 Multiply a single digit number by a four digit number using an area model

Lesson

Multiplying a single digit number by a $4$4 digit number for area is a tricky task. One strategy we can use is to break it up into $4$4 separate multiplications and then add them all together.

When we multiply area, we multiply one side by another side. We've already looked at how to do this with a three digit number. Now let's look at how to do it with a four digit number.

We can break a four digit number up into $4$4 separate values and multiply it by each. For example, to find the area of the rectangle below, we can break the $4$4 digit number up into $4000+300+50+1$4000+300+50+1 which is the same as $4351$4351, then multiply each value by $2$2. The video below will show you with an demonstration on how to do just that.

Remember!

When multiplying a number by a four digit number, we can:

• break the four digit number up into thousands, hundreds, tens and ones,
• solve each multiplication separately, then

Worked Examples

Question 1

Find $2255\times4$2255×4 using the area model. 1. Find the area of the first rectangle. 2. Find the area of the second rectangle. 3. Find the area of the third rectangle. 4. Find the area of the fourth rectangle. 5. What is the total area of all four rectangles?

6. So what is $2255\times4$2255×4?

Question 2

Find $8669\times5$8669×5 using the area model. 1. Find the area of the first rectangle. 2. Find the area of the second rectangle. 3. Find the area of the third rectangle. 4. Find the area of the fourth rectangle. 5. What is the total area of all four rectangles?

6. So what is $8669\times5$8669×5?

Question 3

Use the area model to find $5054\times2$5054×2.

1. Fill in the areas of each rectangle.

 $5000$5000 $50$50 $4$4 $2$2 $\editable{}$ $\editable{}$ $\editable{}$
2. What is the total area of all three rectangles?

3. So what is $5054\times2$5054×2?

Outcomes

NA3-6

Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality