7th Grade Math Worksheets, Lessons and Tests (Free PDF)
These grade 7 math worksheets follow the Common Core State Standards chapter by chapter: each chapter has a lesson, a worksheet of at least 20 worksheet problems with solutions, a timed test with its answer key and an online quiz, all with a free PDF.
Key takeaway: 7th grade math focuses on proportional relationships and percent problems, operations with positive and negative rational numbers, multi-step equations and inequalities, scale drawings, circles, angles, surface area and volume, random sampling and probability models.
Grade 7 math worksheets: all chapters
1. Unit Rates with Fractions
Understand a unit rate · Find a unit rate when the numbers are fractions · Compare two rates
2. Proportional Relationships and y = kx
Tell from a graph · Write the equation y = kx
3. Percent Problems: Tax, Tips, Discounts and Markups
Understand a percent of a number · Find tax, tips, markups and discounts · Solve a multistep percent problem · Understand simple interest and percent error
4. Adding and Subtracting Rational Numbers
Understand rational numbers and opposites · Add rational numbers on a number line · Subtract rational numbers
5. Multiplying and Dividing Rational Numbers
Multiply signed numbers · Divide signed numbers · Turn a fraction into a decimal
6. Solving Real-World Problems with Rational Numbers
Choose the operation · Solve a multistep problem · Work with fractions and decimals in the same problem · Understand a complex fraction
7. Equivalent Linear Expressions
Understand equivalent expressions · Combine like terms · Expand and factor
8. Multistep Problems with Rational Numbers
Solve a problem that mixes fractions, decimals and percents · Understand a good plan for a multistep problem · Work with a budget
9. Solving Two-Step Equations
Understand a two-step equation · Solve px + q = r · Solve p(x + q) = r
10. Two-Step Inequalities
Solve \(px + q > r\) · Use inequalities in word problems
11. Scale Drawings
Understand a scale drawing · Find an actual length · Redraw at a different scale
12. Drawing Triangles from Given Conditions
To draw a triangle from given conditions, check them first.
13. Cross-Sections of Three-Dimensional Figures
A cross-section is the two-dimensional shape formed when a plane slices a three-dimensional figure.
14. Circumference and Area of Circles
Understand the parts of a circle · Understand pi · Find circumference and area
15. Angle Relationships and Equations
Understand complementary and supplementary angles · Understand vertical angles · Write an equation for an unknown angle
16. Area, Volume and Surface Area
Find the area of triangles and quadrilaterals · Find the area of a composite polygon · Find the volume of a right prism · Find the surface area of a prism
17. Random Sampling and Inference
Understand a population and a sample · Use a sample to estimate a population
18. Comparing Two Populations
Compare the centers of two data sets · Measure how spread out the data are · Decide if a difference is meaningful
19. Probability and Probability Models
Understand probability · Find theoretical probability · Understand relative frequency · Understand a probability model
What students learn in 7th grade math
Seventh grade deepens proportional reasoning and completes operations with rational numbers. Students add, subtract, multiply and divide positive and negative numbers, including fractions and decimals.
They also solve two-step equations and inequalities, analyze proportional relationships in tables and graphs, and solve percent problems such as tax, tips and discounts. In geometry and probability, they work with scale drawings, circles, angles, random samples and chance.
- Ratios: unit rates with fractions, constant of proportionality, and percent increase and decrease.
- The number system: all four operations with rational numbers and converting fractions to decimals.
- Expressions and equations: equivalent expressions, two-step equations, and inequalities.
- Geometry, statistics and probability: scale drawings, circles, angle relationships, sampling, and probability models.
A year plan with these grade 7 math worksheets
Start with rational number operations, because every equation uses them. Next, work on proportional relationships and percents. Then, move to expressions and two-step equations. Finally, close the year with geometry and probability, which apply the same tools to new situations.
How to use these grade 7 math worksheets
Pick a chapter, read its one-page lesson, then solve the worksheet on paper and check every answer with the solutions page. Take the ten-question quiz to see what is still unclear, and finish with the timed test. Every page can be printed from its PDF button, and the quick practice at the bottom of each page gives ten new questions at every visit.
7th Grade math: common questions
What do you learn in 7th grade math?
Students work with proportional relationships and the constant of proportionality, add, subtract, multiply and divide rational numbers, solve two-step equations and inequalities, and find probabilities of simple and compound events.
Is 7th grade math pre-algebra?
Much of it is: equivalent expressions, two-step equations and inequalities, and proportional relationships prepare students directly for 8th grade linear equations and Algebra 1.
Are there tests with answer keys?
Yes. Every chapter has a 45-minute test scored out of 20 points and a separate solutions page with a scoring guide.
How should a student review for a test?
Reread the lesson, redo the worksheet worksheet problems you missed using the solutions, take the online quiz, then time yourself on the test.
How do you know if a relationship is proportional in 7th grade?
Check that the ratio y/x is the same for every pair in the table, and that the graph is a straight line through the origin. That common ratio is the constant of proportionality k in y = kx.
What are the rules for multiplying negative numbers?
A product of two numbers with the same sign is positive, and a product of two numbers with different signs is negative. For example, (−4)(−3) = 12 and (−4)(3) = −12.