Multiplying 1-digit numbers with 3-digit numbers

Having learned the basic multiplication tables (please see previous blog posts – 1,2,3) for single digit numbers, i.e. 2 to 9, it is now time to generalize multiplication to multi-digit numbers, starting with multiplying 1-digit numbers with 3-digit numbers.

Before jumping into the standard algorithm, it is better to lay some important foundation. Here, a strong grasp of place value is important.

Multiply one-digit whole numbers by multiples of 10

First, let’s start with multiplying by 10. Instead of using rules such as “add a zero behind”, it is better to use place value charts, so that students can visualize the process on each of the place values. For example:

Multiply one-digit whole numbers by multiples of 10

Multiply a 1-digit number with a 3-digit number without regrouping

After we understand multiplication by 10, we’re ready to tackle the main tasks of multiplication. Firs,t we’ll start with cases without regrouping. Again, we start with place value charts, e.g. for 3 x 212:

Multiply a 1-digit number with a 3-digit number without regrouping

Nex,t we’ll introducethe partial product, which is just an abstract representation of the place value example (remember C-P-A). We can help students by adding place value labels at the top (e.g. H T O):

Multiply a 1-digit number with a 3-digit number without regrouping

Now, we’re ready to introduce the standard algorithm for multiplication:

Multiply a 1-digit number with a 3-digit number without regrouping

Multiplication with regrouping – 1-digit number with 2-digit number

That wasn’t so hard, was it? Now, how about cases with regrouping? Now, things get more interesting. We’ll start with multiplication involving 2-digits first.

Before we work on the standard algorithm, let students construct own understanding of multiplication involving regrouping. Use an example, say 3 x 35 and let students come up with different ways to find the product. Here are a few examples.

  • Place value

Multiplication with regrouping – 1-digit number with 2-digit number

  • Using number bond

Multiplication with regrouping – 1-digit number with 2-digit number

  • Partial products

Multiplication with regrouping – 1-digit number with 2-digit number

Finally, we introduce the standard algorithm, explain the concept of regrouping with the help of the place value chart:

Multiplication with regrouping – 1-digit number with 2-digit number

Multiplication with regrouping – 1-digit number with 2-digit number

Multiplication with regrouping – 1-digit number with 3-digit number

Now that we have a good understanding of multiplication with regrouping, multiplying 1-digit numbers with 3-digit numbers is straightforward. E.g. 3 x 145 using standard algorithm:

Multiplying 1-digit numbers with 3-digit numbers

Solve simple 1-step word problems

We’re now ready to introduce simple 1-step word problems.

E.g. Question: Abby earns $890 in one week. How much would she earn in 3 weeks?

Even though students may see the number equation the question is asking in the head already, it is beneficial to visualize what we want to find using bar modeling. This lays the groundwork for more complex multiplication and division word problems later on.

multiplication one-step word problem

Related Resources

Video explanation and lesson plan (member’s resource)

Common Core Standards

  • 3NBT.A3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.
  • 4NBT.B5 Multiply a whole number of up to four digits by a one-digit whole number.

Suggested Workbook Series

  • Math in Focus workbook (3A) Chapter 7 – Multiplication (pages 119 to 146)
  • Primary Mathematics workbook (Common Core Edition) (3A) Chapter 3 – Multiplication and Division (pages 97 to 124)

 

Related Resources

For more related resources, please refer to our Multiplication and Division page.

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