This is the year math shifts from arithmetic to working with letters that stand in for numbers. Students write and solve equations, then graph them as lines, curves, and steep growth patterns. They learn to read a word problem and turn it into a math sentence that predicts what happens next. By spring, students can graph a line, solve a pair of equations together, and sketch a curve that bends.
Students start the year working with straight-line relationships. They write equations, solve for unknowns, and graph lines to describe situations like a phone bill that grows with each text or a savings account that climbs by the same amount each week.
Students work with two equations at once and find the point where both are true. This shows up in problems like comparing two job offers or figuring out when two trucks on the road will meet.
Students move from straight lines to curves shaped like a U. They learn to write, graph, and solve these functions, which model things like the path of a thrown ball or the area of a rectangular garden.
Students study patterns that double, triple, or shrink by half over time. They use these to model how money grows in an account, how a population increases, or how medicine fades from the body.
Students add, subtract, and multiply algebraic expressions, then turn to real data. They look at a set of numbers, find patterns, and use a best-fit line to make predictions about what comes next.
Students read a math problem carefully, figure out what it's actually asking, and keep working even when the answer isn't obvious right away.
Students take a real problem, strip it down to numbers and symbols to solve it, then translate the answer back into plain English to check whether it actually makes sense.
Students back up math claims with clear reasoning, then explain why another student's approach works or where it breaks down. The focus is on talking through the logic, not just getting the right answer.
Students take a real situation, like figuring out how long a road trip takes or how much paint covers a wall, and write an equation or draw a graph to solve it.
Students choose the right tool for the job, whether that means a calculator, a quick estimate in their head, or working it out by hand. The goal is knowing which approach fits the problem.
Students choose words, labels, and units carefully when solving problems. A slope is a slope, not just "a number," and an answer in feet stays in feet.
Students notice patterns in equations and expressions, then use those patterns as shortcuts. Recognizing that a polynomial factors a certain way, or that an equation has a familiar shape, helps students solve problems without starting from scratch each time.
Students notice when the same steps keep showing up in different problems and use that pattern to find a shortcut or write a general rule.
When a math problem feels stuck, students slow down, re-read what's being asked, and try a different approach instead of giving up. The habit is about staying with hard problems long enough to find a way through.
Students take a real situation, strip it down to numbers and symbols to solve it, then translate the answer back into plain language that explains what it actually means.
Students build a logical case for their math answer using numbers and rules, then explain where a classmate's reasoning goes wrong or why it holds up. The focus is on justifying the "why," not just getting the answer.
Students take a real situation (a budget, a population trend, a physics problem) and write equations or draw graphs to make sense of it. The math becomes a tool for understanding something outside the classroom.
Students choose the right tool for the job, whether that means a calculator, a quick estimate, or working it out by hand. The skill is knowing which one fits the problem.
Students choose the right words, labels, and units when solving problems. A graph axis gets labeled, a calculation shows its units, and a definition means what it says.
Students spot patterns and hidden structure in equations, graphs, and expressions, then use what they notice to solve problems more efficiently. It's the habit of seeing a complicated expression as something familiar in disguise.
When the same steps keep appearing in a problem, students pause to ask why. They turn that pattern into a shortcut or rule they can use again.
Students read a math problem carefully, figure out what it's actually asking, and keep trying even when the first approach doesn't work. They check whether their answer makes sense before moving on.
Students take a real problem (a ramp, a fence, a shadow) and translate it into numbers or shapes to solve it, then check whether the answer still makes sense in the real situation.
Students build logical arguments to prove geometric ideas, then explain why a classmate's proof works or where it breaks down. The focus is on reasoning out loud and in writing, not just getting the right answer.
Students use math to make sense of real situations, like figuring out how much paint covers a wall or whether a ramp meets a safety code. The math they choose fits the problem, not the other way around.
Students choose the right tool for the math in front of them. That might mean a calculator, a sketch on paper, or a quick estimate, depending on what the problem actually needs.
Students use the right math words, label measurements with correct units, and check their calculations carefully. Sloppy notation or a missing unit can change the meaning of an answer entirely.
Students notice patterns and hidden structure in math problems, like recognizing that a geometric figure can be broken into simpler shapes. That recognition becomes a tool for solving the problem.
When a calculation or process keeps showing the same pattern, students pause to ask why and write a rule that works every time, not just for that one problem.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems Algebra I | Students read a math problem carefully, figure out what it's actually asking, and keep working even when the answer isn't obvious right away. | VT-MATH.MP.hs-algebra-1.1 |
| Reason Abstractly Algebra I | Students take a real problem, strip it down to numbers and symbols to solve it, then translate the answer back into plain English to check whether it actually makes sense. | VT-MATH.MP.hs-algebra-1.2 |
| Construct Arguments Algebra I | Students back up math claims with clear reasoning, then explain why another student's approach works or where it breaks down. The focus is on talking through the logic, not just getting the right answer. | VT-MATH.MP.hs-algebra-1.3 |
| Model with Mathematics Algebra I | Students take a real situation, like figuring out how long a road trip takes or how much paint covers a wall, and write an equation or draw a graph to solve it. | VT-MATH.MP.hs-algebra-1.4 |
| Use Tools Strategically Algebra I | Students choose the right tool for the job, whether that means a calculator, a quick estimate in their head, or working it out by hand. The goal is knowing which approach fits the problem. | VT-MATH.MP.hs-algebra-1.5 |
| Attend to Precision Algebra I | Students choose words, labels, and units carefully when solving problems. A slope is a slope, not just "a number," and an answer in feet stays in feet. | VT-MATH.MP.hs-algebra-1.6 |
| Use Structure Algebra I | Students notice patterns in equations and expressions, then use those patterns as shortcuts. Recognizing that a polynomial factors a certain way, or that an equation has a familiar shape, helps students solve problems without starting from scratch each time. | VT-MATH.MP.hs-algebra-1.7 |
| Express Regularity Algebra I | Students notice when the same steps keep showing up in different problems and use that pattern to find a shortcut or write a general rule. | VT-MATH.MP.hs-algebra-1.8 |
| Make Sense of Problems Algebra II | When a math problem feels stuck, students slow down, re-read what's being asked, and try a different approach instead of giving up. The habit is about staying with hard problems long enough to find a way through. | VT-MATH.MP.hs-algebra-2.1 |
| Reason Abstractly Algebra II | Students take a real situation, strip it down to numbers and symbols to solve it, then translate the answer back into plain language that explains what it actually means. | VT-MATH.MP.hs-algebra-2.2 |
| Construct Arguments Algebra II | Students build a logical case for their math answer using numbers and rules, then explain where a classmate's reasoning goes wrong or why it holds up. The focus is on justifying the "why," not just getting the answer. | VT-MATH.MP.hs-algebra-2.3 |
| Model with Mathematics Algebra II | Students take a real situation (a budget, a population trend, a physics problem) and write equations or draw graphs to make sense of it. The math becomes a tool for understanding something outside the classroom. | VT-MATH.MP.hs-algebra-2.4 |
| Use Tools Strategically Algebra II | Students choose the right tool for the job, whether that means a calculator, a quick estimate, or working it out by hand. The skill is knowing which one fits the problem. | VT-MATH.MP.hs-algebra-2.5 |
| Attend to Precision Algebra II | Students choose the right words, labels, and units when solving problems. A graph axis gets labeled, a calculation shows its units, and a definition means what it says. | VT-MATH.MP.hs-algebra-2.6 |
| Use Structure Algebra II | Students spot patterns and hidden structure in equations, graphs, and expressions, then use what they notice to solve problems more efficiently. It's the habit of seeing a complicated expression as something familiar in disguise. | VT-MATH.MP.hs-algebra-2.7 |
| Express Regularity Algebra II | When the same steps keep appearing in a problem, students pause to ask why. They turn that pattern into a shortcut or rule they can use again. | VT-MATH.MP.hs-algebra-2.8 |
| Make Sense of Problems Geometry | Students read a math problem carefully, figure out what it's actually asking, and keep trying even when the first approach doesn't work. They check whether their answer makes sense before moving on. | VT-MATH.MP.hs-geometry.1 |
| Reason Abstractly Geometry | Students take a real problem (a ramp, a fence, a shadow) and translate it into numbers or shapes to solve it, then check whether the answer still makes sense in the real situation. | VT-MATH.MP.hs-geometry.2 |
| Construct Arguments Geometry | Students build logical arguments to prove geometric ideas, then explain why a classmate's proof works or where it breaks down. The focus is on reasoning out loud and in writing, not just getting the right answer. | VT-MATH.MP.hs-geometry.3 |
| Model with Mathematics Geometry | Students use math to make sense of real situations, like figuring out how much paint covers a wall or whether a ramp meets a safety code. The math they choose fits the problem, not the other way around. | VT-MATH.MP.hs-geometry.4 |
| Use Tools Strategically Geometry | Students choose the right tool for the math in front of them. That might mean a calculator, a sketch on paper, or a quick estimate, depending on what the problem actually needs. | VT-MATH.MP.hs-geometry.5 |
| Attend to Precision Geometry | Students use the right math words, label measurements with correct units, and check their calculations carefully. Sloppy notation or a missing unit can change the meaning of an answer entirely. | VT-MATH.MP.hs-geometry.6 |
| Use Structure Geometry | Students notice patterns and hidden structure in math problems, like recognizing that a geometric figure can be broken into simpler shapes. That recognition becomes a tool for solving the problem. | VT-MATH.MP.hs-geometry.7 |
| Express Regularity Geometry | When a calculation or process keeps showing the same pattern, students pause to ask why and write a rule that works every time, not just for that one problem. | VT-MATH.MP.hs-geometry.8 |
Students write and solve equations for a straight line, then graph those lines and use them to answer real questions like predicting costs or comparing rates.
Students write two or more equations or inequalities together and find the values that satisfy all of them at once. This shows up in real problems like splitting costs or comparing plans with different rates.
Students study functions shaped like a U-curve, writing equations and sketching graphs to model real situations like a ball's path through the air or the area of a rectangle as its dimensions change.
Students read graphs and write equations that show how something grows fast (like money earning interest) or shrinks over time (like a car losing value). The work connects the equation to a curve on a graph.
Students add, subtract, and multiply expressions with variables and exponents, then read data sets and graphs to draw conclusions about patterns and relationships.
| Standard | Definition | Code |
|---|---|---|
| Linear Functions Algebra I | Students write and solve equations for a straight line, then graph those lines and use them to answer real questions like predicting costs or comparing rates. | VT-MATH.A1.hs-algebra-1.1 |
| Systems Algebra I | Students write two or more equations or inequalities together and find the values that satisfy all of them at once. This shows up in real problems like splitting costs or comparing plans with different rates. | VT-MATH.A1.hs-algebra-1.2 |
| Quadratic Functions Algebra I | Students study functions shaped like a U-curve, writing equations and sketching graphs to model real situations like a ball's path through the air or the area of a rectangle as its dimensions change. | VT-MATH.A1.hs-algebra-1.3 |
| Exponential Functions Algebra I | Students read graphs and write equations that show how something grows fast (like money earning interest) or shrinks over time (like a car losing value). The work connects the equation to a curve on a graph. | VT-MATH.A1.hs-algebra-1.4 |
| Polynomials and Statistics Algebra I | Students add, subtract, and multiply expressions with variables and exponents, then read data sets and graphs to draw conclusions about patterns and relationships. | VT-MATH.A1.hs-algebra-1.5 |
Students read graphs of advanced functions, including curves that model growth, decay, and wave patterns, to spot key features like peaks, valleys, and where the graph crosses zero.
Students add, subtract, multiply, and divide polynomial and rational expressions, then solve equations that contain them. This is the algebra of fractions and multi-term expressions that show up in physics, engineering, and data analysis.
Students use sine and cosine functions to describe real-world patterns that repeat, like sound waves or seasonal temperature changes. They apply trig identities to simplify and solve those models.
Students use data collected from a sample group to draw conclusions about a much larger population. This standard covers the reasoning behind why a well-chosen sample can stand in for a group too large to survey directly.
| Standard | Definition | Code |
|---|---|---|
| Functions and Graphs Algebra II | Students read graphs of advanced functions, including curves that model growth, decay, and wave patterns, to spot key features like peaks, valleys, and where the graph crosses zero. | VT-MATH.A2.hs-algebra-2.1 |
| Polynomial and Rational Algebra II | Students add, subtract, multiply, and divide polynomial and rational expressions, then solve equations that contain them. This is the algebra of fractions and multi-term expressions that show up in physics, engineering, and data analysis. | VT-MATH.A2.hs-algebra-2.2 |
| Trigonometry Algebra II | Students use sine and cosine functions to describe real-world patterns that repeat, like sound waves or seasonal temperature changes. They apply trig identities to simplify and solve those models. | VT-MATH.A2.hs-algebra-2.3 |
| Statistics and Probability Algebra II | Students use data collected from a sample group to draw conclusions about a much larger population. This standard covers the reasoning behind why a well-chosen sample can stand in for a group too large to survey directly. | VT-MATH.A2.hs-algebra-2.4 |
Students use flips, slides, and rotations to show that two shapes are exactly the same size and match up perfectly. If one shape can be moved onto another without stretching or shrinking it, the shapes are congruent.
Right triangles show up in buildings, maps, and ramps. Students use scale, angle measures, and ratios like sine and cosine to find missing side lengths and distances they can't measure directly.
Students use the relationships between angles, arcs, and line segments inside and around a circle to solve geometry problems. This includes finding missing angles or lengths when chords, tangents, or secants intersect.
Students use algebra and coordinates on a graph to prove geometric properties, such as showing two lines are parallel or finding the exact center of a shape.
Students calculate the area, surface area, and volume of shapes, then apply those skills to real problems like figuring out how much paint covers a wall or how much water fills a tank.
| Standard | Definition | Code |
|---|---|---|
| Congruence Geometry | Students use flips, slides, and rotations to show that two shapes are exactly the same size and match up perfectly. If one shape can be moved onto another without stretching or shrinking it, the shapes are congruent. | VT-MATH.GEO.hs-geometry.1 |
| Similarity, Right Triangles, and Trigonometry Geometry | Right triangles show up in buildings, maps, and ramps. Students use scale, angle measures, and ratios like sine and cosine to find missing side lengths and distances they can't measure directly. | VT-MATH.GEO.hs-geometry.2 |
| Circles Geometry | Students use the relationships between angles, arcs, and line segments inside and around a circle to solve geometry problems. This includes finding missing angles or lengths when chords, tangents, or secants intersect. | VT-MATH.GEO.hs-geometry.3 |
| Coordinate Geometry Geometry | Students use algebra and coordinates on a graph to prove geometric properties, such as showing two lines are parallel or finding the exact center of a shape. | VT-MATH.GEO.hs-geometry.4 |
| Measurement and Modeling Geometry | Students calculate the area, surface area, and volume of shapes, then apply those skills to real problems like figuring out how much paint covers a wall or how much water fills a tank. | VT-MATH.GEO.hs-geometry.5 |
Federally administered sample-based assessment in reading, mathematics, science, and writing. NAEP results inform state-by-state comparisons rather than individual student or school accountability.
Students work with four big families of equations: lines, systems of two lines together, parabolas (quadratics), and growth or decay patterns (exponentials). They also add, subtract, and multiply polynomials, and use data to spot trends. The year is about moving from arithmetic to using letters and graphs to describe real situations.
Ask them to read the problem out loud and tell you what the question is asking before touching any numbers. Then ask what they already know and what they need to find. Most homework struggles come from rushing past those two steps, not from missing math skills.
By winter, students should solve linear equations and graph a line from a word problem without much help. By spring, they should set up two equations for a situation with two unknowns and recognize when a graph curves like a parabola or grows quickly. If word problems still feel impossible in May, that is the signal to ask the teacher.
Yes, by the end of the year. It is one of the few formulas worth committing to memory because it solves any quadratic equation. Quizzing it on the drive to school for a week usually does the trick.
Most teachers start with linear equations and inequalities, move to systems, then spend a long stretch on quadratics, and finish with exponentials and a short data unit. Polynomial operations slot in right before quadratics so students can factor. Leaving six weeks for quadratics is usually the right call.
Negative numbers, distributing a negative sign, and fraction operations come back to bite students all year. Factoring trinomials and interpreting word problems are the two new skills that take the longest to stick. Plan a short warm-up each week that recycles signed numbers and fractions through May.
Students can take a real situation, decide whether it is linear, quadratic, or exponential, write the equation, graph it, and explain what the graph means. They can solve a system two ways and factor a basic quadratic. That package is what Geometry and Algebra II will assume they have.
Loan payments, phone plan comparisons, and anything that grows over time (like savings or a virus) all use the math from this year. The bigger payoff is learning to set up a problem from a messy description, which shows up in almost every job. They do not have to love it, just finish it.