What is this skill?
Fourth graders move from single-digit times tables to multiplying bigger numbers: a number with up to four digits times a one-digit number (like 574 × 6), and a two-digit number times a two-digit number (like 23 × 19). The skill is not a new kind of multiplication. It is the same equal-groups idea, split into pieces that are easy to handle.
The key idea is the place-value split. 574 × 6 is the same as 500 × 6 plus 70 × 6 plus 4 × 6, which is 3,000 + 420 + 24 = 3,444. For 23 × 19, a child can work out 23 × 10 and 23 × 9 separately and add the two. Schools show this with an area model (a rectangle cut into boxes) and later with the standard method, where the same partial products are stacked and carried. The model comes first because it shows why the standard method works.
Why it matters
Almost every later topic leans on this one. Multiplying fractions, finding the area of larger rooms and fields, working with money, and long division in fifth grade all use partial products. A child who only memorized a carrying routine tends to freeze when a zero shows up in the middle of a number or when the digits are lined up wrongly. A child who understands that each digit is worth a different amount can check whether an answer is sensible.
It also builds estimation. Knowing that 574 × 6 is a bit more than 500 × 6 gives a quick reasonableness check of about 3,000, which catches the common slip of an answer that is ten times too big or too small. That habit of asking “does this size make sense?” is worth as much as the arithmetic itself.
Common mistakes
- Forgetting what a digit is worth, such as writing 7 × 6 = 42 for the tens digit instead of 70 × 6 = 420. Saying the full number aloud (“seventy times six”) fixes this.
- Dropping the placeholder zero in two-digit by two-digit problems. When multiplying by the tens digit of the second number, the answer is really tens, so the ones place stays empty.
- Mishandling a zero inside a number, as in 606 × 4. The tens digit contributes nothing, but it still has to be held in place.
- Carrying the wrong amount or adding the carried number before multiplying instead of after.
- Multiplying only the matching digits (the ones by the ones, the tens by the tens) and skipping the cross products.
How to help at home
- Ask for an estimate first. “About how much is 48 × 6?” (close to 50 × 6, so about 300) before working out the exact answer.
- Draw a box split into tens and ones and fill in the partial products. Seeing the rectangle often makes the method click.
- Use real totals: 24 rows of 12 seats, 15 boxes of 36 crayons, 52 weeks of 7 days. Have your child say which parts they will multiply.
- Keep graph paper handy. Neat columns prevent most of the lining-up mistakes.
- When an answer looks wrong, ask your child to check it with the estimate rather than telling them it is wrong.
Worked examples
These are real questions from the Tutorsaurus multi-digit multiplication practice, with the answers worked out.
Example 1
64 × 3 = ?
Answer: 192. 60 × 3 = 180 and 4 × 3 = 12. Add them: 192.
Example 2
606 × 4 = ?
Answer: 2424. Multiply each place: 600 × 4 + 6 × 4 = 2424.
Example 3
29 × 16 = ?
Answer: 464. 29 × 10 = 290 and 29 × 6 = 174. Add: 464.