3rd Grade · 3.NBT.A.3

How to multiply by 10 in 3rd grade

When you multiply by 10, every one becomes a ten, so 7 becomes 70. In 3rd grade, your child uses this idea to multiply a one-digit number by 20, 30 and the other tens up to 90. A problem such as $4 \times 60$ turns into a basic fact about tens.

What the standard says

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

3.NBT.A.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

What it means, in plain words

A multiple of 10 is a number you say when you count by tens: 10, 20, 30 and so on up to 90. Multiplying by multiples of 10 in 3rd grade means problems such as $3 \times 40$ or $8 \times 70$ , where a one-digit number is multiplied by one of these tens.

The method rests on place value, the idea that a digit's place sets its value. In 70, the 7 sits in the tens place, so 70 means 7 tens. That makes $8 \times 70$ the same as 8 groups of 7 tens, which is 56 tens. Ten tens make a hundred, so 56 tens is 560.

Multiplying by tens this way reuses facts your child already knows. Since $8 \times 7 = 56$ , 8 times 7 tens is 56 tens. Children also write it as $8 \times 7 \times 10$ : they find $8 \times 7$ first, then multiply by 10. Many notice that the product, the answer to a multiplication, is the basic fact with a zero on the end. The pattern holds here, and your child should be able to say why it works.

Your child should be able to:

Say how many tens are in a number such as 80
Multiply a one-digit number by a multiple of 10, such as $6 \times 30$
Explain an answer in tens, such as "6 times 3 tens is 18 tens"
Use a basic fact, then multiply by 10, to find a product

Example

What is $4 \times 60$ ?

60 is 6 tens.
$4 \times 6 = 24$ , so 4 times 6 tens is 24 tens.
10 tens make 100, so 24 tens is 2 hundreds and 4 tens, which is 240.
So $4 \times 60 = 240$ . The answer is 240.

Example

A class buys 7 packs of paper plates. Each pack has 50 plates. How many plates does the class have?

There are 7 groups of 50, so the problem is $7 \times 50$ .
50 is 5 tens, and $7 \times 5 = 35$ , so the product is 35 tens.
35 tens is 3 hundreds and 5 tens, which is 350.
The class has 350 paper plates.

Where children usually get stuck

Your child writes $4 \times 60 = 24$ .
Your child multiplied the digits 4 and 6 and forgot that the 6 in 60 means 6 tens. The answer 24 is the right number of tens, but it was written as ones.
What helps. Use dimes. Make 4 piles of 6 dimes and count all of them by tens: 10, 20, 30 and on. The total is 240 cents, not 24.
Your child writes $5 \times 60 = 30$ .
Your child learned "put a zero on the end" as a rule without the reason. The basic fact $5 \times 6 = 30$ already ends in zero, so it looks as if the zero is already there.
What helps. Say the problem in tens every time: "5 times 6 tens is 30 tens." Then ask how much 30 tens is. Ten tens make 100, so 30 tens is 300.
Your child says "24 tens" correctly but writes the number as 204.
Your child does not yet see that 10 tens make 100. To write 24 tens as a number, it has to be regrouped as 2 hundreds and 4 tens, which is 240.
What helps. Bundle craft sticks into tens with rubber bands, then put 10 bundles together to make 100. Build 24 tens with your child and read the number together.

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
Maria is finding $3 \times 20$ using the base-ten model below. She said the product is $6$ ones.
Maria wrote: "I counted $3 \times 2 = 6$ rods, so the model shows $6$ ones."
Select the statement that best describes Maria's work.
A
Maria's answer of $6$ ones is correct for $3$ groups of $2$ tens.
B
Maria's answer of $6$ ones comes from counting only the tens rods and ignoring that each rod stands for $10$ ones.
C
Maria's answer of $6$ ones comes from counting only one group's worth of tens rods.
D
Maria's answer of $6$ ones comes from adding the number of groups and the number of tens per group instead of multiplying.
Show the answer and how to solve it
Maria's task is $3 \times 20 = 60$ , but she said $6$ . The tens-rods-only mechanism gives $3 \times 2 = 6$ , which matches her value. The other mechanisms give $20$ (one group) or $5$ (added) — none of which equals $6$ . So the option saying Maria's answer of $6$ ones comes from counting only the tens rods and ignoring that each rod stands for $10$ ones is the matching statement.
1. 1Look at the base-ten model. There are $3$ groups, and each group has $2$ tens rods.
2. 2Each tens rod stands for $10$ ones. Each group has $2$ tens, or $20$ ones. The $3$ groups have $6$ tens altogether. Those $6$ tens are $60$ ones, so the product is:
3. 3Maria said the product is $6$ , but $3 \times 20 = 60$ . So Maria's answer is not correct.
4. 4Now check which mechanism actually produces $6$ from this model. Counting only one group's worth of tens gives $2 \times 10 = 20$ — not $6$ . Adding the number of groups and tens-per-group would give $3 + 2 = 5$ — not $6$ . Counting only the tens rods would give $3 \times 2 = 6$ — this matches Maria's value.
5. 5The matching statement is the option saying Maria's answer of $6$ ones comes from counting only the tens rods and ignoring that each rod stands for $10$ ones.
Common mistake. A common mistake is to scan the choices for the number Maria stated and pick whichever choice contains that number. With every option naming Maria's answer of $6$ ones, that shortcut no longer works — the student must compute each mechanism's result ( $3 \times 2 = 6$ , $2 \times 10 = 20$ , $3 + 2 = 5$ ) and pick the one that matches.
The idea underneath. $3$ groups of $2$ tens make $6$ tens. $6$ tens are $60$ ones. Each tens rod represents $10$ ones, so each group of $2$ tens is worth $20$ . Maria's task is $3 \times 20 = 60$ . When the student's stated value differs, check each mechanism in turn (just-the-rods $\rightarrow 3 \times 2$ , just-one-group $\rightarrow 2 \times 10$ , added $\rightarrow 3 + 2$ ) to find the one that actually produces the stated value.
2On level
Carlos wants to find the total number of markers in 5 boxes of 40 markers each. Carlos's work is shown below.
$\displaystyle \begin{aligned}5 \times 40 &= 5 \times 4 \times 10 \\ &= 200\end{aligned}$
Select the statement that best describes Carlos's work.
A
Carlos dropped the zero, getting 20 instead of 200.
B
Carlos added an extra zero, getting 2000 instead of 200.
C
Carlos added instead of multiplied, getting 45 instead of 200.
D
Carlos's computation is correct.
Show the answer and how to solve it
Carlos's computation is correct. $5 \times 40 = 200$ , and Carlos wrote $200$ as his answer.
1. 1Carlos wants to find the total markers in $5$ boxes of $40$ markers each. To check the work, multiply $5 \times 40$ and compare to what Carlos wrote.
2. 2To multiply by a multiple of $10$ , first multiply the non-zero digits, then attach the trailing zero.
3. 3Carlos wrote $5 \times 40 = 200$ , which matches our product. The computation is correct.
Common mistake. A common mistake is assuming there must be an error to find. Always verify by computing $5 \times 40$ yourself: $5 \times 4 = 20$ , then attach the trailing zero to get $200$ .
The idea underneath. Multiplying a single-digit number by a multiple of $10$ follows a simple pattern — multiply the non-zero digits, then attach the same number of trailing zeros.
3On level
Use place value to find $3 \times 70$ . Drag tiles into the blanks to complete the explanation.
$\displaystyle 3 \times 70 = ?$
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.
$\displaystyle 70 =$
tens, so
$\displaystyle 3 \times 70 =$
tens =
7
21
70
210
3
10
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
$3 \times 70 = 210$ . The chain reads: $70$ is $7$ tens, so $3 \times 70 = 21$ tens, and $21$ tens equals $210$ .
1. 1Break apart the multiple of $10$ . Since each ten equals $10$ , $70$ is $7$ tens:
2. 2Use the basic multiplication fact for the number of tens:
3. 3So $3 \times 70 = 21$ tens. Convert tens to ones by multiplying by $10$ :
Common mistake. A common mistake is to put the multiple itself ( $70$ ) in the first slot, thinking ' $70 = 70$ tens.' Each ten equals $10$ , so $70$ is actually $7$ tens.
The idea underneath. Multiplying by a multiple of $10$ has two parts: use a basic fact for the number of tens, then multiply by $10$ to convert tens to ones.
4Stretch
A garden has 6 rows of flowers. Each row has 80 flowers. How many flowers are there in all?
A
48
B
480
C
4800
D
86
Show the answer and how to solve it
There are $480$ flowers in all. To multiply $6 \times 80$ , first find $6 \times 8 = 48$ , then multiply by $10$ to get $480$ .
1. 1The garden has 6 rows of flowers, and each row has 80 flowers. To find the total, multiply the number of rows by the number of flowers in each row.
2. 2Use the multiply-by-tens strategy. First multiply $6 \times 8$ , then multiply by 10 to attach the zero from 80.
3. 3The total is 480 flowers.
Common mistake. A common mistake is to drop the zero — computing $6 \times 8 = 48$ and forgetting that $80$ is $8$ tens. The product needs to be $10$ times bigger than $48$ , which gives $480$ .
The idea underneath. Multiplying by a multiple of $10$ means multiplying the digits and then attaching one zero. $6 \times 80 = 6 \times 8 \times 10 = 480$ .