7th Grade Math · Parent guide
What Math Should a 7th Grader Know?
Complete Parent Guide
By the end of 7th grade, your child should recognize and use proportional relationships (including the constant of proportionality in tables, graphs and equations), solve multi-step percent problems such as tax, tips, discounts and percent change, add, subtract, multiply and divide positive and negative numbers, solve two-step equations like 3x + 5 = 20 and two-step inequalities, use scale drawings, find the area and circumference of circles, and find probabilities of simple and compound events. The Common Core names four focus areas for grade 7: proportional relationships; operations with rational numbers and linear equations; scale drawings, area, surface area and volume; and drawing conclusions about a population from samples.
Reviewed against the Common Core standards.
What 7th Graders Learn in Math, by Domain
These are the Common Core State Standards for Grade 7 math, grouped by domain and put into plain English. Many states use them as written or in an adapted version, so your school's wording may differ slightly. The code after each skill is the standard it comes from, and each domain links to the full text on the Common Core site. Read the official Grade 7 introduction.
Ratios & Proportional Relationships
Common Core 7.RP- Find unit rates with fractions, such as 1/2 mile every 1/4 hour = 2 miles per hour (7.RP.1)
- Decide whether two quantities are proportional using a table or a graph through the origin (7.RP.2a)
- Find the constant of proportionality and write equations like t = pn (7.RP.2b, 7.RP.2c)
- Solve multi-step percent problems: tax, tips, markups, discounts, interest, percent change and percent error (7.RP.3)
The Number System
Common Core 7.NS- Add and subtract positive and negative numbers and show it on a number line (7.NS.1)
- Understand subtraction as adding the opposite: p - q = p + (-q) (7.NS.1c)
- Multiply and divide signed numbers, including why (-1)(-1) = 1 (7.NS.2)
- Convert fractions to decimals by long division and know they either end or repeat (7.NS.2d)
Expressions & Equations
Common Core 7.EE- Expand, factor and combine like terms in linear expressions (7.EE.1)
- See that "increase by 5%" is the same as "multiply by 1.05" (7.EE.2)
- Solve equations like px + q = r and p(x + q) = r fluently (7.EE.4a)
- Solve and graph two-step inequalities like 3x + 50 > 200 (7.EE.4b)
Geometry
Common Core 7.G- Use scale drawings to find real lengths and areas (7.G.1)
- Know and use the area and circumference formulas for circles (7.G.4)
- Use supplementary, complementary, vertical and adjacent angles to find unknown angles (7.G.5)
- Solve area, volume and surface area problems for prisms and composite shapes (7.G.6)
Statistics & Probability
Common Core 7.SP- Use random samples to draw conclusions about a population (7.SP.1, 7.SP.2)
- Compare two data sets using their centers and spreads (7.SP.3, 7.SP.4)
- Understand probability as a number from 0 to 1 and compare predicted and observed results (7.SP.5-7.SP.7)
- Find probabilities of compound events with lists, tables and tree diagrams (7.SP.8)
What 7th Grade Math Problems Look Like
Original practice problems written to match the standards above, with the answer and the thinking we would hope to hear.
Percent change (7.RP.3)
A jacket costs $60. It is on sale for 25% off, and then 8% sales tax is added. What is the final price?
Answer: $48.60. 25% off $60 is $45, and $45 × 1.08 = $48.60.
Negative numbers (7.NS.1)
At 6 a.m. the temperature was -7°F. By noon it was 12°F. How many degrees did it rise?
Answer: 19 degrees. 12 - (-7) = 12 + 7 = 19.
Two-step inequality (7.EE.4b)
You are paid $50 a week plus $3 per sale. You want to earn more than $100 this week. How many sales do you need?
Answer: 50 + 3s > 100, so 3s > 50 and s > 16 2/3. You need at least 17 sales.
Circles (7.G.4)
A circular garden has a diameter of 10 feet. About how much fencing goes around it? Use 3.14 for pi.
Answer: About 31.4 feet, because circumference = pi × diameter = 3.14 × 10.
Compound probability (7.SP.8)
You flip a coin and roll a number cube. What is the probability of heads and a 6?
Answer: 1/12. There are 2 × 6 = 12 equally likely outcomes and only one is heads-6.
Signs Your 7th Grader May Be Behind in Math
Seventh grade is where arithmetic turns into algebra. These signs suggest your child needs support now rather than in 8th grade:
- !Gets -3 - (-5) wrong by guessing at sign rules, and cannot show it on a number line
- !Takes 25% off and then adds 25% back and expects the original price
- !Solves 3x + 5 = 20 by trial and error only, or subtracts 5 from one side and not the other
- !Cannot tell from a table whether two quantities are proportional
- !Mixes up the area and circumference formulas for a circle
Short At-Home Activities (10 Minutes or Less)
Sale-price challenge
In a store or online, ask for the final price after a discount and tax. Then ask whether 20% off and then another 10% off is the same as 30% off. (It is not.)
Debt and deposit
Use a pretend bank balance. Owing $15 is -15; paying off $15 brings it to 0. This makes adding opposites concrete.
Balance-scale equations
Write 2x + 3 = 11 and talk about it as a balance: whatever you do to one side, you do to the other. Ask your child to say each step out loud.
Measure round things
Measure the distance around and across a plate, a can and a bike wheel, then divide. Every answer lands near 3.14.
Two-dice table
Make a 6 by 6 table of sums of two dice and ask for the probability of rolling a 7. Then roll 50 times and compare.
Find Your Child's Exact Level
Seventh grade is the bridge from arithmetic to algebra. Our diagnostic checks proportions, negative numbers and equations, plus the 6th grade skills underneath, in about 10 minutes.
Start the DiagnosticQuestions Parents Ask
What is the hardest part of 7th grade math?
For most students, it is negative numbers combined with equations. Seventh graders add, subtract, multiply and divide signed numbers (7.NS.1, 7.NS.2) and then use them in two-step equations and inequalities (7.EE.4). A shaky grasp of either one shows up in both.
Is 7th grade math pre-algebra?
Much of it is. Seventh graders combine like terms, expand and factor expressions, and solve two-step equations and inequalities (7.EE). Eighth grade then adds linear functions and systems of equations.
How do I help my 7th grader with percents?
Practice with real prices. The standard lists simple interest, tax, markups and markdowns, tips, commissions, fees, percent increase and decrease and percent error (7.RP.3). Have your child explain why multiplying by 0.75 is the same as taking 25% off.
My 7th grader memorized the sign rules but still makes mistakes. Why?
Rules without meaning are easy to mix up. Go back to the number line: adding a negative moves left, subtracting a negative moves right. The standard asks students to explain these rules, not just recite them (7.NS.1, 7.NS.2).
What probability do 7th graders learn?
They learn that probability is a number from 0 to 1, compare predicted probabilities with results from experiments, and find probabilities of compound events with organized lists, tables and tree diagrams (7.SP.5-7.SP.8).