What should a Pre-Algebra student know in math?
Fluent rational-number arithmetic, ratios and percents, linear expressions and equations, intro functions, and core geometry and statistics.
Pre-Algebra math practice — adaptive, verified, parent-run
10,630 verified practice questions across 99 Common Core concepts for Pre-Algebra
What should a Pre-Algebra student know?
Pre-Algebra is the bridge from arithmetic to algebra. It consolidates integers, fractions, decimals, ratios, and percents until they're automatic — the fluency algebra quietly assumes.
On top of that base: linear expressions and equations, a first formal look at functions, geometry essentials, and statistics and probability. If any middle-school year has gaps, this is where they surface — and where they're cheapest to fix.
The curriculum map
Every Common Core concept we cover for Pre-Algebra
Expressions and Equations
- Add, subtract, factor, and expand linear expressions
- Assess reasonableness of answers using estimation
- Assess reasonableness using estimation with rationals
- Classify linear equations by number of solutions
- Combine like terms in linear expressions with rational coefficients
- Compare proportional relationships in different representations
- Construct and solve equations and inequalities
- Derive equations y = mx and y = mx + b
- Derive slope and y = mx + b
- Explain why slope is constant using similar triangles
- Factor and expand linear expressions using the distributive property
- Generate equivalent linear expressions
- Graph proportional relationships and interpret slope
- Graph proportional relationships and interpret unit rate as slope
- Interpret equivalent forms of expressions in context
- Solve and graph inequalities of the form px + q > r
- Solve linear equations in one variable
- Solve linear equations with rational coefficients
- Solve multi-step problems with rational numbers in any form
- Solve multi-step problems with rationals in any form
- Understand rewriting expressions reveals relationships
Geometry
- Apply angle relationships formed by parallel lines and a transversal
- Apply coordinate rules for dilations
- Apply coordinate rules for translations, reflections, and rotations
- Apply the angle-angle criterion for triangle similarity
- Apply the Pythagorean Theorem in three-dimensional contexts
- Calculate volume of cones using V = (1/3) * pi * r^2 * h
- Calculate volume of cylinders using V = pi * r^2 * h
- Calculate volume of prisms and composite 3D shapes
- Calculate volume of spheres using V = (4/3) * pi * r^3
- Compute actual lengths and areas from scale drawings
- Compute area of circles using A = πr²
- Compute circumference of circles using C = πd or C = 2πr
- Construct triangles from three given measurements
- Describe the transformation sequence mapping congruent figures
- Determine similarity using sequences of transformations including dilations
- Find the distance between two points on the coordinate plane
- Find unknown side lengths in right triangles using the Pythagorean Theorem
- Informally derive the relationship between circumference and area
- Reproduce a scale drawing at a different scale
- Solve area problems for composite 2D shapes
- Solve problems with scale drawings
- Use angle relationships to write and solve equations
- Use circle area and circumference formulas
- Verify that rotations, reflections, and translations preserve segment lengths and angle measures
Ratios and Proportional Relationships
- Calculate percent increase and percent decrease
- Compute unit rates involving fractions
- Identify the constant of proportionality from tables and graphs
- Interpret unit rates in real-world ratio contexts
- Recognize and represent proportional relationships
- Solve multistep percent problems (tax, markup, discount, commission)
- Solve multistep ratio and percent problems
- Solve percent increase and decrease problems
- Solve percent problems involving tax, tip, markup, and discount
- Test whether two quantities are proportional
- Write equations of the form y = kx for proportional relationships
Statistics and Probability
- Approximate probability from relative frequency
- Approximate probability using experimental relative frequency
- Assess variability across multiple random samples
- Assess visual overlap of two data distributions
- Compare model probabilities to observed frequencies
- Compare populations using measures of center and variability
- Compare two populations informally
- Design simulations to estimate compound event probabilities
- Determine theoretical probability of simple events
- Develop and use probability models
- Distinguish between population and sample
- Draw comparative inferences about two populations
- Draw inferences about a population from sample data
- Draw inferences from random samples
- Evaluate whether a sample is representative
- Express center difference as multiple of variability
- Find probabilities of compound events
- Generate multiple samples to gauge variation in estimates
- Interpret probability as a measure of likelihood between 0 and 1
- Make predictions about a population from sample data
- Represent compound event sample spaces using lists, tables, and tree diagrams
- Understand probability as a number between 0 and 1
- Understand probability of chance events
- Understand random sampling and representative samples
- Understand representative samples and valid inferences
- Use center and variability to compare two populations
The Number System
- Add and subtract rational numbers
- Add rational numbers including negative fractions and decimals
- Approximate and locate irrational numbers on a number line
- Approximate irrational numbers
- Classify numbers as rational or irrational
- Convert a repeating decimal to a rational number
- Convert rational numbers between fraction and decimal forms
- Convert repeating decimals to fractions
- Divide signed rational numbers using sign rules
- Estimate values of expressions involving irrationals
- Evaluate complex expressions with multiple rational number operations
- Know rational and irrational numbers
- Know that irrational numbers exist and rationals have repeating decimals
- Model addition and subtraction of rationals on a number line
- Multiply and divide rational numbers
- Multiply signed rational numbers using sign rules
- Solve real-world problems using four operations with rationals
Diagnosis, not just marking
Where Pre-Algebra students actually go wrong
For these concepts we've written up the specific mistaken rules children apply — what each one sounds like at the kitchen table, and why it feels right to them. Free to read, no account needed.
Pre-Algebra math — questions parents ask
How much math practice does a Pre-Algebra student need each day?
Short and daily beats long and rare. Most families set a 10–30 minute time budget; Algo School sizes each Pre-Algebra session to that budget and to your child's pace — a quick day never becomes a marathon.
How does Algo School help with Pre-Algebra math at home?
Algo School generates short daily sessions from 10,630 verified Pre-Algebra questions, checks every answer, and adapts the next session to what your child actually mastered. When they're stuck, an answer-guarded AI tutor coaches with questions and hints — and you get an email brief after every tutoring session. Homeschool families use the per-concept mastery record as their assessment evidence.
Math practice for every band — home and homeschool, Grade 1 through Algebra 2.
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