Multiplication: Single-digit by Double-digit Numbers

Contributor: Ashley Nail. Lesson ID: 13101

3 x 5 is easy, but what happens when you have bigger numbers to multiply, like 3 x 79?! Learn how to multiply single-digit numbers by double-digit numbers with dogs and cats to help!

categories

Elementary, Middle School

subject
Math
learning style
Auditory, Visual
personality style
Otter, Beaver
Grade Level
Intermediate (3-5)
Lesson Type
Quick Query

Lesson Plan - Get It!

Audio:

Have you ever been to an animal shelter? They have a lot of dogs and cats and even several volunteers working to take care of all those pets. There is one thing shelters do not have a lot of - supplies! It takes a lot of blankets, food, treats, toys, and leashes to make sure all of the dogs and cats are happy.

Let's imagine we are planning a donation drive for our local animal shelter! But before we start collecting supplies, we need to figure out how many animals are in the shelter. You notice there are 3 dogs in each pen and that there are 24 dog pens in the shelter.

How can we use this information to figure out how many dogs are in the shelter?

We want to collect enough blankets so each dog has its own cuddly bed, which means we need to know how many dogs are at the shelter.

Remember, this is the information we already know:

  • 24 dog pens with 3 dogs in each pen

There are three ways to find the total number of dogs:

  • You could count each dog, but that would take forever!
  • You could use repeated addition and add 3, 24 times.
    • 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = ?
  • OR, you could multiply 3 by 24!

Multiplication is the best method to figure out how many blankets we need to collect!

multiplication problem

First, look at the factors, or the numbers being multiplied together, in this equation.

  • What do you notice about the numbers 3 and 24?

I bet you noticed that 3 is a one-digit number and 24 is a two-digit number. You know that 24 is made up of 2 tens and 4 ones.

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Let's use an area model to help us multiply these two numbers.

diagram 1

When using an area model, the two factors of the equation are on the top and side of the model. The factor 3 is on the side, and the factor 24 is represented on the top of the model.

Since 24 can be broken into 20 and 4, we will write that on the top of the area model.

Now, we will multiply 3 x 20.

diagram 2

Next, we multiply 3 x 4.

diagram 3

The last step is to add the two products together to find the answer. So, 60 + 12.

diagram 4

We have a final answer!

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There are 72 dogs at the animal shelter!

Wait! Let's double check our answer before we start collecting all those blankets. There is one more way to multiply 3 x 24.

Instead of drawing an area model, we will solve for the product by placing the factors on top of each other.

You need to make sure the 3 is perfectly under the 4 since both of those numbers represent the ones place. Since 3 is a single digit, nothing goes under the 2. 2 is the only number in the tens place.

multiplication problem

Now, we can multiply. First multiply the ones place, so 3 x 4. The product is 12, but we can only write one number in the ones place. Write the 2 in the ones place under the line. Since the 1 is in the tens place, we will write it above the tens place. You will use that 1 later.

diagram 5

Next, multiply the 3 times the tens place. 3 x 2 = 6. But, don't forget that 1 we wrote earlier! Add the 1 to the product you just got. So, 6 + 1 = 7. You will write the 7 under the line in the tens place.

diagram 6

Look at the final product! We solved for 72 again!

So, I guess we need to collect 72 blankets for the 72 dogs in the shelter!

dog snuggled in blanket

Next, visit the Got It? section to help figure out how many supplies we need for the cats at the shelter.

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