6th grade math: what your child learns this year

Math for 6th graders moves from arithmetic toward algebra. Your child learns to reason with ratios and unit rates, to divide fractions by fractions and to work with negative numbers. Variables, letters that stand for numbers, appear in expressions and in one-step equations. Area, volume and statistics fill the rest of the year. A child who finishes 6th grade solid in ratios, expressions and equations starts 7th grade ready.

The one-minute check

Before the checklist, try this

Ask your child how many quarter-cup scoops of flour make 3 cups. No calculator, and ask for the reason behind the answer.

If they get it

Your child says 12, because each cup takes 4 quarter-cup scoops and 3 × 4 = 12. That means division by a fraction makes sense from 5th grade, and 6th grade has something to build on.

If they do not

Your child says 3/4 or 1/12, or cannot decide whether to multiply or divide. That is the gap, and it comes from 5th grade.

Sixth grade divides fractions by fractions, in recipes, in measurements and in equations. All of it needs the idea that dividing by a number less than 1 gives a bigger answer. A child who expects division to always make a number smaller will choose the wrong operation, even with every step memorized.

The 6th grade skills checklist

Read each line as "my child can…". Confident checks are strengths; hesitations are where to look closer.

Not every topic weighs the same. Ratios, dividing fractions, negative numbers, expressions and equations are where most of 6th grade goes, and most state test questions come from them. Area, volume, statistics and long division are real topics, but a smaller share of the year.

Where most of the year goes

Ratios and unit rates

A ratio compares two amounts, such as 3 red marbles for every 5 blue ones. Ratios open the year, and your child uses them and unit rates (the amount for one) to solve real problems.

Describes a ratio in words and finds a unit rate, such as the price of one notebook when 4 cost $10
Uses tables of equivalent ratios, tape diagrams and double number lines to solve problems
Finds a percent of a number, such as 25% of 60, and the whole from a part and a percent
Converts measurement units with ratios, such as inches to feet

Comes from last year: Fifth grade had to make multiplication and division quick. If the facts are still slow, every ratio table turns into a struggle.

6.RP.1 · 6.RP.2 · 6.RP.3

Dividing fractions

Your child divides a fraction by a fraction, such as how many 1/6-pound bags 2/3 of a pound of trail mix fills, and explains the answer with a drawing or a number line.

Divides a fraction by a fraction and checks the answer by multiplying
Writes a division to match a word problem, with the two amounts in the right order
Knows that dividing by a fraction less than 1 gives an answer bigger than the starting number

Comes from last year: Fifth grade divided whole numbers by unit fractions (fractions with 1 on top), such as 4 ÷ 1/5 = 20. A child who only memorized "flip and multiply" without that picture cannot tell when an answer makes sense.

6.NS.1

Negative numbers and the coordinate grid

Numbers below zero arrive, for temperatures, debts and depths below sea level. Your child places them on a number line and plots points in all four quadrants (the four sections) of the coordinate grid.

Uses negative numbers for real situations and says what 0 means in each one
Orders numbers such as -3, 2 and -7, and knows that absolute value is the distance from 0
Plots points in all four quadrants of the coordinate grid
Finds the distance between two points such as (2, 5) and (2, -3)

Comes from last year: Fifth grade plotted points only where both numbers are positive. A child who mixes up which number goes across and which goes up will misplace every point once negatives appear.

6.NS.5 · 6.NS.6 · 6.NS.7 · 6.NS.8

Expressions and exponents

An expression is a math phrase with no equals sign, such as 3x + 2. Your child writes expressions from words, finds their value and rewrites them in equivalent forms (forms that look different but always have the same value).

Evaluates expressions with exponents, such as 2⁴ = 16
Writes an expression from words, such as "5 less than y" as y - 5
Finds the value of a formula, such as A = 6s² when s = 3
Rewrites 3(x + 2) as the equivalent expression 3x + 6, and y + y + y as 3y

Comes from last year: Fifth grade wrote expressions with parentheses, such as 2 × (8 + 7), and used powers of 10 like 10³. A child who ignores the parentheses will get most expressions here wrong.

6.EE.1 · 6.EE.2 · 6.EE.3 · 6.EE.4

Equations and inequalities

An equation says two amounts are equal, such as x + 7 = 15. Your child solves one-step equations, writes simple inequalities and studies two quantities that change together.

Checks whether a number makes an equation true by putting it in place of the letter
Solves one-step equations such as x + 4.5 = 10 and 3x = 24
Writes an inequality such as h > 48 for "taller than 48 inches" and shows its solutions on a number line
Writes an equation such as d = 50t for two quantities that change together, and connects it to a table and a graph

Comes from last year: Fifth grade graphed pairs of numbers made from two patterns, the first look at two quantities that change together. Fraction and decimal arithmetic also has to be reliable, because 6th grade equations use both.

6.EE.5 · 6.EE.6 · 6.EE.7 · 6.EE.8 · 6.EE.9

Also covered, smaller share of the year

Area, surface area and volume

Your child finds the area of triangles and other shapes by splitting them into simpler pieces. Volume uses fraction side lengths, and surface area comes from nets (flat patterns that fold into a solid).

Finds the area of triangles, parallelograms and trapezoids, using a height that meets the base at a right angle
Finds the volume of a box with fraction side lengths
Uses a net to find the surface area of a box or a pyramid
Draws a shape on the coordinate grid from its corner points and finds the length of a side

Comes from last year: Fifth grade found the volume of a box with whole-number sides and the area of a rectangle with fraction sides. Sixth grade combines the two, so both have to be secure.

6.G.1 · 6.G.2 · 6.G.3 · 6.G.4

Long division, decimals and factors

Long division and decimal arithmetic with the standard method, which should be quick and accurate by the end of the year, plus common factors and multiples.

Divides multi-digit numbers with long division, such as 7,452 ÷ 18
Adds, subtracts, multiplies and divides decimals, such as 4.8 ÷ 0.16
Finds the greatest common factor and the least common multiple of two numbers, and rewrites 24 + 30 as 6(4 + 5)

Comes from last year: Fifth grade divided by two-digit numbers and worked with decimals to hundredths, often with drawings. A child who still needs a drawing for every step will be slow here.

6.NS.2 · 6.NS.3 · 6.NS.4

Statistics and data displays

A statistical question expects many different answers, such as "How tall are the students in my class?" Your child describes data by its center and by how spread out it is.

Tells a statistical question from a question with only one answer
Makes and reads dot plots, histograms and box plots
Finds the mean and the median, and describes spread with the interquartile range (the spread of the middle half)

Comes from last year: Most of this is new. Fifth grade line plots are the direct link, and a child who misreads them will misread dot plots too.

6.SP.1 · 6.SP.2 · 6.SP.3 · 6.SP.4 · 6.SP.5

All 29 6th grade math standards, in plain English

These are the Common Core standards for 6th grade math. Each link opens a page that explains the topic in simple words, with examples, the usual sticking points and four practice questions.

Statistics and Probability

What schools teach in 6th grade math, at a glance

Area	What schools teach	Share of the year
Ratios and unit rates	A ratio compares two amounts, such as 3 red marbles for every 5 blue ones. Ratios open the year, and your child uses them and unit rates (the amount for one) to solve real problems.	Major
Dividing fractions	Your child divides a fraction by a fraction, such as how many 1/6-pound bags 2/3 of a pound of trail mix fills, and explains the answer with a drawing or a number line.	Major
Negative numbers and the coordinate grid	Numbers below zero arrive, for temperatures, debts and depths below sea level. Your child places them on a number line and plots points in all four quadrants (the four sections) of the coordinate grid.	Major
Expressions and exponents	An expression is a math phrase with no equals sign, such as 3x + 2. Your child writes expressions from words, finds their value and rewrites them in equivalent forms (forms that look different but always have the same value).	Major
Equations and inequalities	An equation says two amounts are equal, such as x + 7 = 15. Your child solves one-step equations, writes simple inequalities and studies two quantities that change together.	Major
Area, surface area and volume	Your child finds the area of triangles and other shapes by splitting them into simpler pieces. Volume uses fraction side lengths, and surface area comes from nets (flat patterns that fold into a solid).	Smaller
Long division, decimals and factors	Long division and decimal arithmetic with the standard method, which should be quick and accurate by the end of the year, plus common factors and multiples.	Smaller
Statistics and data displays	A statistical question expects many different answers, such as "How tall are the students in my class?" Your child describes data by its center and by how spread out it is.	Smaller

What 6th grade math actually looks like

Five real problems from our 6th grade bank. Work through them with your child, check each answer, and see the steps for any problem.

Problem 1
Maya evaluated the expression. Her work is shown below.
Original
$\displaystyle 3^2 + 2^3 \times 4$
Step 1
$\displaystyle = 6 + 8 \times 4$
Step 2
$\displaystyle = 6 + 32$
Step 3
$\displaystyle = 38$
Select the statement that correctly describes Maya's work.
A
There is no mistake in the work.
B
The student treated $3^{2}$ as $3 \times 2$ .
C
The student treated $2^{3}$ as $2 \times 3$ .
D
The first mistake is multiplying $8$ by $4$ before adding $6$ .
Show the answer and how to get it
The correct statement is that the student treated $3^{2}$ as $3 \times 2$ . The correct value of the expression is $41$ .
1. Check each line from top to bottom, starting with Step 1.
2. In Step 1, $3^{2}$ was replaced with $6$ and $2^{3}$ was replaced with $8$ . Checking both: $2^{3} = 8$ is correct, but $3^{2} = 9$ , not $6$ . The first mistake is right here in Step 1.
3. With the correct value for $3^{2}$ , the expression evaluates to $41$ .
Problem 2
Look at the parallelogram below. One side is marked as the base.
Select the letter of the segment that shows the matching height.
A
A
B
B
C
C
Show the answer and how to get it
The matching height is the lettered segment with the right-angle marker at the base: it is perpendicular to the marked base and connects the opposite parallel side to the base.
1. Start with the side labeled base.
2. A matching height must be perpendicular to the base and connect the opposite parallel side to the base. Look for the lettered segment that has the right-angle marker where it meets the base.
3. One lettered segment is a slanted side of the parallelogram — it touches the base but is not perpendicular to it. Another lettered segment is a diagonal from one corner to the opposite corner — it is also not perpendicular to the base. Only the segment with the right-angle marker at the base is perpendicular to the marked base, so that is the matching height.

Problem 3

Look at Aisha's work for the fraction-division problem below.

	$\displaystyle \frac{2}{9} \div \frac{5}{6}$
Step 1	$\displaystyle = \frac{2}{9} \times \frac{5}{6}$
Step 2	$\displaystyle = \frac{10}{54}$
Step 3	$\displaystyle = \frac{5}{27}$

Select the statement that best describes Aisha's work.

The work is correct.

The divisor was not changed to its reciprocal.

The reciprocal step is correct, but the later arithmetic is wrong.

The dividend was flipped instead of the divisor.

Show the answer and how to get it

The divisor $\frac{5}{6}$ was kept unchanged instead of being flipped to $\frac{6}{5}$ , so the correct category is 'The divisor was not changed to its reciprocal.'

Start by checking the multiplication step. When dividing by $\frac{5}{6}$ , you should multiply by the reciprocal of $\frac{5}{6}$ , which is $\frac{6}{5}$ .
Aisha wrote $\frac{2}{9} \times \frac{5}{6}$ instead of $\frac{2}{9} \times \frac{6}{5}$ . The divisor $\frac{5}{6}$ was never changed to its reciprocal.
Because the divisor was not flipped, the entire chain of work is built on a wrong setup. Even though $\frac{10}{54}$ correctly reduces to $\frac{5}{27}$ , the setup itself is wrong. The correct statement is that the divisor was not changed to its reciprocal.

Problem 4
Look at the table of fruit by type.
Type Count
Apple 5
Orange 4
Grape 6
Select all descriptions that compare one part to the whole set.
A
orange to apple
B
apple to all the fruit
C
apple to orange
D
grape to apple and orange
E
grape to the whole set
Show the answer and how to get it
The correct choices are apple to all the fruit and grape to the whole set because each compares one type with the entire set of 15 pieces of fruit.
1. First find the whole set by adding the counts in the table.
2. A part-to-whole description names one type and all 15 pieces of fruit. The phrases "all the fruit" and "the whole set" both mean the entire collection.
3. So apple to all the fruit and grape to the whole set are part-to-whole descriptions.
4. The other choices are not correct because they compare one type to another type or to only some of the types, not to the entire set.
Problem 5
Students in one class were asked, "Which pet would you most like to have?" The bar graph shows the class results.
Select the statement that best describes the graph and shows that students had different answers.
A
Cat was chosen more than any other pet, and students had different answers.
B
Dog was chosen more than any other pet, and students had different answers.
C
The answer is Dog.
D
The answer is 9 students.
E
Everyone chose Dog.
Show the answer and how to get it
The correct statement is the one that names Dog as the most-chosen pet AND notes that students had different answers: Dog has the highest bar at 9, and the Cat, Fish, and Bird bars are not 0, so the class did not all choose the same pet.
1. Look at the bar graph. The Dog bar reaches 9 and the Cat bar reaches 8. Those two bars are very close, so read carefully — Dog's bar is one unit taller than Cat's.
2. The Fish bar is at 5 and the Bird bar is at 4. Neither bar is 0, which shows that students did not all give the same answer.
3. The correct statement must name Dog as the most-chosen pet AND note that students had different answers. The statement that says 'Dog was chosen more than any other pet, and students had different answers' is the only one that does both.

Type	Count
Apple	5
Orange	4
Grape	6

Where 6th grade math usually goes wrong

These are not careless mistakes. Each one is a rule that worked perfectly well until this year, applied consistently to a place where it no longer holds, which is why the same wrong answer keeps coming back. Recognising the specific rule is far more useful than more practice.

Says 2³ is 6.
The small 3 is read as "times 3". Writing it out as 2 × 2 × 2 = 8 shows that an exponent counts how many times the number is multiplied by itself.
Says -8 is greater than -2, because 8 is greater than 2.
The sign is ignored and only the digits are compared. On a number line -8 sits further left, and a temperature of -8 degrees is colder than -2 degrees.
Scales up a recipe of 2 cups of flour to 3 cups of milk as 4 cups to 5 cups.
Earlier grades made adding the usual way to grow an amount. In a ratio, both parts are multiplied by the same number, so 2 to 3 becomes 4 to 6.
Works out 1/2 ÷ 1/4 as 1/8.
Division is read as "make it smaller", so an answer bigger than both fractions looks wrong. Asking how many quarters fit in a half shows that the answer is 2.

Roughly when each part comes up

Schools vary, but most 6th grade classrooms move in about this order. Useful if you are trying to work out whether something is genuinely behind or simply has not been taught yet.

September to OctoberRatios, rates, unit rates and percents
October to DecemberDividing fractions; long division, decimal arithmetic, factors and multiples
December to JanuaryNegative numbers, absolute value and the four-quadrant coordinate grid
January to FebruaryExponents, expressions and equivalent expressions
February to MarchOne-step equations and inequalities
March to AprilTwo quantities that change together; area, surface area and volume
April to JuneStatistical questions, center and spread, dot plots, histograms and box plots

What 7th grade assumes on day one

Next year does not re-teach these. It starts from them, which is why a gap left open over the summer tends to show up in October rather than in June.

Ratios and unit rates, which grow into proportional relationships and percent problems
Negative numbers on the number line, before adding, subtracting, multiplying and dividing them
Writing and rewriting expressions, including the distributive property
One-step equations, which become two-step equations such as 3x + 5 = 20

6th Grade math resources

Free 6th grade math quick check

Ten questions on the year’s main topics, about 10 to 15 minutes, with a worked solution for every one. Take it online or print it with the answer key.

Start the quick check →

Not sure which grade fits?

Pick the quick check for any grade, kindergarten to 8th.

Grade-by-grade readiness check

What should be solid before next September, K through 8.

Common questions

What do 6th graders learn in math?

Ratios and unit rates, dividing fractions, negative numbers and the coordinate grid, expressions with exponents and variables, one-step equations and inequalities, area, surface area and volume, and statistics. Ratios, expressions and equations carry the most weight.

Is 6th grade math pre-algebra?

Not by name, but it is where algebra starts. Your child uses letters for unknown numbers, rewrites expressions such as 4(x + 5) as 4x + 20 and solves one-step equations such as x + 9 = 14. Seventh and 8th grade build the rest of what Algebra 1 needs.

How can I check if my child is on track in 6th grade math?

Start with the one-minute scoop check on this page. For a broader read, try the free 10-question quick check. The Level Up assessment, about 30 to 40 questions on a computer or tablet, adapts to each answer and shows where your child stands, including gaps from earlier grades.