Using Strip Models to Explain Percent

A strip model shows a percent by dividing a bar into 100 equal parts, or into 10 parts of 10 percent each. Shading the parts you want turns a percentage into something you can see and count.

Step-by-Step Guide Using Strip Models to Explain Percent

1. Understand the problem: Read the problem carefully and identify the information provided and the information that needs to be found.
2. Draw a strip model: Draw a strip divided into equal parts, with each part representing a certain percentage. The strip can be divided into 100 equal parts, with each part representing 1%.
3. Identify the whole: Identify the total amount or quantity that the percent represents.
4. Shade in the appropriate number of parts: Shade in the number of parts that represent the percent. For example, if the problem states that an item is 20% off, shade in 20 parts of the strip.
5. Label the shaded parts: Label the shaded parts with the percent or fraction that they represent.
6. Use the strip model to find the part or whole: Use the strip model to find the part or whole by counting the number of shaded parts or the number of unshaded parts and multiplying by the whole.
7. Write the final answer in a complete sentence: Use the information from the strip model to express the final answer.

Using Strip Models to Explain Percent, Examples 1

1. We are given that the shirt is on sale for 30% off and the original price is $60.
2. Draw a strip divided into 100 equal parts.
3. Identify the whole: The original price is $60.
4. Shade in 30 parts of the strip
5. Label the shaded parts: 30%
6. Use the strip model to find the part or whole: 30% of $60 is $18
7. The sale price of the shirt is $60 − $18 = $42.

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Using Strip Models to Explain Percent, Examples 2

Using Strip Models to Explain Percent, Examples 3

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Which Model Shows 20%?

A model shows 20% when the shaded part is 20 out of every 100 equal parts, which is the same as 1 out of 5 or 2 out of 10. All of these show 20%:

• A strip with 10 equal parts and 2 parts shaded (2/10 = 20%).
• A strip with 5 equal parts and 1 part shaded (1/5 = 20%).
• A strip with 100 equal parts and 20 parts shaded.
• A 10 × 10 grid with 20 of the 100 squares shaded.

To check any model, divide the shaded parts by the total equal parts and multiply by 100. A strip with 4 of 20 parts shaded is 4 ÷ 20 × 100 = 20%. A strip with 2 of 5 parts shaded is 40%, not 20%. The parts must all be the same size, or the model does not show a percent correctly.

Three Kinds of Percent Problems with a Strip Model

A strip model works for every type of percent problem. Draw the strip, label 0% to 100% along the top, and write the amounts underneath.

1. Find the part: What is 40% of 80? Split the strip into 10 parts. Each part is 80 ÷ 10 = 8. Four parts show 40%, so the answer is 4 × 8 = 32.
2. Find the percent: 15 is what percent of 60? Split 60 into 4 equal parts of 15. One part is ¼ of the strip, so 15 is 25% of 60.
3. Find the whole: 12 is 25% of what number? A 25% piece is one of 4 equal parts. If one part is 12, the whole strip is 4 × 12 = 48.

Choose the number of parts that makes the math easy: 10 parts for multiples of 10%, 4 parts for 25%, 5 parts for 20%, and 2 parts for 50%. The same drawing also works outside percent. In earlier grades, students use it to show a whole split into known and unknown parts, such as 24 split into 15 and a missing piece of 9.

Frequently Asked Questions

What is a strip model in math?

A strip model is a long rectangle that stands for a whole, split into equal sections to show parts of that whole. It is also called a strip diagram, tape diagram or bar model. For percent, the whole strip is 100%, and each section is an equal share, such as 10 sections of 10% each. Shading sections makes a percent easy to see.

Which model shows 20%?

A strip split into 5 equal parts with 1 part shaded shows 20%, because 1/5 = 20/100. So does a strip of 10 equal parts with 2 shaded, or 100 parts with 20 shaded. When choosing between pictures, make sure the parts are equal in size; a strip with unequal sections does not show a true percent.

Which model shows 40%?

Look for a strip with 2 of 5 equal parts shaded, since 2/5 = 40/100. A strip of 10 equal parts with 4 shaded shows the same amount. If the strip stands for 60 students, each fifth is 60 ÷ 5 = 12, so 40% of the students is 2 × 12 = 24.

How do you solve percent problems using strip models?

Draw a strip for the whole, split it into equal parts that match the percent, and label what you know. To solve 25% of a number is 18, split the strip into 4 parts, since 25% is one fourth. One part is 18, so the whole strip is 4 × 18 = 72. The same picture works for finding a part, a whole, or a percent.

How do you model 100 using a strip model?

The whole strip stands for 100, or 100%. Split it into 10 equal sections and label each one 10, so the sections count 10, 20, 30 and so on up to 100. Then any percent can be read straight off the strip: shading 7 sections shows 70%. With 100 tiny sections, each one would stand for 1%.