Math Made Easy’s 7th grade math lessons cover all 21 chapters, from unit rates with fractions to compound events. Every 7th grade math lesson is free and aligned to the Grade 7 Common Core standards. Mathbot, our blue robot coach, guides seventh graders and their families through worked examples first.
What the 7th grade math lessons teach
- Unit Rates with Fractions
- Percent Increase, Percent Decrease and Percent Error
- Equivalent Expressions
- Drawing Geometric Figures and Constructing Triangles
- Area, Surface Area and Volume of Prisms
Work in order: read a lesson such as Unit Rates with Fractions, solve the matching worksheet, check it against the answer key, take the chapter test, and finish with the 10-question quiz. The tax, tip, markup and discount lessons reuse a single bar model, so percent work feels like one idea instead of five.
When a problem mentions percent, rewrite it as a proportion or a decimal multiplier before touching a calculator. Domains covered by the 7th grade math lessons: Ratios & Proportional Relationships, The Number System, Expressions & Equations, Geometry, and Statistics & Probability.
Chapter 1 · Grade 7 · 7.RP.A.1
Finding Unit Rates When Quantities Are Fractions
Compute unit rates when the numbers themselves are fractions, such as 1/2 mile in 1/4 hour, which is 2 miles per hour. You will handle lengths, areas, and other quantities, even in different units. Read the lesson on fraction rates, solve the worksheet and check it with the answer key, then take the quiz and the test.
- Complex fractions
- Unit rates
- Mixed units
Chapter 2 · Grade 7 · 7.RP.A.2a, 7.RP.A.2b, 7.RP.A.2d
Spotting Proportional Relationships in Tables and Graphs
Decide whether two quantities are proportional by checking tables and graphs for a straight line through the origin. Find the constant of proportionality, and explain what the points (0, 0) and (1, r) mean. Work through the proportionality lesson, test yourself on the worksheet with its answer key, and finish with the quiz and the scored test.
- Testing proportionality
- Constant of proportionality
- Graph of a ratio
Chapter 3 · Grade 7 · 7.RP.A.2c
Writing and Using y = kx Equations
Write y = kx from a table, graph, or story, then use it to find missing values. If 6 notebooks cost $15, then t = 2.5n, and you can compare it with another rate given as a graph. Mathbot suggests the lesson first, then the worksheet with answer key, and finally the quiz and test to prove your proportional equations skills.
- Writing y = kx
- Missing values
- Comparing relationships
Chapter 4 · Grade 7 · 7.RP.A.3
Solving Multistep Percent Problems with Tax, Tips and Discounts
Solve multistep percent situations: sales tax, tips, markups, markdowns, discounts, commissions, and simple interest I = Prt. A $40 jacket at 25% off plus 8% tax shows how to chain the steps. Every page pairs a lesson with a worksheet and answer key, plus a quiz and a test whose scoring guide shows where percent applications points were earned.
- Tax and tips
- Discounts and markups
- Simple interest
Chapter 5 · Grade 7 · 7.RP.A.3
Calculating Percent Change and Percent Error
Calculate percent increase, percent decrease, and percent error, and work backward to an original amount. A price rising from $50 to $62 is a 24% increase, and you can compare growth between situations. Read, solve the worksheet, grade it with the answer key; the quiz is a quick check on percent change, and the test comes with a scoring guide.
- Percent increase
- Percent decrease
- Percent error
Chapter 6 · Grade 7 · 7.NS.A.1a, 7.NS.A.1b, 7.NS.A.1c, 7.NS.A.1d
Adding and Subtracting Positive and Negative Numbers
Add and subtract integers and rational numbers using a number line and opposites, treating subtraction as adding the additive inverse. Distance becomes the absolute value of a difference, as with -8 degrees and 5 degrees. Learn integer addition and subtraction in the lesson, build speed on the worksheet, correct mistakes with the answer key, and confirm mastery with the quiz and test.
- Opposites
- Subtracting rationals
- Distance on a line
Chapter 7 · Grade 7 · 7.NS.A.2a, 7.NS.A.2b, 7.NS.A.2c
Multiplying and Dividing Signed Numbers
Learn the sign rules for products and quotients and the reason (-1)(-1) = 1. You will also see why division by zero is undefined and use properties to simplify, such as (-3/4)(-8) = 6. After the lesson, the worksheet and answer key let you fix errors in integer multiplication and division before you attempt the quiz and the test.
- Sign rules
- Rational products
- Undefined division
Chapter 8 · Grade 7 · 7.NS.A.2d, 7.NS.A.3
Fractions, Decimals and Rational Number Word Problems
Convert fractions to terminating or repeating decimals by long division, then solve real situations that mix fractions, decimals, and negatives. For example, a bank balance of -$12.50 drops further after buying 3/4 of a $20 item. Take the quiz first to see what you know about rational numbers, then study the lesson, finish the worksheet, and use the test scoring guide.
- Fraction to decimal
- Mixed operations
- Rational word problems
Chapter 9 · Grade 7 · 7.EE.A.1, 7.EE.A.2
Rewriting Linear Expressions in Equivalent Forms
Add, subtract, factor, and expand linear expressions with rational coefficients, and rewrite them to show meaning. Adding a 5% fee to a price p gives p + 0.05p, which is simply 1.05p. Do the lesson, then the worksheet and answer key, then the scored test on equivalent expressions; the short quiz gives a fast check on the way.
- Expanding and factoring
- Like terms
- Rewriting expressions
Chapter 10 · Grade 7 · 7.EE.B.3, 7.EE.B.4a
Solving Two-Step Equations with Rational Numbers
Solve px + q = r and p(x + q) = r, compare an algebraic path with an arithmetic one, and estimate to test your answer. A $12 fee plus $4 per ride totaling $40 gives 4r + 12 = 40. Lesson first, worksheet next: the answer key confirms each two-step equations result, and the quiz and test with scoring guide close the chapter.
- Two-step equations
- Distributive form
- Checking answers
Chapter 11 · Grade 7 · 7.EE.B.4b
Solving and Graphing Two-Step Inequalities
Solve px + q > r and px + q < r, flip the inequality sign when you multiply or divide by a negative, and graph the solution set. Then explain it, such as how many $3 snacks fit a $20 budget after a $5 ticket. Read the lesson on two-step inequalities, solve the worksheet and check it with the answer key, then take the quiz and the test.
- Solving inequalities
- Reversing the sign
- Graphing solutions
Chapter 12 · Grade 7 · 7.G.A.1
Scale Drawings: Lengths, Areas and Scale Factors
Use a scale factor to turn map and blueprint measurements into real lengths and areas, or to redraw a figure at a new size. A scale of 1 inch to 8 feet makes a 3-inch wall 24 feet long. Work through the scale drawings lesson, test yourself on the worksheet with its answer key, and finish with the quiz and the scored test.
- Scale factor
- Actual lengths
- Scaled areas
Chapter 13 · Grade 7 · 7.G.A.2
Building Triangles from Sides and Angles
Draw shapes from given conditions with a ruler and protractor, and test the triangle inequality. You will tell when three measures give one triangle, many triangles, or none, like sides of 3, 4, and 9. Mathbot suggests the lesson first, then the worksheet with answer key, and finally the quiz and test to prove your triangle construction skills.
- Triangle inequality
- Drawing with tools
- Unique triangles
Chapter 14 · Grade 7 · 7.G.A.3
Cross Sections of Prisms and Pyramids
Picture the flat shape left when a plane slices a rectangular prism or pyramid, parallel or perpendicular to the base. Slicing a pyramid parallel to its square base gives a smaller square. Every page pairs a lesson with a worksheet and answer key, plus a quiz and a test whose scoring guide shows where cross sections points were earned.
- Slicing solids
- Prism sections
- Pyramid sections
Chapter 15 · Grade 7 · 7.G.B.4
Circles: Circumference and Area Made Clear
Use radius and diameter to find circumference C = 2 pi r and area A = pi r^2, and see where the area formula comes from. A circular pool of radius 6 feet and half-circle patios show real uses. Read, solve the worksheet, grade it with the answer key; the quiz is a quick check on circles, and the test comes with a scoring guide.
- Circumference
- Area of circles
- Semicircles
Chapter 16 · Grade 7 · 7.G.B.5
Angle Relationships and Unknown Angles
Identify supplementary, complementary, vertical, and adjacent angles, then write and solve a short equation for the unknown one. If two angles on a line measure x and 3x + 20, you can find both. Learn angle relationships in the lesson, build speed on the worksheet, correct mistakes with the answer key, and confirm mastery with the quiz and test.
- Angle pairs
- Vertical angles
- Angle equations
Chapter 17 · Grade 7 · 7.G.B.6
Prisms: Surface Area, Volume and Composite Figures
Break composite figures into triangles and rectangles for area, then find surface area and volume of right prisms and of solids built from cubes. A triangular prism tent shows how the pieces fit together. After the lesson, the worksheet and answer key let you fix errors in prisms before you attempt the quiz and the test.
- Composite area
- Prism volume
- Prism surface area
Chapter 18 · Grade 7 · 7.SP.A.1, 7.SP.A.2
Random Samples and Population Inferences
Distinguish a population from a sample, spot biased selection, and use a random sample to estimate a whole group. If 12 of 40 surveyed students walk to school, estimate for 800 students and compare repeated samples. Take the quiz first to see what you know about sampling, then study the lesson, finish the worksheet, and use the test scoring guide.
- Random samples
- Bias
- Population estimates
Chapter 19 · Grade 7 · 7.SP.B.3, 7.SP.B.4
Comparing Two Data Sets with Variability
Place two data sets side by side on dot plots or box plots and compare their centers, measuring the gap in units of variability. If two teams differ by 4 points and the mean absolute deviation is 2, that is twice the spread. Do the lesson, then the worksheet and answer key, then the scored test on comparing data; the short quiz gives a fast check on the way.
- Comparing centers
- Mean absolute deviation
- Side-by-side plots
Chapter 20 · Grade 7 · 7.SP.C.5, 7.SP.C.6, 7.SP.C.7
Probability Models and Chance Experiments
Rate chance on a scale from 0 to 1, from impossible to certain, and contrast experimental with theoretical probability. You will build uniform and non-uniform models, then compare predictions with results from 50 spins. Lesson first, worksheet next: the answer key confirms each probability models result, and the quiz and test with scoring guide close the chapter.
- Probability scale
- Experimental probability
- Probability models
Chapter 21 · Grade 7 · 7.SP.C.8
Compound Events, Sample Spaces and Simulations
List sample spaces with organized lists, tables, and tree diagrams, then find the probability of compound events as a fraction of outcomes. Flipping a coin and rolling a die gives 12 outcomes, and you can design a simulation. Read the lesson on compound events, solve the worksheet and check it with the answer key, then take the quiz and the test.
- Sample spaces
- Tree diagrams
- Simulations
Grade 7 Math Lessons: frequently asked questions
Are the 7th grade math lessons free?
Yes. All 21 7th grade math lessons are free to read, with no account needed. Each 7th grade math lesson points ahead to its worksheet, test and quiz.
Which standards do the 7th grade math lessons follow?
They follow the Grade 7 Common Core State Standards for Mathematics, which organizes the course into Ratios & Proportional Relationships, The Number System, Expressions & Equations, Geometry, and Statistics & Probability. Each 7th grade math lesson is tagged with codes such as 7.RP.A.2, 7.NS.A.1 and 7.EE.B.4.
What should I know before starting 7th grade math?
Students should know ratios, unit rates, integer basics and one-step equations from Grade 6. If a gap shows up, begin with the lesson on unit rates with fractions.
How are the 7th grade math lessons organized?
Proportional reasoning anchors the first third of the course, then rational numbers, equations, geometry and probability follow. The 7th grade math chapters can be read in order or picked by topic.
What comes after 7th grade math?
Grade 8 moves from proportional relationships to slope, linear equations and the Pythagorean theorem. Finishing the 21 chapters on unit rates with fractions through compound events leaves students ready for that step.