What should a Grade 7 student know in math?
Proportional relationships, rational-number arithmetic with negatives, linear expressions and equations, percent problems, and probability.
Grade 7 math practice — adaptive, verified, parent-run
9,724 verified practice questions across 92 Common Core concepts for Grade 7
What should a Grade 7 student know?
Seventh grade is the proportionality year: unit rates, constant of proportionality, and percent applications from tax to interest. Rational arithmetic now includes negatives in every operation.
Expressions become linear equations and inequalities in one variable. Geometry adds circles, angle relationships, and scale drawings; probability becomes a formal topic with models, not just intuition.
The curriculum map
Every Common Core concept we cover for Grade 7
Expressions and Equations
- Add, subtract, factor, and expand linear expressions
- Assess reasonableness of answers using estimation
- Assess reasonableness using estimation with rationals
- Combine like terms in linear expressions with rational coefficients
- Compare algebraic and arithmetic solution methods
- Construct and solve equations and inequalities
- Factor and expand linear expressions using the distributive property
- Generate equivalent linear expressions
- Interpret equivalent forms of expressions in context
- Solve and graph inequalities of the form px + q > r
- Solve multi-step problems with rational numbers in any form
- Solve multi-step problems with rationals in any form
- Solve two-step equations of the form px + q = r
- Solve two-step inequalities and graph solutions
- Understand rewriting expressions reveals relationships
Geometry
- 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 geometric shapes with given conditions
- Construct triangles from given conditions
- Describe cross-sections of 3D figures
- Determine when conditions give unique, multiple, or no triangles
- Informally derive the relationship between circumference and area
- Reproduce a scale drawing at a different scale
- Solve area, volume, and surface area problems with composite shapes
- Solve composite area, volume, and surface area problems
- Solve problems with scale drawings
- Use angle relationships to solve for unknown angles
- Use circle area and circumference formulas
- Use supplementary, complementary, vertical, and adjacent angle facts
- Write and solve equations for unknown angles
Ratios and Proportional Relationships
- Calculate percent increase and percent decrease
- Compute unit rates involving fractions
- Determine whether a relationship is proportional
- Identify the constant of proportionality
- Identify the constant of proportionality from tables and graphs
- Interpret points on a proportional relationship graph
- 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 for proportional relationships
- 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 and use simulations for compound events
- Design simulations to estimate compound event probabilities
- Determine theoretical probability of simple events
- Develop and use probability models
- Develop a probability model from observed frequencies
- Develop a uniform probability model
- 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
- Represent sample spaces for compound events
- 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
- Add rational numbers using number line and properties
- Apply properties to multiply and divide rational numbers
- Convert rational numbers between fraction and decimal forms
- Convert rational numbers to decimals using long division
- Divide signed rational numbers using sign rules
- Evaluate complex expressions with multiple rational number operations
- 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
- Subtract rational numbers as adding the additive inverse
- Understand additive inverses and opposite quantities summing to zero
- Understand and apply rules for dividing signed numbers
- Understand and apply rules for multiplying signed numbers
Diagnosis, not just marking
Where Grade 7 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.
Grade 7 math — questions parents ask
How much math practice does a Grade 7 student need each day?
Short and daily beats long and rare. Most families set a 10–30 minute time budget; Algo School sizes each Grade 7 session to that budget and to your child's pace — a quick day never becomes a marathon.
How does Algo School help with Grade 7 math at home?
Algo School generates short daily sessions from 9,724 verified Grade 7 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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