Linear equations and lines
Students work with straight-line relationships, finding the slope and starting point of a line and writing equations that describe real situations like pay rates or phone plans.
What does a student learn in
This is the year math shifts from arithmetic to thinking with letters that stand for numbers. Students learn to write equations for lines, then graph them and find where two lines cross. They work with curves that bend, like the path of a thrown ball, and with patterns that grow or shrink quickly, like money in a savings account. By spring, students can take a word problem from real life and turn it into an equation they can solve.
- Linear equations
- Slope and graphs
- Systems of equations
- Quadratic functions
- Exponential growth
- Exponent rules
- Word problems
Year at a glance
How the year usually goes. Every school and district set their own curriculum, so treat this as a guide, not official pacing.
- 1
- 2
Systems of equations
Students solve two equations at once to answer questions with more than one unknown, such as comparing two pricing plans or mixing two amounts to hit a target.
- 3
Exponents and exponential growth
Students simplify expressions with powers and study patterns that double or shrink by half, the math behind interest, populations, and things that fade over time.
- 4
Quadratic functions
Students explore U-shaped curves and use them to model situations like a ball in the air or the area of a rectangle. They learn to find where the curve crosses zero and where it peaks.
- 5
Problem solving and reasoning
Across the year, students explain their thinking with graphs, tables, equations, and words. They check whether an answer makes sense and pick the right tool for the job.
Mastery Learning Standards
The required skills a student should display by the end of Grade 9.
Mathematical Process Standards
Mathematical Process Standards
- Algebra I
Apply Mathematics
Students use math to solve real problems, not just textbook exercises. That means reading a phone bill, figuring out a fair split, or estimating a paycheck, and showing the math behind the answer.
- Algebra I
Problem-Solving Model
Students work through math problems step by step: reading what's given, making a plan, solving it, and then checking whether the answer actually makes sense.
- Algebra I
Select Tools and Techniques
Students choose the right tool for the problem at hand, whether that means a calculator, pencil and paper, or a quick mental estimate. The goal is picking the approach that actually gets to a correct answer.
- Algebra I
Communicate Mathematical Ideas
Students explain their math thinking in more than one way, such as drawing a graph, writing an equation, or putting the idea into words. The goal is to show that the same math idea can be expressed in different forms.
- Algebra I
Form Representations
Students turn math ideas into diagrams, tables, graphs, or equations to make sense of a problem and explain their thinking to someone else.
- Algebra I
Analyze Relationships
Students look for patterns and connections between math ideas, then explain how those ideas fit together. This standard shows up whenever students justify a step, interpret a graph, or explain why an answer makes sense.
- Algebra I
Justify Reasoning
Students explain their math thinking clearly, in writing or out loud, using the right terms so their reasoning makes sense to someone else.
- Geometry
Apply Mathematics
Students use geometry to solve real problems, like figuring out how much paint covers a wall or how a city block is laid out. The math connects to things that exist outside the classroom.
- Geometry
Problem-Solving Model
Students work through math problems in steps: read the problem carefully, plan an approach, solve it, then check whether the answer actually makes sense.
- Geometry
Select Tools and Techniques
Students choose the right tool for the job, whether that means sketching by hand, using a calculator, or estimating in their head, to work through a math problem.
- Geometry
Communicate Mathematical Ideas
Students explain their math thinking in more than one way, using words, labeled diagrams, graphs, or equations to make the reasoning clear to someone else.
- Geometry
Form Representations
Students turn math ideas into diagrams, tables, or graphs to make sense of a problem and share their thinking. The form they choose depends on what makes the idea clearest.
- Geometry
Analyze Relationships
Students look for patterns and connections across the math they already know, then explain how those ideas fit together to solve new problems.
- Geometry
Justify Reasoning
Students explain their math work out loud or in writing, using exact terms so their reasoning is clear to someone else. Getting the right answer matters, but so does showing why it's right.
| Standard | Definition | Code |
|---|---|---|
| Apply Mathematics Algebra I | Students use math to solve real problems, not just textbook exercises. That means reading a phone bill, figuring out a fair split, or estimating a paycheck, and showing the math behind the answer. | TX-MATH.PROC.hs-algebra-1.1 |
| Problem-Solving Model Algebra I | Students work through math problems step by step: reading what's given, making a plan, solving it, and then checking whether the answer actually makes sense. | TX-MATH.PROC.hs-algebra-1.2 |
| Select Tools and Techniques Algebra I | Students choose the right tool for the problem at hand, whether that means a calculator, pencil and paper, or a quick mental estimate. The goal is picking the approach that actually gets to a correct answer. | TX-MATH.PROC.hs-algebra-1.3 |
| Communicate Mathematical Ideas Algebra I | Students explain their math thinking in more than one way, such as drawing a graph, writing an equation, or putting the idea into words. The goal is to show that the same math idea can be expressed in different forms. | TX-MATH.PROC.hs-algebra-1.4 |
| Form Representations Algebra I | Students turn math ideas into diagrams, tables, graphs, or equations to make sense of a problem and explain their thinking to someone else. | TX-MATH.PROC.hs-algebra-1.5 |
| Analyze Relationships Algebra I | Students look for patterns and connections between math ideas, then explain how those ideas fit together. This standard shows up whenever students justify a step, interpret a graph, or explain why an answer makes sense. | TX-MATH.PROC.hs-algebra-1.6 |
| Justify Reasoning Algebra I | Students explain their math thinking clearly, in writing or out loud, using the right terms so their reasoning makes sense to someone else. | TX-MATH.PROC.hs-algebra-1.7 |
| Apply Mathematics Geometry | Students use geometry to solve real problems, like figuring out how much paint covers a wall or how a city block is laid out. The math connects to things that exist outside the classroom. | TX-MATH.PROC.hs-geometry.1 |
| Problem-Solving Model Geometry | Students work through math problems in steps: read the problem carefully, plan an approach, solve it, then check whether the answer actually makes sense. | TX-MATH.PROC.hs-geometry.2 |
| Select Tools and Techniques Geometry | Students choose the right tool for the job, whether that means sketching by hand, using a calculator, or estimating in their head, to work through a math problem. | TX-MATH.PROC.hs-geometry.3 |
| Communicate Mathematical Ideas Geometry | Students explain their math thinking in more than one way, using words, labeled diagrams, graphs, or equations to make the reasoning clear to someone else. | TX-MATH.PROC.hs-geometry.4 |
| Form Representations Geometry | Students turn math ideas into diagrams, tables, or graphs to make sense of a problem and share their thinking. The form they choose depends on what makes the idea clearest. | TX-MATH.PROC.hs-geometry.5 |
| Analyze Relationships Geometry | Students look for patterns and connections across the math they already know, then explain how those ideas fit together to solve new problems. | TX-MATH.PROC.hs-geometry.6 |
| Justify Reasoning Geometry | Students explain their math work out loud or in writing, using exact terms so their reasoning is clear to someone else. Getting the right answer matters, but so does showing why it's right. | TX-MATH.PROC.hs-geometry.7 |
Algebra I
Algebra I
- Algebra I
Linear Functions
Slope measures how fast something changes; the y-intercept is where a line starts. Students use both to write equations and inequalities that model real patterns, like how cost rises with hours worked.
- Algebra I
Systems of Linear Equations
Students set up and solve pairs of equations or inequalities with two unknowns to answer real-world questions, like finding when two phone plans cost the same or which combination of items fits a budget.
- Algebra I
Quadratic Functions
Students study U-shaped graphs to find key points like the peak, the zeros, and the direction the curve opens, then use those features to write an equation that fits a real situation like the path of a thrown ball.
- Algebra I
Exponential Functions
Students study how quantities like population, savings, or radioactive material grow or shrink at a steady percentage over time, then write and interpret equations that match those patterns.
- Algebra I
Number and Algebraic Methods
Working with exponents means knowing the rules that let you simplify expressions like x² times x³ into x⁵. Students use those rules, along with basic operation properties, to clean up algebraic expressions and solve equations.
| Standard | Definition | Code |
|---|---|---|
| Linear Functions Algebra I | Slope measures how fast something changes; the y-intercept is where a line starts. Students use both to write equations and inequalities that model real patterns, like how cost rises with hours worked. | TX-MATH.A1.hs-algebra-1.1 |
| Systems of Linear Equations Algebra I | Students set up and solve pairs of equations or inequalities with two unknowns to answer real-world questions, like finding when two phone plans cost the same or which combination of items fits a budget. | TX-MATH.A1.hs-algebra-1.2 |
| Quadratic Functions Algebra I | Students study U-shaped graphs to find key points like the peak, the zeros, and the direction the curve opens, then use those features to write an equation that fits a real situation like the path of a thrown ball. | TX-MATH.A1.hs-algebra-1.3 |
| Exponential Functions Algebra I | Students study how quantities like population, savings, or radioactive material grow or shrink at a steady percentage over time, then write and interpret equations that match those patterns. | TX-MATH.A1.hs-algebra-1.4 |
| Number and Algebraic Methods Algebra I | Working with exponents means knowing the rules that let you simplify expressions like x² times x³ into x⁵. Students use those rules, along with basic operation properties, to clean up algebraic expressions and solve equations. | TX-MATH.A1.hs-algebra-1.5 |
Geometry
Geometry
- Geometry
Coordinate and Transformational Geometry
Students use the coordinate plane to move, flip, and rotate flat shapes, then use those transformations to solve problems about distance, position, and congruence.
- Geometry
Logical Argument and Constructions
Students prove geometric ideas are true by building precise diagrams with a compass and straightedge, then explaining step by step why each relationship holds.
- Geometry
Proof and Congruence
Students write formal proofs to show why triangles, quadrilaterals, and other shapes must have the properties they do, using theorems as the logical backbone of each argument.
- Geometry
Similarity, Proof, and Trigonometry
Students use ratios and angle measurements to find missing sides and angles in right triangles. This includes scaling triangles up or down and applying sine, cosine, and tangent to real measurements.
- Geometry
Two- and Three-Dimensional Figures
Students calculate the area, surface area, and volume of shapes like prisms, pyramids, cylinders, and spheres. They apply the right formula for each figure to solve real problems involving size, space, or materials needed.
- Geometry
Circles
Students use the relationships between angles, line segments, and curved arcs inside and around a circle to solve geometry problems. That includes tangent lines that touch a circle at exactly one point.
- Geometry
Probability
Students find the odds of two or more events happening together, then use area and length to solve probability problems grounded in real situations, like finding the chance a dart lands in a shaded region.
| Standard | Definition | Code |
|---|---|---|
| Coordinate and Transformational Geometry Geometry | Students use the coordinate plane to move, flip, and rotate flat shapes, then use those transformations to solve problems about distance, position, and congruence. | TX-MATH.GEO.hs-geometry.1 |
| Logical Argument and Constructions Geometry | Students prove geometric ideas are true by building precise diagrams with a compass and straightedge, then explaining step by step why each relationship holds. | TX-MATH.GEO.hs-geometry.2 |
| Proof and Congruence Geometry | Students write formal proofs to show why triangles, quadrilaterals, and other shapes must have the properties they do, using theorems as the logical backbone of each argument. | TX-MATH.GEO.hs-geometry.3 |
| Similarity, Proof, and Trigonometry Geometry | Students use ratios and angle measurements to find missing sides and angles in right triangles. This includes scaling triangles up or down and applying sine, cosine, and tangent to real measurements. | TX-MATH.GEO.hs-geometry.4 |
| Two- and Three-Dimensional Figures Geometry | Students calculate the area, surface area, and volume of shapes like prisms, pyramids, cylinders, and spheres. They apply the right formula for each figure to solve real problems involving size, space, or materials needed. | TX-MATH.GEO.hs-geometry.5 |
| Circles Geometry | Students use the relationships between angles, line segments, and curved arcs inside and around a circle to solve geometry problems. That includes tangent lines that touch a circle at exactly one point. | TX-MATH.GEO.hs-geometry.6 |
| Probability Geometry | Students find the odds of two or more events happening together, then use area and length to solve probability problems grounded in real situations, like finding the chance a dart lands in a shaded region. | TX-MATH.GEO.hs-geometry.7 |
Assessments
The state tests students at this grade and subject take.
STAAR EOC Algebra I
End-of-course exam taken at the completion of Algebra I, typically grade 8 or 9. Students must pass all five STAAR EOCs to graduate from a Texas public high school.
- When given:
- end-of-course
- Frequency:
- by course completion
Common Questions
What does this year of math look like?
Students move from arithmetic into working with variables and graphs. The main topics are linear equations and inequalities, systems of two equations, quadratic functions, exponential growth and decay, and the rules for exponents.
How can I help at home if my student gets stuck on a word problem?
Ask them to read the problem out loud and say what is known and what the question is asking. Then ask them to sketch a quick picture, table, or graph before reaching for an equation. Five minutes of talking through the setup often unlocks the rest.
What is slope and why does it matter so much this year?
Slope is how fast one thing changes compared to another, like dollars earned per hour worked. Almost every linear problem this year comes back to slope and a starting value, so getting comfortable reading slope from a graph, a table, and a real situation pays off all year.
How should I sequence the year?
Most teachers start with linear functions and equations, move into systems, then spend a long block on quadratics. Exponential functions and exponent rules tend to sit near the end. Building strong habits with tables, graphs, and equations early makes quadratics and exponentials much easier later.
Which skills usually need the most reteaching?
Solving multi-step equations with fractions, interpreting slope in context, factoring quadratics, and the difference between linear and exponential growth. Brief weekly spiral practice on these four areas tends to hold the line better than reteaching whole units later.
Does my student need a graphing calculator?
A graphing calculator helps, especially for quadratics and exponentials, and is allowed on the state test. A free graphing app on a phone or laptop works for homework. Ask the teacher which model is used in class so practice at home matches.
What does mastery look like by the end of the year?
Students can read a real situation, decide whether it is linear, quadratic, or exponential, and write an equation that fits. They can solve it by graphing, substitution, factoring, or the quadratic formula, and explain what the answer means in the original situation.
How do I know my student is ready for the next math course?
They can solve linear equations and systems without much prompting, factor simple quadratics, and explain what a graph is showing in plain language. If word problems still feel like a wall, spend the summer on short, mixed practice rather than a new topic.
How much should I weight procedures versus modeling?
The process standards expect students to explain reasoning and connect equations to real situations, so plan for both. A rough split of half procedural fluency and half modeling and justification tends to match what shows up on the state test.