LabPathCourse replacement path

Algebra I LabPath

A complete Algebra I course where students learn algebra as a system of relationships: they model, manipulate, graph, test, explain, revise, and defend every important idea.

Start first mission Assign to class

10/10replacement gate

10units

30missions

9math simulators

Day 1

Start with meaning, not procedures.

The first mission teaches what a variable represents, then lets students manipulate the relationship and produce evidence before they are asked for formal fluency.

algebralab

Variables Are Quantities, Not Mystery Letters

Define a variable from a real situation and use it consistently.

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Student loop

Every mission follows the same learning contract.

Teach the idea visually before controls appear.
Ask for one prediction before symbolic work starts.
Let the student act on a mode-native model.
Show the consequence in graph, table, equation, and story form.
Require explanation, revision, defense, and transfer before mastery moves.

Representative missions

Algebra becomes tactile, visible, and defensible.

algebralab

Variables Are Quantities, Not Mystery Letters

Changing the input updates the table, graph point, and expression value together.

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wordproblemengine

Choose The Form That Helps

Choosing the right form reveals zeros, starts, totals, or rates faster.

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equationsolver

Why The Sign Flips

Negative scaling mirrors the number line and reverses the order relationship.

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graphverse

Linear Function Machine

Slope rotates the line; intercept shifts the line; table and story update instantly.

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wordproblemengine

Two Plans, One Decision

Changing fixed or variable cost changes the break-even point and best decision region.

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graphverse

Vertex, Zeros, And Meaning

Changing zeros or vertex changes the graph and the contextual event points.

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Course map

Ten units from variable meaning to modeling capstone.

Unit 1

Variables, Patterns, And Structure

How can a changing situation become a mathematical rule?

Variables Are Quantities, Not Mystery LettersDefine a variable from a real situation and use it consistently.Build A Rule From A PatternCreate a rule from a table, graph, and story pattern.Same Relationship, Four RepresentationsTranslate the same relationship across words, table, graph, and equation.

Mastery gate: Student translates a pattern among table, graph, words, and expression, then defends what the variable means.

Unit 2

Expressions And Equivalent Forms

What makes two expressions the same?

Equivalent Expression StudioShow why two expressions are equivalent or not equivalent.Distributive Property As AreaUse area and algebra tiles to expand and factor expressions.Choose The Form That HelpsChoose an equivalent form that makes a question easier.

Mastery gate: Student proves equivalence with structure, substitution, and a visual model.

Unit 3

One-Variable Equations

How do legal moves preserve the solution?

Balance Both SidesSolve equations by applying legal moves to both sides.Multi-Step Equation Flight PlanPlan and solve multi-step linear equations efficiently.Equation Error DetectiveIdentify and repair errors in an equation solution.

Mastery gate: Student solves multi-step equations and proves each operation preserved equality.

Unit 4

Inequalities And Constraint Reasoning

How do solution sets work when there is more than one answer?

Boundary And Solution SetRepresent inequality solutions on a number line and test points.Why The Sign FlipsExplain why multiplying or dividing by a negative reverses an inequality.Model A Real ConstraintWrite and interpret inequalities from real constraints.

Mastery gate: Student solves and graphs inequalities, explains boundary behavior, and transfers to constraints.

Unit 5

Coordinate Plane And Graphing

How does a graph show a relationship rather than a drawing?

Coordinates Are Two MeasurementsInterpret ordered pairs as linked input-output measurements.Slope Is A Rate Of ChangeInterpret slope as a unit rate in graph, table, and story.Match The Graph To The StoryInterpret graph features as events in a story.

Mastery gate: Student reads and creates graphs from coordinated table, equation, and story evidence.

Unit 6

Linear Functions

What makes a relationship linear?

Linear Function MachineBuild a linear function from rate and starting value.Forms Of A LineConvert among slope-intercept, standard, and point-slope forms with purpose.Fit A Linear ModelFit and interpret a linear model with residual evidence.

Mastery gate: Student models a linear relationship, interprets slope and intercept, and compares forms.

Unit 7

Systems Of Equations

What does it mean for two conditions to be true at once?

Intersection Means Same Time, Same ValueInterpret the intersection of two graphs as a shared solution.Choose Substitution Or EliminationSolve systems by choosing an efficient algebraic method.Two Plans, One DecisionModel and interpret a real decision with a system of equations.

Mastery gate: Student solves systems graphically and algebraically, then interprets the intersection in context.

Unit 8

Exponents And Polynomial Structure

How do repeated operations create structure?

Exponent Laws From Repeated MultiplicationDerive exponent rules from repeated multiplication.Polynomial Terms As ObjectsAdd, subtract, and multiply polynomials by tracking term structure.Factoring Pattern LabRecognize and justify factoring patterns.

Mastery gate: Student explains exponent rules and polynomial operations from structure, not memorized shortcuts.

Unit 9

Quadratic Functions

How do quadratic relationships grow differently from linear ones?

Why Quadratics CurveDistinguish linear and quadratic change using first and second differences.Vertex, Zeros, And MeaningInterpret vertex and zeros in graphs and contexts.Build And Defend A Quadratic ModelModel a quadratic situation and defend its limits.

Mastery gate: Student connects quadratic structure, graph features, and real contexts.

Unit 10

Data, Modeling, And Capstone

How do algebraic models support decisions without pretending to be perfect?

Data Claim LabMake a claim from data with uncertainty and limitations.Choose A Model For The JobChoose linear, quadratic, or constraint model based on evidence.Algebra I Evidence CapstoneUse Algebra I tools to solve, explain, revise, defend, and transfer a complex model.

Mastery gate: Student completes a defended modeling capstone using algebra, data, constraints, and transfer.

TeacherOS

From evidence to action.

Assign the next Algebra I LabPath mission to the class.
See misconception clusters in TeacherOS within the same day.
Launch a repair mission or Studio assessment for the highest-risk cluster.
Practice the intervention in TeachProof when the misconception is persistent.

Parent and district

Readable progress, serious signals.

What concept the student learned this week.
Where the student is stuck and what the next repair is.
A plain-language Learning Evidence Record, not just a score.
Course coverage by Algebra I concept sequence.
Misconception resolution by class, school, and unit.