Finding the Percent of a Number with Bar Models

Percent bars are a great way to get students to understand what it means to find the percent of a number.  Before students start finding the percent of a number, they should have some understanding of equivalent ratios and should understand that percent is a special type of ratio that always compares number to 100.

When we are finding the percent of a number, we are using proportional reasoning to create two equal ratios.  This why percent bars are such a great visual tool.  On the bottom of the bar we are looking at the percent’s and at the top of the bar we are looking at the number we are finding the percent of.

Example 1

What is 80% of 20?”  First, we have to break our bar model into 10% sections.  20 is the whole amount that we are trying to find the percent of.  Therefore, we want to line it up with 100%.  Explain to students that if we had 20 out of 20, that would be 100%.

Have students ignore the percent’s for a minute and just look at the 20.  If 20 represents the whole bar, what is each box worth?  Students should see that since there are 10 boxes, each box is worth 2 because 20 divided by 10 is 2.

Since the question is asking us to find 80% of the number, we are going to shade in up to the 80%.  Now we can easily see that 80% of 20 is 16.  To relate this to a real-life example, we could say if you received an 80% on a test out of 20 questions (all worth the same amount), that means you got 16 questions right.

Example 2:

“What is 15% of 40?”  We are going to start by placing 40 at the end, above 100%.

Since 40 divided by 10 if 4, we can fill in the top number line by counting by 4’s.

If we want 15%, that would be a full box and half of a box.  A full box is worth 4, half a box is worth 2, so 15% would be 6.  15% of 40 is 6.

Example 3

What happens when out last number is not divisible by 10 like in the problem “What is 20% of 36?”  Start by placing 36 above 100%.  36 divided by 10 is 3.6, so we can fill in the top number line by counting by 3.6.  Shade in 2 boxes for 20% and see that 20% of 36 is 7.2.

Example 4

You can even use this visual for smaller percents.  For instance, what is 2% of 30?  We would place 30 above 100%.  Since 30 divided by 10 is 3, we would place a 3 in each box.  If 10% is equal to 3, then 1% would be one-tenth of 3 or 0.3.  If 1% is 0.3, then 2% would be 0.6.  2% of 30 is 0.6.

Using bar models will be monumental for your students understanding of what it means to take the percent of a number!  Once students practice solving percent problems this way, they will start to gain a deeper understanding of what it means to find the percent of a number.  Once that deeper understanding starts to happen, students can move to a more abstract way to solve percents problems such as the percent proportion.

~MN

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