Mathematical Architects
Algebra I
Where scholars learn to read the structure of change — and build the equations that describe it.
Algebra I is the blueprint year. Across five modules, scholars move from spotting patterns to engineering
the functions behind them — linear, exponential, and quadratic. Every unit pairs hands-on modeling with the
precise notation of the working mathematician, so the leap from \(y = mx + b\) to \(y = ax^2 + bx + c\) feels
like adding tools to a kit, not starting over. The course is built on the Texas Essential Knowledge and Skills
(TEKS) and front-loaded so that quadratics are mastered before the State of Texas STAAR
End-of-Course exam in early May.
5
Modules
~144
Beta Class Days
60/40
Major / Daily
STAAR
EOC · Early May
Process standards A.1A–A.1G — problem-solving, tools, communication,
representations, and reasoning — are embedded in every module, every day.
📈
Concepts in Action
Drag the sliders and watch the graph rebuild itself. This is the same move a mathematician makes — change a parameter, read the consequence.
Function Grapher. Switch between a line and a parabola, then move the sliders to see how each
coefficient reshapes the curve. The line mode is the heart of Module 2 · Linear Functions
(slope, intercepts, \(y = mx + b\)); the parabola mode previews Module 5 · Quadratics
(vertex, axis of symmetry, and real roots from \(y = ax^2 + bx + c\)).
△
Module by Module
Five modules, each a stage in the build. Day counts follow the TEA Bluebonnet pacing, compressed for the Beta calendar. STAAR readiness standards are marked.
Module 01
Searching for Patterns
22 days
A function is a rule with a job: every input gets exactly one output — and patterns are how we hear that rule.
Topic 1 · Quantities & Relationships (12d) — identifying functions, domain & range, and the families of graphs that describe real situations.
Topic 2 · Sequences (10d) — arithmetic and geometric sequences as the first taste of recursive and explicit rules.
You'll be able to…
- Decide whether a table, graph, or mapping represents a function.
- State the domain and range of a relationship and read them off a graph.
- Sort relationships into families — linear, exponential, quadratic — by their shape.
- Write the explicit rule for an arithmetic or geometric sequence.
Worked example · arithmetic sequence
For \(5,\ 8,\ 11,\ 14,\dots\) the common difference is \(d = 3\), so the explicit rule is
\[ a_n = 5 + 3(n - 1) = 3n + 2 \]
Then \(a_{10} = 3(10) + 2 = 32\).
A.2AA.3CA.6A
A.7AA.9AA.9D
A.12AA.12CA.12D
Module 02
Exploring Constant Change
32 days
A constant rate of change draws a straight line — and slope is the one number that captures it.
Topic 1 · Linear Functions (22d) — slope, intercepts, and writing \(y = mx + b\) from tables, graphs, and situations.
Topic 2 · Transforming & Comparing Linear Functions (10d) — how changes to parameters shift a line, and comparing models side by side.
You'll be able to…
- Compute slope from two points, a table, or a graph.
- Write a linear equation in slope-intercept and point-slope form.
- Interpret slope and intercept as the rate and starting value of a real situation.
- Predict how changing \(m\) or \(b\) transforms the graph — and compare two linear models.
Worked example · line through two points
Through \((2,\,1)\) and \((5,\,7)\):
\[ m = \frac{7 - 1}{5 - 2} = \frac{6}{3} = 2 \]
Using point-slope, \(y - 1 = 2(x - 2)\), which simplifies to \(y = 2x - 3\). Try these values in the grapher above.
A.2AA.2BA.2C
A.2DA.3AA.3B
A.3CA.3EA.3F
A.4AA.4BA.4C
A.12AA.12BA.12D
Module 03
Modeling Linear Equations & Inequalities
27 days
Solving means finding the inputs that make a statement true — one line, or two lines meeting at a point.
Topic 1 · Linear Equations & Inequalities (10d) — solving and graphing, with inequalities like \(2x - 5 \ge 7\) modeled as constraints.
Topic 2 · Systems of Linear Equations & Inequalities (17d) — substitution, elimination, and graphing solution regions.
You'll be able to…
- Solve multi-step linear equations and justify each step.
- Solve and graph linear inequalities, flipping the sign when dividing by a negative.
- Solve a system by substitution, elimination, and graphing.
- Decide whether a system has one solution, none, or infinitely many.
Worked example · system by elimination
\[ \begin{aligned} 2x + y &= 7 \\ x - y &= 2 \end{aligned} \]
Adding the equations cancels \(y\): \(3x = 9 \Rightarrow x = 3\). Back-substitute: \(3 - y = 2 \Rightarrow y = 1\). Solution \((3,\,1)\).
A.2BA.2CA.2H
A.2IA.3AA.3D
A.3FA.3GA.3H
A.5AA.5BA.5C
A.12E
Module 04
Investigating Growth & Decay
25 days
When the rate of change is a constant multiplier instead of a constant difference, growth bends — that's exponential.
Topic 1 · Introduction to Exponential Functions (15d) — recognizing \(y = a\,b^{x}\) and the meaning of growth versus decay.
Topic 2 · Using Exponential Equations (10d) — building and applying exponential models to data.
You'll be able to…
- Tell an exponential pattern from a linear one in a table or graph.
- Read the initial value \(a\) and base \(b\) from \(y = a\,b^{x}\).
- Classify a model as growth \((b>1)\) or decay \((0
- Build an exponential model from a real scenario and use it to predict.
Worked example · growth vs. decay
A \$500 investment growing 8% per year: \(y = 500(1.08)^{x}\). After 3 years,
\[ y = 500(1.08)^{3} \approx 629.86 \]
A car worth \$20{,}000 losing 15% per year decays as \(y = 20000(0.85)^{x}\).
A.3BA.3CA.9A
A.9BA.9CA.9D
A.9EA.11AA.11B
A.12BA.12CA.12D
Module 05 · Capstone before the EOC
Maximizing & Minimizing
44 days
A parabola has a turning point — the highest or lowest value a quadratic situation can reach — and finding it is the whole game.
Topic 1 · Introduction to Quadratic Functions (15d) — the parabola \(y = ax^2 + bx + c\), its vertex, and axis of symmetry.
Topic 2 · Polynomial Operations (10d) — adding, subtracting, multiplying, and factoring polynomial expressions.
Topic 3 · Solving Quadratic Equations (19d) — factoring, the quadratic formula, and interpreting roots.
You'll be able to…
- Identify the vertex, axis of symmetry, and direction a parabola opens.
- Add, subtract, and multiply polynomials — and factor quadratic trinomials.
- Solve quadratic equations by factoring, square roots, and the quadratic formula.
- Use the discriminant to predict whether a quadratic has two, one, or no real roots.
- Interpret roots and the vertex as answers to a real maximizing/minimizing question.
Worked example · solve by factoring
Solve \(x^2 - 5x + 6 = 0\). Factor:
\[ (x - 2)(x - 3) = 0 \;\Rightarrow\; x = 2 \text{ or } x = 3 \]
Confirm both roots on the parabola in the grapher above.
Worked example · quadratic formula
For \(2x^2 + 3x - 2 = 0\),
\[ x = \frac{-3 \pm \sqrt{3^2 - 4(2)(-2)}}{2(2)} = \frac{-3 \pm 5}{4} \]
so \(x = \tfrac{1}{2}\) or \(x = -2\). The discriminant \(b^2 - 4ac = 25 > 0\) confirms two real roots.
A.6AA.6BA.6C
A.7AA.7BA.7C
A.8AA.8B
A.10AA.10BA.10C
A.10DA.10EA.10F
A.11A
STAAR readiness standard (RDY)
Supporting standard
Module, topic, and day-count structure follow the TEA Bluebonnet Learning — Secondary
Mathematics open curriculum (Edition 1, adapted from Carnegie Learning), licensed
CC BY-NC 4.0.
Classroom use is non-commercial.
🛠
What You'll Build
Algebra I is less about memorizing and more about constructing. By May, every scholar can:
📊
Model Real Change
Translate a situation into a linear, exponential, or quadratic function — then read the story back out of the graph.
⚖️
Solve & Justify
Solve equations, inequalities, and systems, and defend each step with the reasoning of a mathematician.
📐
Connect Representations
Move fluently between tables, graphs, equations, and words — the four blueprints of every function.
The Toolkit
Required Materials
- Graphing calculator (TI-84 or equivalent) or a school Chromebook with Desmos
- Interactive notebook (composition or spiral)
- Pencils — mathematics is always drafted in pencil
- Graph paper for precise constructions
Curriculum
Built on the TEKS
This course is organized around the Texas Essential Knowledge and Skills for Algebra I, using the
TEA Bluebonnet Learning — Secondary Mathematics framework (Edition 1, adapted
from Carnegie Learning), licensed
CC BY-NC 4.0.
Module and topic structure follow that open curriculum; classroom use is
non-commercial.
📚
Learning Resources & Supports
Free, vetted places to practice between class days. Start with the textbook, then drill the skills you're shakiest on.
TEA OER · Textbook
Bluebonnet Learning — Algebra I
The official Texas open-source student edition this course is built on. Free, online, and aligned module-for-module to our itinerary above.
Open the student edition →
Skill Practice
IXL — Algebra I
Targeted skill sets for slope, systems, exponentials, and quadratics. Use it to find the one skill that's slowing you down and grind it.
Practice IXL skills →
Video + Practice
Khan Academy — Algebra I
Short videos and worked-step practice for every topic in the course. Best when you missed a class or want a second explanation.
Watch & practice →
Graphing Tool
Desmos Graphing Calculator
The full-power version of the grapher above. Plot anything, explore sliders, and check your by-hand graphs. Allowed on the STAAR EOC.
Open Desmos →
Coming Soon
EOC & Benchmark Practice
STAAR-style module checkpoints and a full EOC benchmark are being built for this course in the Assessment Center. A math practice layer with progress views is on the way — not live yet.
In the Assessment Center (coming)
Self-Help
Stuck? Here's the move.
Re-read the worked example in the matching module above, then test the idea in the grapher. Still stuck after an honest attempt? Bring your written work to office hours — that's where the real learning happens.
Jump to the modules ↑
How to use these well: practice tools are for active retrieval — attempt the problem
first, then check. Watching a video is not the same as solving. Aim for short, daily reps over one long cram session,
and always finish a session in the grapher to see what the algebra means.
👪
Family & Curriculum Resources
The official TEA Bluebonnet Learning family materials for Algebra I — what your scholar is learning, in plain language, plus the standards and supplies behind the course.
Family Guide
Family Guide (English)
A plain-language tour of every Algebra I module — what scholars learn, why it matters, and how to support the work at home.
Open the Family Guide (PDF) →
Guía Familiar
Guía para la Familia (Español)
La misma guía de la familia para Álgebra I, en español — un recorrido por cada módulo y cómo apoyar en casa.
Abrir la Guía (PDF) →
Materials
Materials List
The supplies and tools the curriculum recommends for the year — handy when shopping for the course.
Open the Materials List (PDF) →
Curated family materials from the TEA Bluebonnet Learning open curriculum,
licensed CC BY-NC 4.0. Non-commercial classroom use.
🔗
Where to Go Next
Three doors into the course. Start with the syllabus.
Course Syllabus
Policies, the studio learning environment, grading, expectations, and the full itinerary by grading period. Acknowledgment due on ParentSquare by the second week.
Read the Syllabus
Pacing Guide
Every module mapped to the ~144-day Beta calendar, by grading period, showing how Module 5 finishes before the STAAR EOC.
View the Pacing Guide
Coming Soon
Practice in the Assessment Center
Module checkpoints and STAAR-style practice will live in the Assessment Center. Question sets and progress views are being built for this course now.
Assessment Center
Instructor: Dr. Goodluck Ijezie-Desbois, PharmD · Beta Academy · Room: TBA
Reach out by appointment, at gijezie-desbois@betaacademy.org, or through ParentSquare.