2nd grade math: what your child learns this year

Q: What do 2nd graders learn in math?

Place value to 1,000, addition and subtraction facts within 20, adding and subtracting within 100 and then 1,000, word problems, measuring length, time, money, graphs, odd and even numbers, arrays and shapes. Place value and adding and subtracting carry the most weight.

Q: Do 2nd graders need to know math facts by heart?

For addition, yes. By the end of 2nd grade, the Common Core expects children to know every sum of two one-digit numbers from memory, such as 8 + 7 = 15. Subtraction within 20 should be quick too, often by thinking of the matching sum: 15 - 8 = 7 because 8 + 7 = 15.

Q: How can I check if my child is on track in 2nd grade math?

Start with the one-minute "10 more, 10 less" 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. It is included in the free trial.

Math for 2nd graders is about numbers up to 1,000 and adding and subtracting them. Your child learns what the hundreds, tens and ones digits mean, adds and subtracts within 100 quickly and works up to 1,000 with blocks and drawings. Measuring length with a ruler is the other big topic. Time, money, graphs and shapes fill out the year. A child who finishes 2nd grade solid in place value and addition facts starts 3rd grade ready for multiplication.

The one-minute check

Before the checklist, try this

Ask your child, without paper or counters: "What is 10 more than 47? What is 10 less than 47?"

If they get it

Your child says 57 and 37 within a few seconds, without counting. That means tens and ones from 1st grade are solid, and 2nd grade has something to build on.

If they do not

Your child counts 48, 49, 50 and on, one number at a time, or answers 48 and 46. That is the gap, and it comes from 1st grade.

Most of 2nd grade is built on tens and ones: three-digit numbers, adding and subtracting within 1,000 and finding 10 or 100 more in one step. A child who counts by ones gets slow and loses track as the numbers grow, even when each new idea makes sense.

The 2nd 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. Place value, adding and subtracting, word problems and measuring length are where most of 2nd grade goes, and they are what 3rd grade builds on. Time, money, graphs, odd and even numbers and shapes are real topics, but a smaller share of the year.

Where most of the year goes

Place value to 1,000

The center of 2nd grade. Your child learns that the digits of a number like 706 mean 7 hundreds, 0 tens and 6 ones, and that 100 is a bundle of ten tens.

Says what each digit of a three-digit number is worth: in 482, the 4 is worth 400
Knows that 100 is ten tens, and that 300 is 3 hundreds with no tens and no ones
Counts to 1,000 and skip-counts by 5s, 10s and 100s
Reads and writes numbers to 1,000 in digits, in words and in expanded form (400 + 80 + 2)
Compares two three-digit numbers and records the result with >, = or <

Comes from last year: First grade taught that a two-digit number is tens and ones, and that 10 is a bundle of ten ones. A child who still sees 47 as "a 4 and a 7" has nothing to build hundreds on.

2.NBT.1 · 2.NBT.2 · 2.NBT.3 · 2.NBT.4

Adding and subtracting to 1,000

Your child adds and subtracts two-digit numbers quickly, then moves to three-digit numbers with blocks and drawings. This is where regrouping comes in: trading 10 ones for a ten, or a ten for 10 ones.

Adds and subtracts within 100 quickly and accurately, such as 38 + 47 = 85 and 64 - 29 = 35
Adds up to four two-digit numbers, such as 23 + 15 + 31 + 12
Adds and subtracts within 1,000 with blocks, drawings or place value, trading tens and hundreds when needed
Finds 10 more, 10 less, 100 more or 100 less than a number such as 456 without counting
Explains why a method works, using hundreds, tens and ones

Comes from last year: First grade added a two-digit number to a one-digit number or to a multiple of 10, such as 34 + 20. A child who still counts by ones to add 34 + 20 will find 2nd grade numbers too big to count.

2.NBT.5 · 2.NBT.6 · 2.NBT.7 · 2.NBT.8 · 2.NBT.9

Addition and subtraction facts

By the end of 2nd grade, your child should know every sum of two one-digit numbers by heart, such as 8 + 7 = 15, and subtract within 20 quickly.

Knows all sums of two one-digit numbers from memory, from 0 + 0 to 9 + 9
Subtracts within 20 quickly by thinking of the matching sum: 15 - 7 = 8 because 7 + 8 = 15
Uses a strategy such as making ten when a fact is slow: 8 + 5 = 8 + 2 + 3 = 13

Comes from last year: First grade made facts within 10 quick and taught strategies for facts up to 20. A child who still counts on fingers for 6 + 3 needs those first.

2.OA.2

Word problems

Story problems with adding and subtracting within 100, in one or two steps. The missing number can be the start, the change or the end. A missing start is the hardest kind.

Solves problems about adding to, taking away, putting together, taking apart and comparing
Solves problems where the start is missing: some birds were on a tree, 6 flew away and 9 are left (15 at the start)
Solves two-step problems: 25 marbles, 10 more from a friend, then 8 lost (27 left)
Writes an equation with a box or a question mark for the missing number, such as 9 + ? = 15

Comes from last year: First grade solved the same kinds of story problems within 20. A child who adds the two numbers in every story, whatever the story says, has learned to hunt for numbers instead of reading.

2.OA.1

Measuring length

Your child measures with a ruler, a yardstick, a meter stick and a measuring tape, in inches, feet, centimeters and meters, and solves story problems about length.

Measures an object with a ruler, starting at the 0 mark
Measures the same object in inches and in centimeters, and explains why the number of centimeters is bigger
Estimates lengths in inches, feet, centimeters and meters
Finds how much longer one object is than another
Shows sums and differences within 100 as jumps on a number line

Comes from last year: First grade measured by laying paper clips or cubes end to end, with no gaps and no overlaps. A child who skipped that step reads a ruler as a list of numbers, not as a row of equal units.

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

Also covered, smaller share of the year

Time and money

Your child tells time to the nearest five minutes and uses a.m. and p.m. Money comes in too, with story problems about bills and coins.

Reads analog and digital clocks to the nearest five minutes
Knows when a time is a.m. and when it is p.m.
Counts a mix of dollar bills, quarters, dimes, nickels and pennies
Solves money story problems and writes amounts with $ and ¢, such as 3 dimes and 4 pennies = 34¢

Comes from last year: First grade told time to the hour and half hour. Money is new in 2nd grade, and it leans on skip-counting by 5s and 10s from earlier in the year.

2.MD.7 · 2.MD.8

Graphs and line plots

Picture graphs and bar graphs with up to four categories, plus line plots of lengths your child has measured.

Draws a picture graph and a bar graph from a small set of data
Answers questions from a bar graph, such as how many more children chose red than blue
Measures several objects and shows the lengths on a line plot

Comes from last year: First grade sorted data into up to three categories and asked "how many more?" Comparing two bars is a subtraction problem, so slow subtraction slows graphs too.

2.MD.9 · 2.MD.10

Odd, even and equal groups

The first steps toward multiplication. Your child sorts groups of up to 20 objects into odd and even, and counts objects set out in rows and columns.

Tells whether a group of up to 20 objects is odd or even, by pairing them or counting by 2s
Writes an even number as a double, such as 14 = 7 + 7
Finds the total in an array of up to 5 rows and 5 columns by adding: 3 rows of 4 is 4 + 4 + 4 = 12

Comes from last year: First grade facts include doubles such as 6 + 6 and 7 + 7. An even number is a double, so a child who knows doubles already has the idea.

2.OA.3 · 2.OA.4

Shapes and equal shares

Your child names and draws shapes by their sides and corners, splits a rectangle into rows of equal squares and cuts shapes into halves, thirds and fourths.

Names triangles, quadrilaterals, pentagons, hexagons and cubes, and draws a shape from a clue such as "5 sides"
Splits a rectangle into rows and columns of same-size squares and counts them
Cuts circles and rectangles into 2, 3 or 4 equal shares and calls them halves, thirds or fourths
Knows that equal shares of the same shape can look different

Comes from last year: First grade cut circles and rectangles into halves and fourths. Thirds are new this year, and so is the idea that two halves can have different shapes.

2.G.1 · 2.G.2 · 2.G.3

All 26 2nd grade math standards, in plain English

These are the Common Core standards for 2nd grade math. Each link opens a page that explains the topic in simple words, with examples, the usual sticking points and four practice questions.

Geometry

Measurement and Data

2.MD.A.1 Measuring with a Ruler
2.MD.A.2 Measuring
2.MD.A.3 Estimating Length
2.MD.A.4 Comparing Lengths
2.MD.B.5 Adding Lengths
2.MD.B.6 Addition on a Number Line
2.MD.C.7 Telling Time
2.MD.C.8 Counting Money
2.MD.D.9 Line Plots
2.MD.D.10 Bar Graphs

Number and Operations in Base Ten

Operations and Algebraic Thinking

2.OA.A.1 Addition and Subtraction Word Problems
2.OA.B.2 Addition Facts
2.OA.C.3 Odd and Even Numbers
2.OA.C.4 Repeated Addition

What schools teach in 2nd grade math, at a glance

Area	What schools teach	Share of the year
Place value to 1,000	The center of 2nd grade. Your child learns that the digits of a number like 706 mean 7 hundreds, 0 tens and 6 ones, and that 100 is a bundle of ten tens.	Major
Adding and subtracting to 1,000	Your child adds and subtracts two-digit numbers quickly, then moves to three-digit numbers with blocks and drawings. This is where regrouping comes in: trading 10 ones for a ten, or a ten for 10 ones.	Major
Addition and subtraction facts	By the end of 2nd grade, your child should know every sum of two one-digit numbers by heart, such as 8 + 7 = 15, and subtract within 20 quickly.	Major
Word problems	Story problems with adding and subtracting within 100, in one or two steps. The missing number can be the start, the change or the end. A missing start is the hardest kind.	Major
Measuring length	Your child measures with a ruler, a yardstick, a meter stick and a measuring tape, in inches, feet, centimeters and meters, and solves story problems about length.	Major
Time and money	Your child tells time to the nearest five minutes and uses a.m. and p.m. Money comes in too, with story problems about bills and coins.	Smaller
Graphs and line plots	Picture graphs and bar graphs with up to four categories, plus line plots of lengths your child has measured.	Smaller
Odd, even and equal groups	The first steps toward multiplication. Your child sorts groups of up to 20 objects into odd and even, and counts objects set out in rows and columns.	Smaller
Shapes and equal shares	Your child names and draws shapes by their sides and corners, splits a rectangle into rows of equal squares and cuts shapes into halves, thirds and fourths.	Smaller

What 2nd grade math actually looks like

Five real problems from our 2nd grade bank. Work through them with your child, check each answer, and see the steps for any problem.

Problem 1
What is the name of the polygon below?
A
Triangle
B
Pentagon
C
Quadrilateral
D
Hexagon
Show the answer and how to get it
The polygon has 4 sides, so it is a quadrilateral.
1. Look at the polygon. Count its sides one by one.
2. This polygon has 4 sides.
3. A polygon with 4 sides is called a quadrilateral. So the answer is Quadrilateral.
Problem 2
Maya says the park bench is 2 meters. Look at the meter stick to check her answer.
Select the statement that best describes Maya's answer.
A
Maya's answer is correct.
B
The park bench is one meter longer than Maya says.
C
The park bench is one meter shorter than Maya says.
D
The park bench is two meters longer than Maya's answer.
Show the answer and how to get it
The park bench is 1 meter long, and Maya said 2 meters. The correct statement is: "The park bench is one meter shorter than Maya says."
1. Look at the meter stick below. The left end of the park bench lines up with 0. Find the mark where the right end of the park bench lines up.
2. The right end of the park bench lines up with the 1 m mark. So the park bench is 1 meter long.
3. Maya said the park bench is 2 meters. The park bench is actually 1 meter — that is 1 meter shorter than what Maya said.
4. The correct statement is: "The park bench is one meter shorter than Maya says."
Problem 3
What number do the blocks show?
A
231
B
132
C
123
D
312
Show the answer and how to get it
The number is 132. The model shows 1 hundred (100), 3 tens (30), and 2 ones (2), and $100 + 30 + 2 = 132$ .
1. Look at the blocks. The big squares are hundreds, the rods are tens, and the small cubes are ones.
2. Count the hundreds flats. There is 1 flat, so that is 1 hundred, or 100.
3. Count the tens rods. There are 3 rods, so that is 3 tens, or 30.
4. Count the ones cubes. There are 2 cubes, so that is 2 ones, or 2.
5. Add the place values together:
Problem 4
Sam has 35 books, and Ava has 12 fewer than Sam. How many books does Ava have?
A
47
B
23
C
32
D
12
Show the answer and how to get it
Ava has 23 books. Subtract: $35 - 12 = 23$ .
1. Look at the tape diagram. Sam's row shows 35 books. Ava's row shows ? books, and the bracket tells us Ava has 12 fewer than Sam.
2. The word 'fewer' tells us Ava has less than Sam. Subtract 12 from 35 to find Ava's count.
3. Ava has 23 books.
Problem 5
How many squares are in this rectangle?
A
9
B
24
C
20
D
4
Show the answer and how to get it
There are 20 squares in the rectangle. You can find this by counting 4 squares in each row, for 5 rows: $4 + 4 + 4 + 4 + 4 = 20$ .
1. Look at the rectangle. It is split into rows and columns of same-size squares.
2. Count the rows. There are 5 rows. Each row has 4 squares.
3. Add 4 squares for each row: $4 + 4 + 4 + 4 + 4 = 20$ . Or skip-count by 4: 4, 8, 12, 16, 20. Or count all the squares one by one.

Where 2nd 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.

Writes "three hundred six" as 3006 or as 36.
The number is written the way it sounds: 300, then 6. The 0 in 306 shows that there are no tens. With three-digit numbers, a zero in the middle is easy to drop.
Works out 52 - 17 and gets 45.
In each column the smaller digit is taken from the bigger one (7 - 2 and 5 - 1). The 52 needs a ten broken into 10 ones first, which gives 12 - 7 = 5 ones and 35 in all.
Says a crayon is 7 inches long because it ends at the 7, when it starts at the 1.
The numbers on a ruler get read like counting numbers. Length is the number of spaces between the marks, so a crayon from 1 to 7 is 6 inches long.
Reads a clock with the minute hand on the 4 as 4 minutes past the hour.
The numbers on a clock face count hours. For minutes, each number stands for 5 more, so the 4 means 20 minutes past.

Roughly when each part comes up

Schools vary, but most 2nd 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 OctoberAddition and subtraction facts within 20; one-step word problems
October to NovemberPlace value: hundreds, tens and ones; counting, reading and comparing numbers to 1,000
November to FebruaryAdding and subtracting within 100, then within 1,000; two-step word problems
February to MarchMeasuring and estimating length; length problems on a number line
March to AprilOdd and even numbers; arrays
April to MayTime to five minutes and money; picture graphs, bar graphs and line plots
May to JuneShapes, rows of equal squares and equal shares

What 3rd 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.

Adding and subtracting within 1,000 quickly and accurately
Addition facts from memory, since 3rd grade adds multiplication and division facts on top
Equal groups and arrays as the starting point for multiplication
Halves, thirds and fourths, which become fractions on a number line

2nd Grade math resources

Free 2nd 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 2nd graders learn in math?

Place value to 1,000, addition and subtraction facts within 20, adding and subtracting within 100 and then 1,000, word problems, measuring length, time, money, graphs, odd and even numbers, arrays and shapes. Place value and adding and subtracting carry the most weight.

Do 2nd graders need to know math facts by heart?

For addition, yes. By the end of 2nd grade, the Common Core expects children to know every sum of two one-digit numbers from memory, such as 8 + 7 = 15. Subtraction within 20 should be quick too, often by thinking of the matching sum: 15 - 8 = 7 because 8 + 7 = 15.

How can I check if my child is on track in 2nd grade math?

Start with the one-minute "10 more, 10 less" 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. It is included in the free trial.