Each unit includes:
🎯 Objective – A quick summary of what you’ll learn
📝 Class Handouts The papers that we passed out in class
🎥 Teacher Videos – Direct instruction from one of your teachers
📺 Supplementary Videos – Curated YouTube videos with different teaching styles (visual, fast-paced, contextual)
📝 Practice Activities – Opportunities to try problems and check your understanding
💡 Tips for Success:
▶️ Watch the teacher video first to learn the core idea
👀 Explore extra videos if you need a different explanation
✍️ Do the practice — it’s how you’ll get better and more confident
🙋 Ask your teacher if you get stuck — we’re here to help
By the end of Unit 3, you will be able to solve systems of linear equations by graphing, substitution, and elimination, decide which method fits a given system or context, classify systems by number of solutions, and model real situations with systems and interpret the solution.
Class Handouts
🎥 Teacher-created video(s)
(Prior concept refreshers)
Slope & y-intercept (y = mx + b) – identifying slope and intercept and graphing quickly. Glasp
Graphing linear equations – reading/creating graphs, finding intersections visually. OpenStax
Solving single-variable linear equations – isolating a variable cleanly to prepare for substitution/elimination. Mometrix
🔍 Need More Help? Try One of These
(Each subtopic includes a Beginner, Visual/Conceptual, and Challenge option. We used a variety of sources.)
🎥 Beginner: Graphs of Systems of Equations (with built-in video & guided tasks). Purpose: see solutions as intersections. OpenStax
🎥 Visual/Conceptual: Algebra I Systems Playlist (curated video study set). Purpose: see many graphing examples in one place. SchoolTube
🎥 Challenge: MathIsPower4U: Solve by Graphing (one/no/infinite solutions) (library page with targeted clips). Purpose: tricky cases & special solutions. Math Is Power 4 U
🎥 Beginner: Patrick (Pearson Channels): Two-Variable Systems — Substitution (short, targeted teaching video). Purpose: clean step-by-step. Pearson
🎥 Visual/Conceptual: Mike’s Math Videos: Substitution (problem-linked walk-throughs). Purpose: watch full example solutions. Google Sites
🎥 Challenge: Organic Chemistry Tutor: Substitution (harder coefficients/fractions). Purpose: level-up algebra moves. Glasp
🎥 Beginner: Mike’s Math Videos: Elimination (click-to-example set). Purpose: build fluency with “make opposites then add.” Google Sites
🎥 Visual/Conceptual: blackpenredpen: Graphing vs. Substitution vs. Elimination (side-by-side comparison). Purpose: see how the methods connect. Glasp
🎥 Challenge: Organic Chemistry Tutor: Elimination (manipulation & multi-step). Purpose: LCM/multipliers & careful arithmetic. Glasp
🎥 Beginner: OpenStax: Adding/Subtracting Systems + Using Graphs (includes video and tech tips). Purpose: standard-form ➜ elimination. OpenStax
🎥 Visual/Conceptual: blackpenredpen: All three methods in one example. Purpose: decision-making based on structure. Glasp
🎥 Challenge: Organic Chemistry Tutor: Substitution and Elimination in one lesson. Purpose: compare/choose under pressure. Glasp
🎥 Beginner: OpenStax: Graphs of Systems (explicit examples of parallel & coincident lines). Purpose: connect slope/intercept to solution count. OpenStax
🎥 Visual/Conceptual: MathIsPower4U library — clips titled “No Solution / Infinite Solutions.” Purpose: classify quickly using slopes & intercepts. Math Is Power 4 U
🎥 Challenge: SchoolTube playlist (Systems of Linear Equations) — mix of cases & reviews. Purpose: rapid mixed practice via video. SchoolTube
🎥 Beginner: TeacherTube: Systems Word Problems by Graphing. Purpose: set up equations from a context and read the intersection. TeacherTube
🎥 Visual/Conceptual: Mometrix: Substitution & Elimination for Linear Systems (video + quick practice). Purpose: choose a path from the context. Mometrix
🎥 Challenge: Pearson/Patrick channel section with practice items (systems). Purpose: multiple word-problem examples with solutions. Pearson
(At least one option per subtopic; mix of print, interactive, and tech.)
Graphing systems
OpenStax practice sets (graph-based items; includes tech tips for Desmos). OpenStax
MathBitsNotebook – Graphical Systems Practice (hand-graph, then check). MathBits Notebook
Desmos Graphing Calculator — plot both lines and click the intersection. (Help article for features & tips.) Desmos Help Center
Substitution
MathBitsNotebook – Algebraic Systems Practice (substitution/elimination mixed). MathBits Notebook
OpenStax (Elementary Algebra 2e) – Solving by Substitution (worked examples + try-it). OpenStax
Elimination
Number of solutions
OpenStax: Graphs of Systems (identify 1/0/∞ from equations & graphs). OpenStax
MathIsPower4U clips — pick “No Solution/Infinite Solutions” examples to practice classifying before solving. Math Is Power 4 U
Modeling & word problems
MathBitsNotebook – Applied Systems Practice (contexts like prices, mixtures, rates). MathBits Notebook
TeacherTube: Word Problems by Graphing (follow with parallel practice you create). TeacherTube
System of equations: A set of two or more equations with the same variables; a solution makes all equations true.
Solution / Point of intersection: The ordered pair where both lines meet; satisfies both equations.
Slope (m): Rate of change; rise/run of a line; equal slopes → parallel or the same line.
y-intercept (b): Where a graph crosses the y-axis; used to write/graph lines in slope-intercept form.
Coefficient: The number multiplying a variable (e.g., 3 in 3x).
Constant term: A standalone number (no variable) in an equation.
Slope-intercept form: y=mx+by = mx + by=mx+b.
Standard form: Ax+By=CAx + By = CAx+By=C (A, B, C integers; A≥0A \ge 0A≥0).
Substitution method: Solve one equation for a variable, substitute into the other, then back-substitute.
Elimination (linear combination): Add/subtract (and sometimes multiply) equations to cancel a variable.
Equivalent equations: Different forms with the same solution set.
Consistent / Inconsistent: Consistent systems have ≥1 solution; inconsistent have none.
Independent / Dependent: Independent → exactly one solution; dependent → infinitely many (same line).
Parallel lines: Equal slopes, different intercepts → no solution.
Coincident lines: Same slope and intercept (same line) → infinitely many solutions.
Isolate a variable: Rearrange to get a variable alone on one side.
Translate a context: Turn words into variables and equations that model the situation.
Match the method to the form:
Already y= …? → Substitution is fast.
Both in standard form with matching/opposite coefficients? → Elimination.
Clean integer slopes & intercepts or a provided graph? → Graphing.
Line check before solving: Same slope & different intercepts ⇒ don’t waste time—no solution.
Neat algebra saves points: Track negatives, distribute carefully, and box your ordered pair.
Interpret the answer: In word problems, label your solution (e.g., x=x=x= apples, y=y=y= oranges).
Verify: Plug the ordered pair into both equations.
Ticket sales, cell-phone plans, mixtures, & budgets: Systems let you compare plans or find exact counts/prices by balancing two relationships at once. Try graphing both cost equations in Desmos and clicking the intersection to see the “break-even” point. Desmos Help Center
By the end of Unit 4, you will be able to write, solve, and graph inequalities in one and two variables, including absolute value inequalities and systems of inequalities, and use them to model and solve real-world situations.
Class Handouts
Lesson 4-3 (cancelled)
🎥 Teacher-created video(s)
Lesson 4-3 (cancelled)
Lesson 4-5
Quick refreshers that help Unit 4 make sense:
Inequality symbols & comparing numbers – “greater than/less than” meaning and symbols. Perkins School for the Blind
Solving one-step equations – inverse operations idea you’ll reuse with inequalities. Google Sites
Graphing linear equations y=mx+by=mx+by=mx+b – drawing boundary lines before shading. YouTube
Each topic has Beginner • Visual/Conceptual • Challenge videos, with a mix of creators.
(Q1, Q2, Q3, Q4 on your test)
🎥 Beginner: Inequalities on the Number Line – Math with Mr. J
Step-by-step: open vs. closed circle, shading direction. Glasp
🎥 Visual/Conceptual: Graphing Single-Variable Inequalities – MashUp Math guide & video
Connects inequality meaning to infinite solution sets on a number line. Mashup Math
🎥 Challenge: Solving Inequalities – Interval Notation & Number Lines – The Organic Chemistry Tutor
Mixed one-variable inequalities, focusing on graphs and notation. Glasp
🎥 Beginner: Solving One-Step Inequalities – Friendly Math 101
Clean examples of add/subtract/multiply/divide with <, >, ≤, ≥. YouTube
🎥 Visual/Conceptual: Solving One-Step Inequalities (Add/Subtract & Mult/Div) – Math with Mr. J
Emphasizes when and why to flip the sign. SafeShare
🎥 Challenge: Solving and Graphing Two-Step Inequalities – Mario’s Math Tutoring
Multi-step examples + number-line graphs. edtech.dnjdesigns.org+1
🎥 Beginner: Absolute Value Inequalities – Basic Intro – The Organic Chemistry Tutor
Shows how one inequality turns into a compound inequality. Glasp
🎥 Visual/Conceptual: Absolute Value Inequalities – Mathispower4u library page
Short clips solving & graphing ∣x−h∣≤k|x-h|\le k∣x−h∣≤k and ∣x−h∣>k|x-h|>k∣x−h∣>k. Math Is Power 4 U
🎥 Challenge: Absolute Value Inequalities – How To Solve It – The Organic Chemistry Tutor
Harder examples with fractions and “no solution/all real numbers” cases. YouTube
(Graph y<2x−1y < 2x-1y<2x−1 etc.)
🎥 Beginner: Graphing Linear Inequalities in Two Variables – Mathispower4u
Draw the boundary line, choose dashed vs solid, then shade. YouTube+1
🎥 Visual/Conceptual: Graphing Linear Inequalities with Desmos – Erin’s Essential Equations
Uses Desmos so you can see shading and test points. YouTube
🎥 Challenge: Solving a Set of Linear Inequalities Graphically (with Desmos) – Oak National Academy
Multi-inequality regions & domain restrictions. The National Academy
(Your test’s system graph and “which point is a solution?” question.)
🎥 Beginner: Graphing Systems of Linear Inequalities – The Organic Chemistry Tutor
Step-by-step shading and finding the overlap. YT Class
🎥 Visual/Conceptual: Graphing Systems of Inequalities in 3 Easy Steps – MashUp Math
Big-picture guide with diagrams and common shading mistakes. Mashup Math
🎥 Challenge: Inequalities & Systems Part 3 – Systems of Linear Inequalities – Perkins School for the Blind
Focus on interpreting intersections and checking specific points (great for conceptual depth). Perkins School for the Blind
(Apples & oranges problem: cost + total pieces.)
🎥 Beginner: Writing Systems of Inequalities (SAT Math) – The Organic Chemistry Tutor
Builds inequalities from fruit and fencing situations. Glasp
🎥 Visual/Conceptual: Solving Problems with Inequalities in Two Variables – Illustrative Mathematics (student-facing lesson)
Uses technology to connect situations → inequalities → graphs. Illustrative Mathematics
🎥 Challenge: Modeling with Systems of Inequalities – IM Algebra 1 culminating lesson
Students create and interpret their own inequality models with constraints. Illustrative Mathematics
MashUp Math – Graphing Inequalities on a Number Line (Worksheet A)
Practice open/closed circles and shading; good match to questions 2–4. Mashup Math
MashUp Math – Solving One-Step Inequalities (Worksheet A)
Straightforward practice with simple inequalities and graphs. Mashup Math
MashUp Math – Solving Two-Step & Multi-Step Inequalities (Worksheets A/B)
Mixed solving problems, including dividing by negatives. Mashup Math
Wayground (Quizizz) – One- and Two-Step Inequalities Interactive Videos
Self-paced, auto-checking practice with instant feedback. Wayground
Mathispower4u – Absolute Value Inequalities Exercise Set
Several examples with accompanying videos and suggested practice. Math Is Power 4 U
TES / Mathispower4u – “Ex 2: Solve and Graph Absolute Value Inequalities”
Short video plus example problems to mirror ∣x−8∣≤4|x-8|\le4∣x−8∣≤4. TES
Desmos – Linear Inequalities (Mr. Berry’s “Graphing Linear Inequalities” activity)
Students practice boundary lines, shading, and test points. Google Sites
Media4Math – Desmos Simple Graphs of Linear Inequalities Activity
Type inequalities into Desmos and analyze the resulting regions. Media4Math
Desmos – Systems of Inequalities Activity Link (TPT free)
Self-checking activity where students graph systems and identify solution regions. Teachers Pay Teachers
Perkins – Systems of Inequalities Activity (Part 3)
Structured sequence for graphing systems and checking whether a point is a solution. Perkins School for the Blind
MashUp Math – Graphing Systems of Inequalities Worksheet (A)
Printable practice that mirrors your test’s shaded-region & point-checking tasks. Mashup Math
Illustrative Mathematics – “Modeling with Systems of Inequalities” Lesson
Realistic constraint problems similar to Jane’s apples and oranges situation. Illustrative Mathematics
West Virginia “Trail Mix – Modeling with Systems of Inequalities” Task
Multi-constraint scenario with cost and quantity limits; excellent extension. West Virginia Department of Education
Inequality: A math statement that compares two values instead of saying they are equal (uses <, >, ≤, ≥).
Solution of an inequality: Any number (or point) that makes the inequality true when substituted in.
Solution set: All the numbers or points that make an inequality true (usually infinitely many).
Greater than (>): Left side is bigger; solutions are to the right on a number line.
Less than (<): Left side is smaller; solutions are to the left on a number line.
Greater/Less than or equal (≥, ≤): Same as > or < but the boundary value is included.
Open circle: Used on a number line when the endpoint is not included (> or <).
Closed circle: Used when the endpoint is included (≥ or ≤).
Linear inequality in one variable: An inequality like −3x+5>11 -3x+5>11−3x+5>11 whose solutions live on a number line.
Boundary line: In a 2-variable inequality, the line that separates points that do and don’t work.
Dashed line: Used for < or >; points on the line are not solutions.
Solid line: Used for ≤ or ≥; points on the line are solutions.
Linear inequality in two variables: An inequality like y<2x−1y<2x-1y<2x−1; its solutions form a shaded half-plane.
System of inequalities: Two or more inequalities considered at the same time; solutions lie in the overlap of all shaded regions.
Feasible region: The overlapping shaded area that satisfies every inequality in a system.
Absolute value: Distance from 0 on the number line; ∣x∣|x|∣x∣ is never negative.
Absolute value inequality: Inequality with ∣ ∣|\;|∣∣, such as ∣x−8∣≤4|x-8|\le4∣x−8∣≤4; often turns into a compound inequality.
Constraint: A condition or limit in a word problem (like total cost ≤ $18 or total fruit ≤ 12).
For one-variable inequalities, solve like an equation, but flip the sign whenever you multiply or divide by a negative.
Always graph your final answer: circle, direction of arrow, and (for 2D) shading matter.
In 2D, think:
< or ≤ → shade below the line (if solved for yyy).
or ≥ → shade above the line.
For systems, lightly shade each inequality in pencil, then darken the overlap.
In word problems, write a sentence for each constraint first, then turn it into an inequality.
To check if a point is a solution, plug it in to each inequality: it must work in all of them.
Budgeting: “You can spend at most $18 on fruit and buy at most 12 pieces” becomes a system of inequalities—exactly like Jane’s apples and oranges problem.
Tickets, data plans, and time limits are all about inequalities: ≤ for limits, ≥ for minimums, and systems when you have more than one rule at once.