2nd Grade · 2.OA.C.4

Repeated addition in 2nd grade

Repeated addition means adding the same number again and again, such as $4 + 4 + 4 = 12$ . In 2nd grade, your child uses arrays and repeated addition to count objects set out in rows, up to 5 rows of up to 5.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

2.OA.C.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

What it means, in plain words

An array is a group of objects set out in straight rows and columns, with the same number in every row. A muffin pan with 3 rows of 4 cups is an array. So is a box of 10 crayons packed in 2 rows of 5.

To count an array, your child adds the number in one row once for every row. A number being added is called an addend. For 3 rows of 4 muffins, the addend is 4 and it is added 3 times: $4 + 4 + 4 = 12$ . Repeated addition in 2nd grade always looks like this, a sum of equal addends.

The same array can be counted by columns too. 3 rows of 4 also make 4 columns of 3, so $3 + 3 + 3 + 3 = 12$ . Seeing both sums give the same total gets your child ready for multiplication in 3rd grade.

Your child should be able to:

Describe an array as rows of the same number, such as 3 rows of 4
Find the total in an array with up to 5 rows and 5 columns by adding
Write a repeated addition equation that matches an array
Count the same array by rows and by columns and get the same total

Example

Chairs are set out in 5 rows with 3 chairs in each row. How many chairs are there?

Each row has 3 chairs, and there are 5 rows.
Add 3 once for each row: $3 + 3 + 3 + 3 + 3 = 15$ .
There are 15 chairs.

Example

An array of dots has 4 rows and 2 columns. Write one equation for the rows and one for the columns.

Each row has 2 dots, and there are 4 rows: $2 + 2 + 2 + 2 = 8$ .
Each column has 4 dots, and there are 2 columns: $4 + 4 = 8$ .
Both equations give the same total: the array has 8 dots.

Where children usually get stuck

For an array of 4 rows with 3 stars in each row, your child writes $4 + 3 = 7$ .
The child adds the two numbers that describe the array. In an array, one number says how many times to add the other, so the sum is $3 + 3 + 3 + 3 = 12$ .
What helps. Have your child touch each row and say how many it holds: 3, 3, 3, 3. Write down exactly what was said, with plus signs in between.
Your child counts every object in a 5 by 5 array one at a time and loses count partway.
Counting by ones ignores the rows. Every row holds the same number, so adding row by row is shorter and much harder to get wrong.
What helps. Skip count the rows out loud together (5, 10, 15, 20, 25) and cover each row with a hand once it is counted.
Your child calls any set of objects in rows an array, even when one row is shorter.
The rows look neat, so the child does not check that every row holds the same number. Repeated addition only works when all the rows are equal.
What helps. Lay out cereal in rows on a plate with one row short. Ask whether you can add the same number for every row, then fix the short row together.

Try four practice questions

Real 2nd grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
Sara worked on this array and made the equation below.
$\displaystyle 2+2=4$
Pick the sentence that best describes what Sara did.
A
Sara is correct.
B
Sara got the total wrong.
C
Sara wrote too many addends.
D
Sara counted rows instead of items in each row.
Show the answer and how to solve it
The answer is "Sara counted rows instead of items in each row." For $2$ rows of $3$ stars, the correct repeated-addition equation is $3+3=6$ . Sara wrote $2+2=4$ — she used the row count ( $2$ ) as her addend value instead of the items in each row ( $3$ ).
1. 1Look at the array. There are 2 rows, with 3 stars in each row.
2. 2For an array, a repeated-addition equation has one addend for each row, and each addend equals the items in that row. The correct equation for this array is shown below.
3. 3Look at Sara's equation: $2+2=4$ . Sara wrote the right number of addends — $2$ addends matches the $2$ rows. But the addend value is $2$ instead of $3$ . Sara used the number of rows as the value of each addend, instead of the items in each row.
4. 4The matching sentence is "Sara counted rows instead of items in each row."
Common mistake. A common mistake is using the number of rows as the addend value in repeated addition. For an array with $2$ rows of $3$ , the addends should be $3$ (items in each row), not $2$ (number of rows). The correct equation is $3+3=6$ .
The idea underneath. In a repeated-addition equation for an array, the number of addends matches the number of rows, and each addend's value matches the items in each row. Don't swap them!
2On level
How many rows? How many columns?
Rows:
Columns:
Show the answer and how to solve it
There are 3 rows and 3 columns in the array.
1. 1Look at the array below. Rows go across, from side to side. Columns go up and down.
2. 2Count the rows from top to bottom. There are 3 rows.
3. 3Now count the columns from left to right. There are 3 columns.
4. 4The array has 3 rows and 3 columns.
Common mistake. A common mistake is mixing up rows and columns. Rows go across (side to side), and columns go up and down.
The idea underneath. Rows are the lines of objects that go across the array. Columns are the lines of objects that go up and down. In any rectangular array, every row has the same number of objects, and every column has the same number of objects.
3On level
Maya wrote a rows equation and a columns equation for the array shown. Select the statement that best describes Maya's equations.
$\displaystyle \begin{array}{l} \text{Rows: } 3 + 3 + 3 + 3 = 11 \\ \text{Columns: } 4 + 4 + 4 = 12 \end{array}$
A
The rows equation is correct, but the columns equation is not.
B
Neither the rows equation nor the columns equation is correct.
C
Both the rows equation and the columns equation are correct.
D
The columns equation is correct, but the rows equation is not.
Show the answer and how to solve it
Maya's columns equation $4 + 4 + 4 = 12$ correctly shows $3$ columns of $4$ , with a total of $12$ . But her rows equation $3 + 3 + 3 + 3 = 11$ has the wrong total — $3 + 3 + 3 + 3$ equals $12$ , not $11$ . So the columns equation is correct, but the rows equation is not.
1. 1Look at the array below. There are 4 rows and 3 columns.
2. 2Check the rows equation. The array has 4 rows, with 3 in each row. So the correct rows equation should be:
3. 3Maya's rows equation says $3 + 3 + 3 + 3 = 11$ . But $3 + 3 + 3 + 3$ equals $12$ , not $11$ . The rows equation has the wrong total.
4. 4Check the columns equation. The array has 3 columns, with 4 in each column. So the correct columns equation should be:
5. 5Maya's columns equation says $4 + 4 + 4 = 12$ . That matches. The columns equation is correct.
6. 6So the columns equation is correct, but the rows equation is not.
Common mistake. A common mistake is checking only the addends without computing the total. Maya's rows equation $3 + 3 + 3 + 3$ has the right addends for $4$ rows of $3$ , but the total $11$ is wrong — $3 + 3 + 3 + 3 = 12$ . Always check both the addends AND the total.
The idea underneath. An equation matches the array only when the addends match the row or column structure AND the total is right. Always check both.
4Stretch
Sam wants to find how many stickers are in 4 rows of 5 stickers. Sam's work is shown below.
$\displaystyle 5 + 5 + 5 + 5 = 20$
Select the statement that best describes Sam's work.
A
Sam's 20 comes from adding one extra row that wasn't there.
B
Sam's 20 is correct.
C
Sam's 20 comes from adding the two numbers in the problem instead of using repeated addition.
D
Sam's 20 comes from leaving out one row when adding.
Show the answer and how to solve it
Sam's equation $5 + 5 + 5 + 5 = 20$ correctly adds $5$ once for each of the $4$ rows, so the total of $20$ matches the array total. The statement that best describes Sam's work is the one that says Sam's $20$ is correct.
1. 1Sam's array has 4 rows with 5 stickers in each row. Look at Sam's equation below.
2. 2To find the total, add 5 once for each row. There are 4 rows, so add 5 four times:
3. 3Sam's equation $5 + 5 + 5 + 5 = 20$ correctly adds $5$ once for each of the $4$ rows. The total is $20$ , which matches the array total.
4. 4So the statement that best describes Sam's work is the one that says Sam's $20$ is correct.
Common mistake. A common mistake in array problems is to add the two numbers from the problem ( $4 + 5 = 9$ ) instead of using repeated addition. But $4$ rows of $5$ stickers means four groups, each with $5$ stickers in it — so the total is $5 + 5 + 5 + 5 = 20$ , found by adding $5$ once for each row.
The idea underneath. The total in an array comes from repeated addition: add the per-row count once for every row. For $4$ rows of $5$ stickers, add $5$ four times: $5 + 5 + 5 + 5 = 20$ . Adding the two dimensions ( $4 + 5$ ) gives the sum of dimensions, not the array total.