Lesson 21
Percentages and Tape Diagrams
Lesson Narrative
In previous lessons students used double number lines to reason about percentages. Double number lines show different percentages when a given amount is identified as 100%, and emphasize that percentages are a rate per 100. In this lesson they use tape diagrams. Tape diagrams are useful for seeing the connection between percentages and fractions. For example, this tape diagram shows that 25% of a whole is the same as \(\frac14\) of that whole by showing that 25% of the whole is one part when 100% of the whole is divided into four equal parts.
![A tape diagram showing 4 parts with each part worth 25% for a total value of 100%. The first piece is colored in.](https://staging-cms-im.s3.amazonaws.com/srGZJTewVg3NA4JBvF1e66tB?response-content-disposition=inline%3B%20filename%3D%226-6.3.D1_Image_1.png%22%3B%20filename%2A%3DUTF-8%27%276-6.3.D1_Image_1.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T053041Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=df820684e327a1b960e985fadda6c1f6578c81b00bd70675e6b340bba9b7a0aa)
Tape diagrams are also useful in solving problems of the form \(A\) is \(B\%\) of \(C\) when you are given two of the numbers and must find the third. When reasoning about percentages, it is important to indicate the whole as 100%, just as it is important to indicate the whole when working with fractions (MP6).
Learning Goals
Teacher Facing
- Choose and create diagrams to solve problems such as A% of B is ? and A% of ? is C.
- Draw and label a tape diagram to represent a situation involving percentages.
- Interpret tape diagrams that represent multiplicative comparisons and express such comparisons using fractions and percentages.
Student Facing
Let's use tape diagrams to understand percentages.
Learning Targets
Student Facing
- I can use tape diagrams to solve different problems like “What is 40% of 60?” or “60 is 40% of what number?”
CCSS Standards
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