Multiplication: Single-digit by Multi-digit

Contributor: Ashley Nail. Lesson ID: 13183

Multiplication is more than just math problems on a worksheet. It can help you solve problems in real life, too! Learn to solve single-digit by multi-digit multiplication.

categories

Elementary, Numbers & Operations

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

Lesson Plan - Get It!

Audio:
  • Have you ever been on a road trip?

They are a great way to see all the best spots. For example, in the United States, you could visit different National Parks and see mountains, deserts, canyons, geysers, rivers, and lakes! You could visit big cities like Chicago and New York City. Or you could visit famous landmarks like the St. Louis Arch or the Hollywood sign!

When you're in a car traveling to all those cool places, it is important to plan ahead and keep track of how far you will be driving and how long it will take to get to each destination!

Road trips are long, which means you'll have big numbers to work with; however, you can use multiplication to help calculate your total time and distance!

Let's plan a pretend road trip together!

We start at the Rocky Mountains in Colorado.

Rocky Mountains, Colorado

The next stop on our trip is to visit the Grand Canyon in Arizona. That's a long drive!

Grand Canyon, Arizona

We decide to make the drive in 4 days. Each day, we can drive about 231 miles before we get too tired.

  • How many total miles will we drive between the Rocky Mountains and the Grand Canyon?
  • How can we figure this out?

My travel journal looks like this:

 

Rocky Mountains to Grand Canyon

  Day One: 231 miles
  Day Two: 231 miles
  Day Three: 231 miles
  Day Four: 231 miles

 

I know I could add each day together to find the total number of miles, but I wonder if there is another way to solve this problem.

Yes! We can multiply 231 by 4 to find the total number of miles to the Grand Canyon. We will set up our equation like this:

equation

Take a minute to look at our factors.

  • What do you notice?

The number 231 has three digits, or is multi-digit, and it can be broken down into three different numbers. The 2 is in the hundreds place and represents 200. The 3 is in the tens place and represents 30. The 1 is in the ones place and just represents 1. This is important to know while we are multiplying.

We can solve this multiplication problem two ways. First, we will use an area model. Since 231 is three digits and can be broken down, we will split our area model into three parts and show 231 across the top of the model.

Since we are multiplying 231 x 4, we will show 4 on the side of the area model.

   

200

30

1

 

     

 

Now, we will fill in the boxes on our area model by multiplying 4 with each number across the top. For example, first you multiply 200 x 4 to get 800.

   

200

30

1

 

4 x 200 = 800 4 x 30 = 120 4 x 1 = 4

 

The last step is to add all of the products, or answers, from each box to get our final product.

800 + 120 + 4 = 924

So, now we know 231 x 4 = 924. We will travel 924 miles to go from the Rocky Mountains to the Grand Canyon!

Wait! Let's check our answer before we plan any more of our road trip! There is another way to solve 231 x 4. It's called the standard algorithm.

First, we set up our equation by writing the factors on top of each other and keeping the bigger number on the top. We also line up the digits so that the ones, tens, and hundreds are all in line.

  hundreds tens ones  
 

2

3

1

 
  x  

4

 
         

 

First, we multiply 4 x 1 and write the answer under the line in the ones place.

  hundreds tens ones  
 

2

3

1

4 x 1 = 4
  x  

4

 
     

4

 

 

Next, we multiply 4 x 3. We know the answer is 12, but we can only write one digit in the tens place. So, we write the 2 below the line and carry the 1 to the hundreds place. The 1 will be added in the next step.

  +1      
  hundreds tens ones  
 

2

3

1

4 x 3 = 12
  x  

4

 
   

2

4

 

 

Last, we multiply 4 x 2 which is 8. But, don't forget that 1! We add the leftover 1 to 8. So, 8 +1 = 9. Now, we write 9 below the line and can see our final product!

  +1      
  hundreds tens ones  
 

2

3

1

4 x 2 = 8
  x  

4

8 + 1 = 9
 

9

2

4

 

 

231 x 4 = 924. We solved for the same answer again! 924 total miles!

Now you're ready to try multiplying even bigger numbers! Visit the Got It? section to show off your knowledge!

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