In this Grade 4 Saxon Math lesson, students learn how to multiply two-digit numbers by a one-digit number using regrouping, carrying the extra tens digit above the tens column when the ones product exceeds nine. The lesson builds on earlier multiplication skills and uses money manipulatives like $10 and $1 bills to model the regrouping process concretely. Part of Chapter 5 in Saxon Math Intermediate 4, the lesson also incorporates estimation with unit conversions as a real-world application.
Section 1
📘 Multiplying Two-Digit Numbers, Part 2
We write the second digit below the line in the ones column and write the first digit above the tens column.
Now, you will apply this regrouping method to solve multiplication problems, including those involving money and estimation.
Section 2
Multiplying with regrouping
When multiplying the ones place results in a two-digit number, we don't write both digits down. Write the second digit (the ones) below the line and carry the first digit (the tens) above the tens column. Then, multiply the tens digit and remember to add the number you carried over to find the final product.
To solve : First, . Write down the 2 and carry the 3. Then, , plus the carried 3 is 7. The answer is 72.
To solve : First, . Write down the 2 and carry the 4. Then, , plus the carried 4 is 28. The answer is 282.
To solve : First, . Write down the 2 and carry the 4. Then, , plus the carried 4 is 39. The answer is 392.
Think of it like a trade-up game! When you get 10 or more ones, you can't keep them all there. You trade 10 ones for a ten, carry it over, and add it in after multiplying.
Section 3
Model multiplication with money
To show multiplication like with money, you lay out the amount multiple times. For this problem, you would create three groups of money, with each group containing one 10 dollars bill and four 1 dollars bills. This gives you a hands-on way to see all the parts before you combine them and regroup.
For , you start with three 10 dollars bills and twelve 1 dollars bills.
Then, you exchange ten of the 1 dollars bills for one 10 dollars bill.
You are left with four 10 dollars bills and two 1 dollars bills, which equals 42 dollars.
It’s like being a banker! You gather all the bills, but you can't have a giant pile of one dollars bills. You exchange every ten 1 dollars bills for a new 10 dollars bill, then count up your neat stacks.
Section 4
Estimate the product
When a problem asks for an estimate or an 'about' answer, you don't need the exact number. Make the math easier by rounding one of the numbers to a friendlier number, like the nearest ten. Then, perform the multiplication with the rounded number to get a quick, close answer that makes sense and is easy to calculate.
To estimate , round 29 to 30. Your estimated product is .
To estimate the cost of 8 items at 48 cents each, round 48 to 50 cents. Your estimated cost is cents, or 4 dollars.
To estimate the quarts in 19 gallons, round 19 to 20. Then calculate quarts.
Why do extra work when you don't have to? Rounding before you multiply is a super-fast shortcut to get an answer that’s close enough. It's perfect for quickly checking if your final answer is in the right ballpark.
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Section 1
📘 Multiplying Two-Digit Numbers, Part 2
We write the second digit below the line in the ones column and write the first digit above the tens column.
Now, you will apply this regrouping method to solve multiplication problems, including those involving money and estimation.
Section 2
Multiplying with regrouping
When multiplying the ones place results in a two-digit number, we don't write both digits down. Write the second digit (the ones) below the line and carry the first digit (the tens) above the tens column. Then, multiply the tens digit and remember to add the number you carried over to find the final product.
To solve : First, . Write down the 2 and carry the 3. Then, , plus the carried 3 is 7. The answer is 72.
To solve : First, . Write down the 2 and carry the 4. Then, , plus the carried 4 is 28. The answer is 282.
To solve : First, . Write down the 2 and carry the 4. Then, , plus the carried 4 is 39. The answer is 392.
Think of it like a trade-up game! When you get 10 or more ones, you can't keep them all there. You trade 10 ones for a ten, carry it over, and add it in after multiplying.
Section 3
Model multiplication with money
To show multiplication like with money, you lay out the amount multiple times. For this problem, you would create three groups of money, with each group containing one 10 dollars bill and four 1 dollars bills. This gives you a hands-on way to see all the parts before you combine them and regroup.
For , you start with three 10 dollars bills and twelve 1 dollars bills.
Then, you exchange ten of the 1 dollars bills for one 10 dollars bill.
You are left with four 10 dollars bills and two 1 dollars bills, which equals 42 dollars.
It’s like being a banker! You gather all the bills, but you can't have a giant pile of one dollars bills. You exchange every ten 1 dollars bills for a new 10 dollars bill, then count up your neat stacks.
Section 4
Estimate the product
When a problem asks for an estimate or an 'about' answer, you don't need the exact number. Make the math easier by rounding one of the numbers to a friendlier number, like the nearest ten. Then, perform the multiplication with the rounded number to get a quick, close answer that makes sense and is easy to calculate.
To estimate , round 29 to 30. Your estimated product is .
To estimate the cost of 8 items at 48 cents each, round 48 to 50 cents. Your estimated cost is cents, or 4 dollars.
To estimate the quarts in 19 gallons, round 19 to 20. Then calculate quarts.
Why do extra work when you don't have to? Rounding before you multiply is a super-fast shortcut to get an answer that’s close enough. It's perfect for quickly checking if your final answer is in the right ballpark.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter