6th Grade Math · Parent guide
What Math Should a 6th Grader Know?
Complete Parent Guide
By the end of 6th grade, your child should use ratios and unit rates to solve problems (including percents and unit prices), divide fractions by fractions, work with negative numbers on number lines and all four quadrants of a coordinate plane, write and evaluate expressions with variables, solve one-step equations like 3x = 18, find the area of triangles and the surface area of boxes, and describe data with mean, median and spread. The Common Core names four focus areas for grade 6: ratios and rates, division of fractions and negative numbers, expressions and equations, and statistical thinking.
Reviewed against the Common Core standards.
What 6th Graders Learn in Math, by Domain
These are the Common Core State Standards for Grade 6 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 6 introduction.
Ratios & Proportional Relationships
Common Core 6.RP- Describe ratios in words, such as "for every 2 wings there is 1 beak" (6.RP.1)
- Find unit rates: $75 for 15 hamburgers is $5 per hamburger (6.RP.2)
- Use tables, tape diagrams and double number lines to solve ratio problems (6.RP.3)
- Find a percent of a number and find the whole from a part and a percent (6.RP.3c)
- Convert units using ratio reasoning (6.RP.3d)
The Number System
Common Core 6.NS- Divide fractions by fractions and explain why it works (6.NS.1)
- Divide multi-digit numbers and compute with multi-digit decimals fluently (6.NS.2, 6.NS.3)
- Find the greatest common factor and least common multiple (6.NS.4)
- Use negative numbers for temperatures, elevation and debts, and place them on number lines (6.NS.5, 6.NS.6)
- Understand absolute value as distance from 0, and graph points in all four quadrants (6.NS.7, 6.NS.8)
Expressions & Equations
Common Core 6.EE- Write and evaluate expressions with exponents and with variables, following order of operations (6.EE.1, 6.EE.2)
- Use the distributive property to write equivalent expressions, such as 3(2 + x) = 6 + 3x (6.EE.3)
- Solve one-step equations like x + 7 = 15 and 4x = 28 (6.EE.7)
- Write inequalities like x > 3 and show their solutions on a number line (6.EE.8)
- Describe how one quantity depends on another with an equation like d = 65t (6.EE.9)
Geometry
Common Core 6.G- Find the area of triangles, special quadrilaterals and polygons by splitting them into rectangles and triangles (6.G.1)
- Find the volume of boxes with fractional edge lengths (6.G.2)
- Use nets to find surface area (6.G.4)
Statistics & Probability
Common Core 6.SP- Recognize a statistical question, one with variability in the answers (6.SP.1)
- Display data in dot plots, histograms and box plots (6.SP.4)
- Summarize data with mean or median and with interquartile range or mean absolute deviation (6.SP.5)
What 6th 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.
Unit rate (6.RP.3b)
It took 7 hours to mow 4 lawns. At that rate, how many lawns can be mowed in 35 hours?
Answer: 20 lawns. 35 hours is 5 times 7 hours, so 5 × 4 = 20.
Dividing fractions (6.NS.1)
How many 3/4-cup servings are in 2 1/4 cups of yogurt?
Answer: 3 servings. 2 1/4 = 9/4, and 9/4 ÷ 3/4 = 3. Your child should be able to draw it: three 3/4 pieces fit in 9/4.
One-step equation (6.EE.7)
Movie tickets cost $9 each. The total was $63. Write and solve an equation for the number of tickets.
Answer: 9t = 63, so t = 7 tickets.
Percent (6.RP.3c)
30% of the students in a club are in 6th grade. There are 12 sixth graders. How many students are in the club?
Answer: 40. If 30% is 12, then 10% is 4, and 100% is 40.
Mean and median (6.SP.5)
Five quiz scores: 6, 8, 8, 9, 19. Find the mean and median. Which better describes a typical score?
Answer: Mean 10, median 8. The median, because the 19 pulls the mean above four of the five scores.
Signs Your 6th Grader May Be Behind in Math
Sixth grade introduces ideas that 7th and 8th grade use every day. These signs mean a gap is forming:
- !Treats ratios as subtraction: thinks 2:3 and 4:5 are the same because each "goes up by 1"
- !Uses "keep, change, flip" for 2/3 ÷ 3/4 but cannot say whether the answer should be more or less than 1
- !Thinks -8 is greater than -3
- !Sees 3x as "3 and x" or cannot find x in 4x = 28 without guessing
- !Can compute a mean but cannot say what it tells you about the data
Short At-Home Activities (10 Minutes or Less)
Unit prices at the store
Compare two sizes of the same cereal: $4.20 for 12 oz or $5.60 for 20 oz. Which is the better deal per ounce? That is a 6th grade unit rate problem.
Recipe scaling
A recipe for 4 people needs 3 eggs. How many for 10 people? Let your child use a table: 4 → 3, 8 → 6, 2 → 1.5, so 10 → 7.5.
Temperature line
Check the weather in a cold city. If it is -5° and rises 12°, what is it now? A vertical number line, like a thermometer, makes negatives make sense.
Mystery number
"I am thinking of a number. Four times it is 36." Then write it as 4x = 36 together. This turns equations into a puzzle instead of a procedure.
Track something for a week
Record bedtime or minutes of screen time for a week, then find the mean, the median and the range together.
Find Your Child's Exact Level
Sixth grade is where ratios, negatives and equations begin. Our diagnostic checks these and the 5th grade fraction skills underneath them, and shows you exactly what needs work, in about 10 minutes.
Start the DiagnosticQuestions Parents Ask
What are the hardest topics in 6th grade math?
Ratios and dividing fractions are the two that most often need extra time. Ratio reasoning is the first focus area the Common Core names for grade 6, and it carries straight into 7th grade proportions and percents.
Is 6th grade math pre-algebra?
Partly. Sixth graders write and evaluate expressions with variables, use the distributive property, solve one-step equations and write simple inequalities (6.EE). Two-step equations come in 7th grade and systems of equations in 8th.
When do kids learn negative numbers?
In 6th grade. They place negative numbers on number lines, compare them, find absolute value and graph points in all four quadrants (6.NS.5-6.NS.8). Adding, subtracting, multiplying and dividing negatives is a 7th grade standard.
My 6th grader struggles with fractions from 5th grade. What should we do first?
Fix the fractions first. Dividing fractions, ratios and percents all lean on fraction sense. Spend a few weeks on equivalent fractions and adding fractions with unlike denominators before pushing on 6th grade work.
What statistics do 6th graders learn?
How to describe a set of data: its center (mean and median), its spread (interquartile range and mean absolute deviation) and its shape, using dot plots, histograms and box plots (6.SP).