations. Essential Questions: • How can you represent and describe functions? • Can functions describe real world situations? • What does the slope of a line indicate about the line? • What information does the equation of a line give you? • How can you make predictions based upon a scatter plot? • How can you solve a system of linear equations or inequalities? • How can systems of equations model real world situations? | Standards | Topics and Objectives | Activities | Materials/Resources | Assessments | | --- | --- | --- | --- | --- | | N.Q.A.1 Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in | Topics
Identifying functions and writing in function notation. Investigating linear equations and their graphs. Writing and | NJSLA Algebra Lessons: | Pearson Realize Chapters 4, | Formative | | | | • Linear Programming | 5, and 6 | Assessments: | | | | • Graphing Equations and Inequalities in Two Variables | NJSLA Lessons (Shared Folder) | Textbook Pages 252, 287–288, 321, 357–358, 393, 411–412 | | | | • Solving Systems of | | | | formulas; choose and interpret the scale and the origin in graphs and data displays.
N.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling.
N.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity.
ASSE.A.2 See the structure of an expression to identify ways to rewrite it.
A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
A.CED.A.3 Represent constraints by equations or | solving systems of linear equations and inequalities.
Objectives
We are learning to/that:
• use units as a way to understand problems and to guide the solution of multi-step problems
• define appropriate quantities to be used in descriptive modeling
• choose an appropriate level of accuracy based on the limitations on measurement
• interpret parts of an expression, such as terms, factors, and coefficients, in context
• interpret the meaning of a complicated expression by viewing one or more parts as a single quantity
• use the structure of an expression to identify ways to rewrite it
• create linear equations to represent relationships between two or more quantities
• graph linear equations on the coordinate plane to represent relationships
• constraints reflect conditions in the modeling process | Eq

FAQs

What does the unit teach about functions and their representations?

Students learn that a function matches each input value to exactly one output value and practice representing functions using words, tables, equations, sets of ordered pairs, and graphs.

How is slope used in this unit?

Students interpret slope as the ratio that indicates the rate of change in the graph of a line, connecting the equation of a line to real-world meaning.

What methods can students use to solve systems of linear equations or inequalities?

Students use graphing, substitution, or elimination methods to solve systems, and then apply those solutions to model real-world situations with two unknowns.

Sep 30, 2026

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