Lesson Video: Multiplying Numbers Using Bar Models Mathematics • 3rd Grade

In this video, we will learn how to draw bar models and write equations to represent one-step multiplication problems with numbers up to 100.

10:19

Video Transcript

Multiplying Numbers Using Bar Models

In this video, we will learn how to draw bar models and write equations to represent one-step multiplication problems with numbers up to 100.

In this problem, we have to calculate the total number of fish. We know there are four fish tanks. We also know that each fish tank contains four fish. One way we could calculate the answer would be to add together our four lots of four: four plus four plus four plus four. One way to work out the answer would be to skip count by four. Four, eight, 12, 16. We skip counted by four four times. Four plus four plus four plus four equals 16. Repeated addition or skip counting by fours is the same as multiplying. There are four fish tanks. Each fish tank contains four fish. Four lots of four or four times four equals 16.

In this video, we’re going to learn how to solve multiplication problems using bar models and multiplication equations. Let’s try one more example. Gel pens are sold in packs of three. If this boy buys five packs of gel pens, how many pens will he have? The first thing we can do to help solve this problem is to sketch a bar model. Our bar model has five parts or five squares to represent the five packs of gel pens. And we know that each pack contains three gel pens. One way we could solve the problem is to use repeated addition: three plus three plus three plus three plus three. But we could also solve the problem using multiplication. If we have five groups of three, we have to add together five lots of three. We could write this as five times three.

To calculate the answer, we could count in threes five times. Three, six, nine, 12, 15. Five times three is 15. The boy has 15 gel pens altogether. First, we read the problem and drew a bar model. Then we used the bar model to help us write our multiplication equation. Then we calculated the answer. Let’s try some questions now where we have to solve one-step multiplication problems using bar models and multiplication equations.

Anthony has three boxes of plates. Each box contains five plates. How many plates are there in total?

In this word problem, we’re being asked to calculate the total number of plates Anthony has. We can see that Antony has already drawn a bar model to represent the problem. Each of the different colored bars represents one box of plates. There are three different colored bars to represent the three boxes. And Anthony has drawn five squares inside each bar because each of his three boxes contains five plates. Anthony has also written five plus five plus five equals what. So we need to calculate three lots of five.

Adding three fives is the same as multiplying five by three. We can calculate five plus five plus five or five times three by counting forward in fives three times along our number line. Five, 10, 15. Five plus five plus five or five times three equals 15. If Anthony has three boxes of plates and each box contains five plates, then he has 15 plates in total.

Elizabeth has three bars of chocolate. Each bar contains two pieces of chocolate. Write an addition sentence to show how many pieces of chocolate there are.

In this word problem, we’re being asked to write an addition sentence to show how many pieces of chocolate Elizabeth has. Elizabeth has already drawn a bar model. Her bar model has three parts to represent the three bars of chocolate. And the question tells us that each of her bars contains two pieces of chocolate. So we can write a number two in each of the bars.

Drawing the bar model in this way helps us to work out our addition sentence. We need to add three lots of two: two plus two plus two. Adding together three twos is the same as multiplying two three times. Let’s count in twos along our number line three times: two, four, six. Two plus two plus two or three times two equals six. If Elizabeth has three bars of chocolate and each bar contains two pieces of chocolate, then she has six pieces of chocolate altogether.

There are four teams in a race. Each team has three people in it. Anthony made this model. How many people are there?

In this problem, we have to work out the total number of people in the race. Antony has drawn this bar model. He’s drawn four bars to represent the four teams. The question tells us that each team has three people in it. If we write the number three next to each bar, now we can see how to calculate the answer.

We could add together our four threes, three plus three plus three plus three, or multiply three by four. And we can add our four threes or multiply three four times by counting forward in threes four times along our number line. One three is three, two threes are six, three threes are nine, and four threes are 12. Three plus three plus three plus three or four times three equals 12. If there are four teams in a race and each team has three people in it, there are 12 people altogether.

David bought three boxes of pencils. Each box has 10 pencils. How many pencils does David have in total?

In this word problem, we’re being asked to work out the total number of pencils that David has. We know that he bought three boxes of pencils and each box contains 10 pencils. Let’s sketch a bar model to help us think about how to calculate the answer. Our bar model has three parts. This is because David bought three boxes of pencils. And we know that each box has 10 pencils inside. We’ve got three lots of 10. So we can multiply 10 by three to find the answer. We just need to count in tens three times: 10, 20, 30. 10 times three is 30. If David bought three boxes of pencils and each box contains 10 pencils, he will have 30 pencils in total.

What have we learned in this video? We have learned how to solve one-step multiplication problems using bar models.

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