Numbers and expressions
Students start the year working with the number system and algebraic expressions. They tell rational numbers apart from irrational ones and practice adding, subtracting, and multiplying polynomials.
What does a student learn in
This is the year math shifts from arithmetic to thinking with variables and functions. Students work with polynomials, then write and graph linear equations and inequalities to model real situations. They also build quadratic and exponential functions and use scatter plots to find patterns in data. By spring, students can solve a system of two equations and explain what the answer means in a real-world problem.
- Linear equations
- Quadratic functions
- Exponential functions
- Polynomials
- Systems of equations
- Data and scatter plots
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
Linear equations and graphs
Students write and solve linear equations and inequalities, then graph them on the coordinate plane. They use these tools to model situations like phone plans, savings, and travel times.
- 3
Systems of equations
Students work with two equations at once to find where lines meet. They solve systems by graphing and by algebra to answer questions with more than one unknown.
- 4
Quadratic and exponential functions
Students move beyond straight lines into curves. They write and graph quadratic functions for things like a tossed ball, and exponential functions for things that double or grow fast over time.
- 5
Data and regression
Students end the year making sense of data. They summarize one set of numbers, plot pairs of numbers on a scatter plot, and fit a line or curve to describe the pattern.
Mastery Learning Standards
The required skills a student should display by the end of Grade 9.
Algebra I
Algebra I
- Algebra I
Number Operations and Expressions
Students work with fractions, decimals, and expressions like 2x squared plus 5x to solve math problems. They use number rules to simplify, combine, and rearrange those expressions accurately.
- Algebra I
Linear Functions and Equations
Students write and solve equations and inequalities with one variable, then graph them to make sense of real-world problems. This includes finding where two lines cross to solve a system.
- Algebra I
Quadratic and Exponential
Students write equations for curves that speed up or grow faster over time, such as a thrown ball or a savings account with compound interest, then use those equations to answer real questions about the situation.
- Algebra I
Data Analysis
Students read graphs and tables to find patterns in data, then use trend lines or equations to describe how two things relate. This covers single sets of data as well as side-by-side comparisons.
| Standard | Definition | Code |
|---|---|---|
| Number Operations and Expressions Algebra I | Students work with fractions, decimals, and expressions like 2x squared plus 5x to solve math problems. They use number rules to simplify, combine, and rearrange those expressions accurately. | PA-MATH.A1.hs-algebra-1.1 |
| Linear Functions and Equations Algebra I | Students write and solve equations and inequalities with one variable, then graph them to make sense of real-world problems. This includes finding where two lines cross to solve a system. | PA-MATH.A1.hs-algebra-1.2 |
| Quadratic and Exponential Algebra I | Students write equations for curves that speed up or grow faster over time, such as a thrown ball or a savings account with compound interest, then use those equations to answer real questions about the situation. | PA-MATH.A1.hs-algebra-1.3 |
| Data Analysis Algebra I | Students read graphs and tables to find patterns in data, then use trend lines or equations to describe how two things relate. This covers single sets of data as well as side-by-side comparisons. | PA-MATH.A1.hs-algebra-1.4 |
Geometry
Geometry
- Geometry
Two-Dimensional Figures
Students use properties of flat shapes to solve problems. That includes sliding, flipping, or rotating shapes, comparing shapes that are the same proportion but different sizes, and applying trigonometry to find missing side lengths or angles.
- Geometry
Three-Dimensional Figures
Students find the total area of a shape's outer surface and the amount of space it holds inside, then use those numbers to solve real problems, like figuring out how much paint covers a box or how much water fills a tank.
- Geometry
Coordinate Geometry
Students plot shapes on a coordinate grid, then use the coordinates to prove that sides are parallel, angles are right, or distances match. It connects the rules of geometry to actual numbers.
- Geometry
Probability and Reasoning
Students use probability and logical reasoning to work through geometric problems, such as figuring out the chances of landing on a shaded region or deciding whether a geometric statement must be true.
| Standard | Definition | Code |
|---|---|---|
| Two-Dimensional Figures Geometry | Students use properties of flat shapes to solve problems. That includes sliding, flipping, or rotating shapes, comparing shapes that are the same proportion but different sizes, and applying trigonometry to find missing side lengths or angles. | PA-MATH.GEO.hs-geometry.1 |
| Three-Dimensional Figures Geometry | Students find the total area of a shape's outer surface and the amount of space it holds inside, then use those numbers to solve real problems, like figuring out how much paint covers a box or how much water fills a tank. | PA-MATH.GEO.hs-geometry.2 |
| Coordinate Geometry Geometry | Students plot shapes on a coordinate grid, then use the coordinates to prove that sides are parallel, angles are right, or distances match. It connects the rules of geometry to actual numbers. | PA-MATH.GEO.hs-geometry.3 |
| Probability and Reasoning Geometry | Students use probability and logical reasoning to work through geometric problems, such as figuring out the chances of landing on a shaded region or deciding whether a geometric statement must be true. | PA-MATH.GEO.hs-geometry.4 |
Assessments
The state tests students at this grade and subject take.
Keystone Algebra I
End-of-course exam in Algebra I, typically grade 8 or 9. Required for graduation under Act 158 pathways.
- When given:
- end-of-course
- Frequency:
- by course completion
Common Questions
What does Algebra I cover this year?
Students work with numbers and expressions, then move into linear equations and inequalities. After that they study quadratic and exponential functions, and finish with data, graphs, and lines of best fit. Most of the year ties algebra to real situations like distance, money, and growth over time.
How can I help with algebra homework if I have forgotten most of it?
Ask students to explain each step out loud before checking the answer. If they are stuck on an equation, suggest they try a simple number first to see how the rule works. Five minutes of patient questions usually beats trying to reteach the method.
What should students be comfortable doing by the end of the year?
Solving linear equations and inequalities, graphing a line from an equation, and using a system of two equations to answer a word problem. Students should also recognize quadratic and exponential patterns and read a scatter plot well enough to describe the trend.
How should the year be sequenced?
Most teachers start with expressions, exponents, and polynomials, then spend a long stretch on linear equations, inequalities, and systems. Quadratics and exponential functions come next, and statistics and regression close the year. Linear work is the spine, so build it carefully before moving on.
Which topics usually need the most reteaching?
Negative numbers and fractions inside algebraic steps, the difference between an expression and an equation, and graphing slope from a real situation. Factoring quadratics and interpreting word problems also tend to need a second pass later in the year.
My child says they are bad at math. What can I do at home?
Keep the stakes low. Talk through tips, sale prices, gas mileage, or sports stats and let students set up the math out loud. Short, regular conversations build more confidence than long study sessions, and they show that algebra is just a way to describe things students already understand.
Does my child need to memorize a lot of formulas?
Less than people expect. Students need slope, the basic forms of a line, and the quadratic formula, plus a few exponent rules. Most of the work is about setting up the problem and reading the answer, not reciting formulas from memory.
How do I know if students are ready for Geometry or Algebra II next year?
Check whether students can solve a multi-step linear equation without prompting, graph a line from a word problem, and factor a basic quadratic. They should also be able to read a scatter plot and describe what the trend means in plain language.