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

Converting Fractions to Percents

10×10 grids are a great tool when introducing percents because they provide a visual for fractions that are out of 100.  Before starting the lesson, discuss with students that the word percent means,  “out of 100.”  As soon as we have a number out of 100, we have a percent.  Percents are a useful tool for comparing because they make every number out of the same thing, 100.  It is much easier to compare 80% and 90% than to compare 4/5 and 9/10.

Have students represent 3/100 by coloring in 3 squares out of 100.  “What percent is this?”   Since 3 are shaded in out of 100, this is 3%.

Have students represent 3/10.  Discuss how the fraction means 3 out of 10, therefore we need to start by breaking our whole into 10 equal groups.  Students may do this differently and that is fine, as long as they have 10 equal groups.

Once students have 10 equal groups, have them shade in 3 of the 10.  Then ask, “what percent is this?”  Since percent is out of 100, we have to think, how many are shaded in out of 100, or how many of the tiny squares are shaded in.  Students should see that 30 out of 100 are shaded and therefore 3/10 = 30/100 or 30%.

Have students represent 3/4.  We need to start by breaking the whole into 4 equal groups.  Again, students may break the whole into fourths differently which is fine, as long as there are 4 equal groups.

Then have students shade in 3 of the 4 groups.  Ask, “what percent is this?”  Since there are 75 shaded out of 100, 3/4 = 75/100 = 75%.

Have students try several examples like this until they have a strong understanding of how fractions and percents relate.  It is so important that students get a visual when making sense of fractions and percents.

~MN