3rd Grade · 3.OA.C.7

Multiplication facts in 3rd grade

Multiplication facts are the products of two one-digit numbers, from $0 \times 0$ up to $9 \times 9$ . By the end of 3rd grade, your child should know all of them from memory and use them to answer division facts quickly.

What the standard says

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

3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

What it means, in plain words

The times tables are the same facts sorted into rows: the 2s, the 3s and so on up to the 9s. Your child learns them in two stages. First come strategies, ways to work out a fact from one already known. Then the facts move into memory, so $6 \times 8 = 48$ comes as fast as reading a word.

Strategies come from the properties of multiplication. A fact turned around has the same answer, so $3 \times 9$ and $9 \times 3$ only need learning once. Doubling helps too. The 4s are double the 2s, so $4 \times 9$ is $2 \times 9 = 18$ doubled, which is 36.

Division facts come from the same memory. Because $8 \times 5 = 40$ , your child also knows $40 \div 5 = 8$ . Multiplication facts in 3rd grade are only finished when both directions come quickly, without counting.

Your child should be able to:

Say any product of two one-digit numbers from memory
Work out a forgotten fact from a nearby one, such as $9 \times 7$ from $10 \times 7$
Answer a division fact by thinking of its multiplication fact
Multiply by 0 and by 1 correctly

Example

What is $9 \times 7$ , if your child does not remember it yet?

Start from an easier fact: $10 \times 7 = 70$ .
$9 \times 7$ is one 7 less than $10 \times 7$ .
$70 - 7 = 63$
So $9 \times 7$ is 63.

Example

What is $72 \div 8$ ?

Think of the multiplication fact: 8 times what number makes 72?
$8 \times 9 = 72$
So $72 \div 8$ is 9.

Where children usually get stuck

Your child answers $8 \times 6$ with 46 one day and 56 the next.
The fact is stored as a sound, with no reason behind it, so a near miss feels right. With no way to check, a wrong answer gets repeated until it sticks.
What helps. Give each shaky fact an anchor. $5 \times 6 = 30$ , and three more 6s add 18, so $8 \times 6 = 48$ . Have your child say the anchor out loud once, then the fact.
Your child writes $7 \times 0 = 7$ and $1 \times 9 = 10$ .
Adding 0 leaves a number the same and adding 1 makes it one bigger. Those addition rules get carried over to multiplication.
What helps. Put out 7 empty bowls and ask how many grapes they hold together. Then put 9 grapes in 1 bowl and ask again.
For $9 \times 8$ , your child counts by 8s on fingers and loses track around 48.
Skip counting (counting by 8s, 6s or 7s) got your child started, but it is slow and one slip throws off every number after it. The fact has not moved into memory yet.
What helps. Write 3 shaky facts on cards each day and mix them in with facts already known. A card moves to the known pile only when the answer comes without counting.

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
Mateo wants to find $4 \times 7$ using a turn-around. His work is shown below.
$\displaystyle 7 \times 4 = 28$
$\displaystyle 4 \times 7 = 28$
Select the statement that best describes Mateo's work.
A
Both equations have the correct product.
B
The second answer is the sum of the factors.
C
The second answer is 1 or 2 away from the correct product.
D
The second answer is one of the factors.
Show the answer and how to solve it
"Both equations have the correct product." Both equations show the correct product, $28$ .
1. 1Look at Mateo's work. The given fact is $7 \times 4 = 28$ , and Mateo wrote $4 \times 7 = 28$ .
2. 2When you swap the factors in a multiplication, the product stays the same. So $4 \times 7$ should give the same product as $7 \times 4$ , which is $28$ .
3. 3Both equations show the correct product, $28$ .
Common mistake. Swapping the factors does not change the product. Both equations correctly show $28$ .
The idea underneath. When you swap the order of two factors, the product stays the same. So $4 \times 7$ and $7 \times 4$ both equal $28$ . This is the turn-around rule.
2On level
Which is equal to the multiplication below?
$\displaystyle 6 \times 7$
A
$\displaystyle 6 \times 4 + {}$
$\displaystyle 3$
B
$\displaystyle 6 \times 4 + {}$
$\displaystyle 6 \times 4$
C
$\displaystyle 6 \times 4 + {}$
$\displaystyle 6 \times 3$
D
$\displaystyle 6 \times 4 - 6 \times 3$
Show the answer and how to solve it
The correct break-apart is $6 \times 4 + 6 \times 3$ , which equals $42$ — the same as $6 \times 7$ . Both parts of the split (the $4$ and the $3$ ) are multiplied by $6$ .
1. 1Look at the multiplication $6 \times 7$ . To break it apart, split one factor into two smaller parts that are easier to multiply.
2. 2Split $7$ as $4 + 3$ . Then multiply each part by $6$ and add the two products.
3. 3Check the math: $6 \times 4 = 24$ and $6 \times 3 = 18$ . Then $24 + 18 = 42$ , and $6 \times 7 = 42$ .
Common mistake. A common mistake is forgetting to multiply both parts of the split by the other factor. In $6 \times 4 + 3$ , the $3$ is missing its $\times 6$ , so the value drops to $27$ instead of $42$ .
The idea underneath. Splitting $7$ as $4 + 3$ means $6 \times 7$ is the same as $6$ groups of $4$ plus $6$ groups of $3$ . Both parts of the split must still be multiplied by the other factor.
3On level
Mia wrote the equation below after calculating $8 \div 8 = 1$ .
$\displaystyle 8 \div 1 = 1$
Select the statement that best describes Mia's work.
A
For $8 \div 1 = 1$ , Mia divided the number by itself instead of by $1$ , getting $1$ .
B
For $8 \div 1 = 1$ , Mia subtracted instead of dividing, getting $7$ .
C
For $8 \div 1 = 1$ , Mia treated $8 \div 1$ like $0 \div 8$ , getting $0$ .
D
The answer is correct.
Show the answer and how to solve it
For $8 \div 1 = 1$ , Mia divided the number by itself instead of by $1$ , getting $1$ . The correct calculation is $8 \div 1 = 8$ .
1. 1Look at Mia's equation and the calculation shown.
2. 2 $8 \div 1$ asks how many groups of $1$ fit in $8$ . There are $8$ groups.
3. 3Mia wrote $1$ , but $8 \div 1 = 8$ . The equation is incorrect.
4. 4The calculation shown is $8 \div 8 = 1$ . Mia divided the number by itself instead of by $1$ . There is $1$ group of $8$ in $8$ , but $8$ groups of $1$ in $8$ .
5. 5Select: "For $8 \div 1 = 1$ , Mia divided the number by itself instead of by $1$ , getting $1$ ."
Common mistake. $8 \div 1 = 8$ counts groups of $1$ . $8 \div 8 = 1$ counts groups of $8$ . Dividing a nonzero number by itself gives $1$ .
The idea underneath. $8 \div 1$ asks how many groups of $1$ fit in $8$ . There are $8$ groups.
4Stretch
Look at each pairing below. Which pairing is NOT in the same fact family?
$\displaystyle \begin{array}{l} \text{A: } 3 \times 8 = 24 \leftrightarrow 24 \div 4 = 6 \\ \text{B: } 5 \times 7 = 35 \leftrightarrow 35 \div 7 = 5 \\ \text{C: } 6 \times 9 = 54 \leftrightarrow 54 \div 6 = 9 \\ \text{D: } 4 \times 8 = 32 \leftrightarrow 32 \div 8 = 4 \end{array}$
A
Pairing C
B
Pairing D
C
Pairing B
D
Pairing A
Show the answer and how to solve it
Pairing A is NOT in the same fact family. The multiplication $3 \times 8 = 24$ uses the numbers $3$ , $8$ , and $24$ . But the division $24 \div 4 = 6$ uses $24$ , $4$ , and $6$ . Only $24$ is shared between them.
1. 1A fact family is a group of facts that all use the same three numbers. For each pairing, check whether the multiplication fact and the division fact use the same three numbers.
2. 2Pairings B, C, and D each use the same three numbers in both their multiplication and their division.
3. 3Now look at Pairing A. The multiplication and the division do NOT share the same three numbers.
4. 4Pairing A is the answer. It is NOT in the same fact family because the multiplication uses 3 and 8, but the division uses 4 and 6 — different numbers. They share only the product 24.
Common mistake. A common mistake is to see a multiplication fact next to a division fact and assume they go together without checking. To be in the same fact family, the multiplication and the division must use the SAME three numbers — just rearranged.
The idea underneath. A fact family always has exactly three numbers — two factors and one product. The same three numbers can be rearranged into one multiplication fact and two related division facts. If a multiplication and a division do not share the same three numbers, they are not in the same family.