✨ Welcome to Quarter 1: Foundations of Algebra
This quarter sets the stage for all future math work. You’ll develop essential algebra skills that will serve as your foundation for the rest of the year. You’ll learn how to:
✏️ Evaluate expressions using the correct order of operations
🧮 Solve one-step, two-step, and multi-step equations — even when variables appear on both sides
📈 Understand linear relationships by analyzing tables, graphs, and equations
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
Below you'll find everything you need for each topic — start with the teacher video, then check out the extras!
📌 School-wide orientation and team-building
💬 No academic instruction, but students complete a welcome survey and meet teachers.
📌 Overview of syllabus, classroom norms, and goals
📎 Includes growth mindset video and short math task (e.g., Four 4’s or Fencing Problem)
🎥 Growth Mindset for Students – https://www.youtube.com/watch?v=pN34FNbOKXc
🎥 Visual: Why Effort Matters – https://www.youtube.com/watch?v=2zrtHt3bBmQ
🎥 Bonus: Math Is Not About Speed – https://www.youtube.com/watch?v=PxL8iFO3Jgo
Build fluency with one-step, two-step, and multi-step linear equations (including distribution & like terms), equations with variables on both sides (one/none/infinitely many solutions), evaluating expressions by substitution, and translating & solving word problems, with targeted error analysis and strategy practice.
Class Handouts
🎥 Teacher video(s)
[Your Video 1: Solving Overview] (placeholder) – unit roadmap & common pitfalls.
[Your Video 2: Strategy First Steps] (placeholder) – choosing efficient first moves on equations like 3x+5=2x+113x+5=2x+113x+5=2x+11.
Quick refreshers (watch in order):
Evaluating expressions by substitution – Mr. J’s clear intro. YouTube
Distributive property – concise concept demo (Mr. J). YouTube
1- & 2-step equations – Math Antics quick starts. YouTube+1
(Each set: Beginner • Visual/Conceptual • Challenge)
🎥 Beginner: Evaluate an Expression Using Substitution (Mr. J). Purpose: step-by-step plug-in practice. YouTube
🎥 Visual: Intro to Evaluating Algebraic Expressions (Mr. J). Purpose: single & two-variable examples. YouTube
🎥 Challenge: Algebraic Expressions—Part 2 (practice-heavy). Purpose: mixed difficulty for confidence. YouTube
🎥 Beginner: Solving Basic Equations, Part 1 (Math Antics). Purpose: add/subtract focus, clear modeling. YouTube
🎥 Visual: Solving Simple Linear Equations (1- & 2-Step) (Eddie Woo). Purpose: balance method intuition. YouTube
🎥 Challenge: 1- & 2-Step Equations (Mario’s Math Tutoring). Purpose: faster methods & mixed practice. YouTube
🎥 Beginner: Solving 2-Step Equations (Math Antics—updated). Purpose: inverse operations fluency. YouTube
🎥 Visual: How To Solve Equations Quickly! (Organic Chemistry Tutor). Purpose: efficient moves incl. fractions. YouTube
🎥 Challenge: Common Mistakes (2-Step) (coaching video). Purpose: error-spotting under pressure. YouTube
🎥 Beginner: Solving Multi-Step Equations (Math with Mr. J). Purpose: distribute → combine → isolate. YouTube
🎥 Visual: Ex: Variables & Parentheses on Both Sides (Mathispower4u). Purpose: see both-sides structure. YouTube
🎥 Challenge: Multi-Step Linear Equations (PatrickJMT). Purpose: quicker algebra with justification. YouTube
🎥 Beginner: Infinitely Many or No Solution? (Mario’s Math Tutoring). Purpose: identify identities/contradictions. YouTube
🎥 Visual: One/None/Infinitely Many Solutions (systems explainer to connect concepts). Purpose: big-picture view. YouTube
🎥 Challenge: Solving w/ Variables on Both Sides (Eddie Woo). Purpose: strategy and structure. YouTube
🎥 Beginner: Translating Problems Into Equations (Level 1) (Math Fortress). Purpose: 3-step plan + easy examples. Math Fortress
🎥 Visual: Translating Words into Simultaneous Equations (Eddie Woo). Purpose: turn language into algebra. YouTube
🎥 Challenge: Translate & Solve: Algebra Word Problems (worked examples). Purpose: set up from “sum/difference” clues. YouTube
🎥 Beginner: Mistakes in Solving Equations (Khan Academy). Purpose: compare wrong vs. right reasoning. YouTube
🎥 Visual: Discussion: Different Approaches / Basic Equations (Eddie Woo series hub). Purpose: choosing smart first steps. Class Central
🎥 Challenge: Algebra—Solve Equations Quickly (OCT). Purpose: pick moves that reduce steps. YouTube
Evaluating & Distribute
Worksheet: Evaluating Expressions (Mr. J mini-course video support). Do 10 plug-in problems. YouTube
Quick practice: Distributive Property explainer (Mr. J). Complete 8 expand/simplify items from your notes. YouTube
One-Step / Two-Step
Kuta: One-Step Equations (PDF). 20 mixed add/sub/mult/div. Kuta Software
Kuta: Two-Step Equations (PDF). 20 problems; show inverse operations. Kuta Software
Multi-Step (Distribute + Like Terms)
Kuta/Adapted: Multi-Step with Distributive Property (PDF). Focus on parentheses + combine. Ms. Broden's Home Page
Practice Set: Multi-Step Equations (multiple-choice, show work). files.masteryconnect.com
Variables on Both Sides & Solution Types
Desmos: Classification of Solutions (card sort: one/none/infinitely many). teacher.desmos.com
Practice: Variables on Both Sides (worksheet bank). Finish one full page. imathworksheets.com
Conceptual Balancing (Great warm-ups/homework)
Desmos: Keeping Equations Balanced (hanger → equation). teacher.desmos.com
Desmos: Balanced Moves (move from mobiles to equations). teacher.desmos.co
SolveMe Mobiles (interactive puzzles). 10 puzzles in “Puzzler.” solveme.edc.org
Word Problems (Numbers)
Number Word Problems – Worksheet 1 (classic “larger/smaller…sum is” sets). algebra-worksheets.s3.amazonaws.com
Algebra Word Problems Notes & Practice (step-by-step to equation). mathplane.com
Equation: A math statement with an equals sign showing two sides are the same.
Expression: A math phrase without an equals sign (can be simplified, not “solved”).
Variable: A letter that stands for an unknown number.
Term: A number, variable, or product of numbers/variables in an expression.
Coefficient: The number in front of a variable (e.g., in 7x, 7 is the coefficient).
Constant: A number without a variable (e.g., −5).
Substitute (Substitution): Plug in a given value for a variable to evaluate or check.
Evaluate: Find the value of an expression after substituting.
Distributive property: Multiply a number to every term inside parentheses, e.g., a(b+c)=ab+ac.
Inverse operation: The undo move (add ↔ subtract, multiply ↔ divide).
Properties of equality: Do the same thing to both sides to keep an equation true.
Combine like terms: Add/subtract terms with the same variable and power.
One-step equation: Solved in one inverse move (e.g., x−7=12).
Two-step equation: Needs two inverse moves (e.g., 2x+3=11).
Multi-step equation: Includes distribute and like terms before isolating the variable.
Identity (infinitely many solutions): Both sides are always equal (e.g., 5=5).
Contradiction (no solution): A false statement remains (e.g., 3=5).
Check a solution: Substitute back to verify the equation is true.
Write the goal line (e.g., x=__)—then work toward it.
Circle like terms before combining; underline inverse pairs you’ll use.
Choose the efficient first step (e.g., clear parentheses/like terms before moving variables).
For both-sides equations, move variables first, then constants.
If you reach 5=5, infinitely many; if 5=3, no solution—state why.
Always check by substitution.
Budgeting & phone plans: Set up an equation and solve to compare options (multi-step & interpretation).
Puzzles & balances: Hanger and pan-balance apps build true equation sense before symbols. Polypad+1
Model, write, interpret, and graph linear relationships; compare line relationships; analyze scatterplots with a line of best fit; and identify domain and range from graphs.
Class Handouts
🎥 Teacher-created video(s)
Two-step equations refresher (balance method): Math Antics. YouTube
Two-step equations (alternate approach): Eddie Woo. YouTube
Plotting points on the coordinate plane: Math with Mr. J. YouTube
Average rate of change from a table (slope idea): Mathispower4u. YouTube
🔍 Need More Help? Try One of These
(Each subtopic has Beginner, Visual/Conceptual, Challenge—from different creators.)
🎥 Beginner: Basic Linear Functions (y = mx + b) — Math Antics. YouTube
🎥 Visual/Conceptual: Slope-Intercept Form (what m and b mean) — Eddie Woo. YouTube
🎥 Challenge: Convert Standard → Slope-Intercept (Ax+By=C → y=mx+b) — Mario’s Math Tutoring. YouTube
🎥 Beginner: Slope & Distance (rise/run, sign of slope) — Math Antics. YouTube
🎥 Visual/Conceptual: Finding slope (worked examples) — PatrickJMT. YouTube
🎥 Challenge: Graph a line given a point and slope (build to equation) — PatrickJMT. YouTube
🎥 Beginner: 2-Point Form / Equation from Two Points — Eddie Woo. YouTube
🎥 Visual/Conceptual: Write an equation from a table (patterns → y=mx+b) — Jenifer Berry (lesson video). YouTube
🎥 Challenge: Determine equation in slope-intercept form from various info — Mathispower4u. YouTube
🎥 Beginner: Graph y = mx + b (quick method) — MashUp Math. YouTube
🎥 Visual/Conceptual: Vertical & Horizontal Lines (slope 0 vs. undefined) — Eddie Woo. YouTube
🎥 Challenge: Graphing straight lines—interpreting equations as graphs — Eddie Woo. YouTube
🎥 Beginner: Linear models & slope-intercept word problems — The Organic Chemistry Tutor. YouTube
🎥 Visual/Conceptual: Using slope & intercept to model situations — Mathispower4u (rate/change & modeling). mathispower4u.com
🎥 Challenge: Word problems with parameters (compare rates & intercepts) — Mathispower4u (mixed examples). mathispower4u.com
🎥 Beginner: Slopes of Parallel & Perpendicular Lines (rules & examples) — Mathispower4u. YouTube
🎥 Visual/Conceptual: Parallel & Perpendicular (slope reasoning) — Cengage Math Clips. YouTube
🎥 Challenge: Equations of parallel/perpendicular lines (write the equation) — Nagwa. Nagwa
🎥 Beginner: Line of Best Fit (overview) — Eddie Woo. YouTube
🎥 Visual/Conceptual: Line of Best Fit (how/why) — Mathcation. YouTube
🎥 Challenge: Use a Line of Best Fit to Make Predictions — Mathispower4u. YouTube
🎥 Beginner: Domain & Range — Introduction — Eddie Woo. YouTube
🎥 Visual/Conceptual: Domain/Range from Graphs (step-by-step) — Mathispower4u. YouTube
🎥 Challenge: Parent functions (compare domains/ranges across families) — MashUp Math. YouTube
Forms & Slope-Intercept
Desmos – Match My Line: Adjust m and b to match targets. classroom.amplify.com
Desmos – Marbleslides: Lines (intro): Precision with m/b through challenges. classroom.amplify.com
Kuta (PDF): Graphing lines in slope-intercept (printable). Kuta Software
Slope & Intercepts
Kuta (PDF): Slope from two points (printable). Kuta Software
Kuta (PDF): Slope from a graph (printable). Kuta Software
Desmos – Slope Intercept Graphing Practice: Quick sketches from equations. teacher.desmos.com
Write Equations from Representations
Kuta (PDF): Writing linear equations (mix of forms). Kuta Software
Mario’s Math Tutoring (video+examples): Write from a table (5 examples). YouTube
MathWarehouse (tutorial+worksheet): Equation of a line from two points. Math Warehouse
Graphing & Special Lines
Eddie Woo: Vertical & horizontal lines review (use with notebooks). YouTube
Maisonet Math: Graphing using y=mx+b, plus perpendicular notes. maisonetmath.com
Desmos – Linear Concepts: Find points, choose equations, finish a marbleslide. teacher.desmos.com
Linear Modeling & Interpretation
Desmos – Water Line (context modeling): Match water height vs. time. museum.desmos.com
Desmos – Water Cooler: Compare uphill vs. downhill slopes. teacher.desmos.com
TI Activity – Stacking Cups & Walking Rates: Collect data, model, interpret slope. Texas Instruments Education
Parallel/Perpendicular/Same/Neither
Nagwa Lesson Video: Write equations for parallel/perpendicular lines. Nagwa
Cengage Clip: Negative reciprocals & same-slope review. YouTube
Kuta (PDF): Writing equations given slope/point & standard↔slope-intercept. Kuta Software
Scatterplots & Line of Best Fit
Desmos Activity: Line of Best Fit (draw, adjust, predict). mathispower4u.com
Minity/Corbett Maths: Draw a line of best fit by eye (practice question). YouTube
Mathispower4u: Make predictions from your fitted line. YouTube
Domain & Range
Eddie Woo: Domain & Range intro (pair with notes). YouTube
MashUp Math (article): Step-by-step domain/range guide & interval notation. Mashup Math
Mathispower4u: Determine domain/range from a graph (worked). YouTube
Linear function: A rule that makes a straight line when graphed (constant rate of change).
Slope (m): The steepness of a line; rise ÷ run; how much yyy changes for each 1 unit of xxx.
Y-intercept (b): Where the line crosses the y-axis; the output when x=0.
X-intercept: Where the graph crosses the x-axis; the input where y=0.
Slope-intercept form: y=mx+b; shows slope m and y-intercept b.
Point-slope form: y−y1=m(x−x1); a line with slope m through (x1,y1)
Standard form: Ax+By=C with integers A,B,C (usually A≥0).
Rate of change: How fast yyy changes compared to xxx (same as slope for linear).
Initial value: The starting amount in a situation; same as the y-intercept.
Independent variable (x): The input you choose or control.
Dependent variable (y): The output that depends on the input.
Function: A relationship where each input has exactly one output.
Domain: All x-values that make sense for the situation/graph.
Range: All y-values that occur in the situation/graph.
Horizontal line: Slope 0; equation y=cy = cy=c.
Vertical line: Undefined slope; equation x=cx = cx=c (fails the vertical-line test).
Parallel lines: Same slope, different intercepts; never meet.
Perpendicular lines: Slopes are negative reciprocals (product = −1); form right angles.
Coincident (same) lines: Exactly the same line; all points overlap.
Direct variation: y=kxy = kxy=kx; line through the origin; kkk is the constant of proportionality.
Proportional vs. non-proportional: Through the origin (proportional) vs. nonzero intercept (not proportional).
Intercept idea: Use where a graph hits the axes to build or check an equation.
Increasing/Decreasing: yyy goes up/down as xxx increases.
Residual: Actual yyy minus predicted yyy from a model (scatterplots).
Correlation: Direction/strength of a relationship (positive, negative, none).
Trend line / Line of best fit: A line that models the overall pattern in a scatterplot.
Interpolation: Predict within the data range (safer).
Extrapolation: Predict beyond the data range (less reliable—use caution).
Piecewise function (preview): A function defined by different rules on different x-intervals.
Box m and b in any y=mx+b you see; label units.
From two points → find slope first, then plug a point to solve for b.
Parallel? same slope. Perpendicular? slopes multiply to −1.
Sketch before solving—sanity-check your equation against the graph.
For domain/range, watch endpoints (open/closed) and arrows.
Cell & streaming plans: base fee + rate per month.
Ride-share costs: base fare + cost per mile/min.
Personal data: use a line of best fit to forecast steps, savings, or study time.