3rd Grade · 3.OA.A.3

Multiplication word problems in 3rd grade

Multiplication word problems are short stories where the answer comes from multiplying or dividing. In 3rd grade, your child solves multiplication and division word problems with numbers up to 100. The stories are about equal groups, arrays and measurements, and your child learns to show each one with a drawing and an equation.

What the standard says

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

3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

What it means, in plain words

Every story in this standard has three numbers: the number of groups, the size of each group and the total. A multiplication word problem gives the first two and asks for the total. Division word problems give the total and one of the other two numbers.

The stories come in three kinds. Some are about equal groups, such as 6 bags with 5 apples in each. Some are about arrays, objects set out in rows and columns with the same number in every row, such as a tray of muffins. Others are about measurements, such as 9 bags of flour that each weigh 5 kilograms.

Your child shows the story first, with a drawing or an equation. An equation is a number sentence with an equal sign, and a symbol such as $?$ stands for the number you do not know yet. For 4 shelves with 9 books on each shelf, the equation is $4 \times 9 = ?$ . Writing the unknown this way keeps the story and the math lined up.

Your child should be able to:

Decide whether a story asks for the total, the number of groups or the size of each group
Draw a picture that shows the groups in a word problem
Write an equation with a symbol for the unknown number, such as $? \times 5 = 35$
Solve multiplication and division word problems within 100 and label the answer

Example

A sheet of stickers has 5 rows with 8 stickers in each row. How many stickers are on the sheet?

The stickers form an array of 5 rows of 8.
The total is unknown, so the equation is $5 \times 8 = ?$ .
$5 \times 8 = 40$ .
There are 40 stickers on the sheet.

Example

Juice boxes come in packs of 6. A class needs 42 juice boxes. How many packs does the class need?

The total is 42 and each pack holds 6, so the number of packs is unknown.
The equation is $? \times 6 = 42$ , which is the same as $42 \div 6 = ?$ .
$7 \times 6 = 42$ , so $? = 7$ .
The class needs 7 packs of juice boxes.

Where children usually get stuck

For a sheet with 5 rows of 8 stickers, your child writes $5 + 8 = 13$ .
Your child takes the two numbers in the story and adds them. The story was read for its numbers, not for what the numbers mean.
What helps. Have your child sketch the story before doing any math. A quick drawing of 5 rows of 8 makes 13 look wrong right away.
In the juice box problem, your child sees the word "each" and multiplies $42 \times 6$ .
Many children learn that "each" means multiply. Here the total is already given and the question is how many groups, so it is division.
What helps. Ask one question before any numbers: "Do we know the total, or are we looking for it?"
Your child draws all 42 juice boxes one by one, loses count and gets 41.
Your child has not yet linked division to multiplication facts, so drawing every object is the only tool. With a big total, a counting slip is easy.
What helps. Ask "6 times what makes 42?" and skip count by 6 together on your fingers.

Try four practice questions

Real 3rd 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
Jake has 4 ribbons. Each ribbon is 9 inches long. Which tape diagram shows this problem?
A
B
C
D
Show the answer and how to solve it
The correct diagram has a brace labeled '?' above 4 equal segments each labeled '9 in.'.
1. 1Jake has 4 ribbons, and each ribbon is 9 inches long. The count is 4; each piece is 9 inches; the total length is unknown.
2. 2A tape diagram shows the whole bar split into equal pieces. The brace above the bar shows the total. Because the total is unknown, the brace should be labeled '?'. Each of the 4 segments should be labeled '9 in.' for the known per-ribbon length.
3. 3The correct diagram is the one with 4 equal segments each labeled '9 in.' under a brace labeled '?'.
Common mistake. A common mistake is miscounting the number of ribbons. Jake has 4 ribbons, so the diagram needs exactly 4 segments — not 3 or 5.
The idea underneath. The brace shows the total. Each equal segment shows one part. The '?' on the brace marks the unknown total measurement. Choose the diagram with the given number of parts and measurement for each part.
2On level
A student tried to solve this question. Their work is shown below.
Ms. Lee has a piece of rope 36 centimeters long. She cuts it into 4 equal pieces. How long is each piece?
$\displaystyle 4 \div 36 = ?$
Look at the student's work. Which statement best describes it?
A
The student used the wrong operation.
B
The student used numbers that are not from the problem.
C
The student wrote a correct equation.
D
The student wrote the numbers in the wrong order.
Show the answer and how to solve it
The correct choice is 'The student wrote the numbers in the wrong order.' The correct equation is $36 \div 4 = ?$ (each piece is $9$ centimeters long), but the student wrote $4 \div 36 = ?$ , swapping the dividend and divisor.
1. 1First, think about what the question asks. The rope is $36$ centimeters long and cut into $4$ equal pieces. To find each piece's length, share the total ( $36$ centimeters) into $4$ equal groups — that means divide.
2. 2The correct equation puts the total first, then divides by the number of equal pieces:
3. 3Now look at the student's work: $4 \div 36 = ?$ . The operation (division) is right, but the numbers are in the wrong order. The total ( $36$ ) should be the dividend and come first, not the number of pieces ( $4$ ).
Common mistake. A common mistake is thinking $4 \div 36$ and $36 \div 4$ are the same. The order matters in division — $36 \div 4 = 9$ , but $4 \div 36$ does not give the same answer.
The idea underneath. In division, order matters: $36 \div 4$ is not the same as $4 \div 36$ . When you split a total amount into equal parts, the total goes first.
3On level
Sam put $21$ oranges into $3$ equal rows. How many oranges are in each row?
Drag tiles into the boxes to write an equation for this problem. Use the $?$ tile for the unknown.
Tap or click a tile to drop it into the highlighted blank, or tap an empty blank first to choose a different one. Tap a filled blank to send its tile back.
=
21
3
7
?
×
÷
+
Tap an item to place it in the next empty slot, or drag it to a specific slot. With a keyboard: select an item with Enter or Space, then select a slot to place it. Press Delete or Backspace on a slot to remove an item.
Show the answer and how to solve it
The equation $3 \times ? = 21$ represents the problem. The symbol $?$ stands for the unknown number of oranges in each row. You could also write $? \times 3 = 21$ or $21 \div 3 = ?$ — all three describe the same array.
1. 1Look at the array. Sam has $3$ equal rows of oranges, with $21$ oranges in all. We need to find how many oranges are in each row.
2. 2The question asks for the number of oranges in each row. Use $?$ for that number in the equation, even though the array shows its value.
3. 3Each row has $?$ oranges. There are $3$ rows. So $3$ groups of $?$ oranges equals $21$ oranges. Write this as a multiplication equation.
Common mistake. A common mistake is writing the equation as $3 \times 7 = 21$ instead of using $?$ . Even though you can count the array and see each row has $7$ oranges, the equation should use $?$ to represent the unknown number.
The idea underneath. An array equation tells the math story. The symbol $?$ is a placeholder for the number we are looking for, even when we can count and see what it is.
4Stretch
Maya has 4 vases with 4 flowers in each vase. Which picture shows Maya's flowers?
A
B
C
D
Show the answer and how to solve it
The correct picture has 4 groups, with 4 flowers in each group, matching Maya's 4 vases of 4 flowers.
1. 1Read the problem to find the two numbers. The problem says Maya has 4 vases, and each vase has 4 flowers. So the picture should show 4 equal groups, with 4 flowers in each group.
2. 2Look at each picture. First count the GROUPS of flowers. Then count the flowers in ONE group. The picture you want has exactly 4 groups, and each group has exactly 4 flowers.
3. 3The picture with 4 groups of 4 flowers matches Maya's vases. The other pictures either have a different number of groups or a different number of flowers in each group — even when the total looks like 16.
Common mistake. A common mistake is mixing up which number tells the groups and which tells the items in each group. The first number (4) is the number of vases, so it counts how many GROUPS the picture should have. The second number (4) is the flowers in EACH vase, so it counts how many items go in each group. Since both numbers are the same here, also watch out for pictures that have the right total (16) but split into different groups — like 2 groups of 8 or 8 groups of 2.
The idea underneath. Equal-groups problems always have two different jobs for two different numbers: one tells how many GROUPS to make, and the other tells how many ITEMS go in each group. Read carefully to match each number to its job — they are not interchangeable.