Fluency with Percents

Examples, videos, and solutions to help Grade 7 students find 100% of a quantity (the whole) when given a quantity that is a percent of the whole by using a variety of methods including finding 1%, equations, mental math using factors of 100, and double number line models.

New York State Common Core Math Grade 7, Module 4, Lesson 6

Worksheets for Grade 7

Lesson 6 Student Outcomes

• Students solve various types of percent problems by identifying the type of percent problem and applying appropriate strategies.
• Students extend mental math practices to mentally calculate the part, the percent, or the whole in percent word problems.

Lesson 6 Classwork

Opening Exercise
Solve the following problem using mental math only. Be prepared to discuss your method with your classmates.
Cory and Everett have collected model cars since the third grade. Cory has 80 model cars in his collection, which is 25% more than what Everett has. How many model cars does Everett have?

Example 1: Mental Math and Percents
a. 75% of the students in Jesse’s class are 60 inches or taller. If there are 20 students in her class, how many students are 60 inches or taller?
b. Bobbie wants to leave a tip for her waitress equal to 15% of her bill. Bobbie’s bill for her lunch is $18. How much money represents 15% of the bill?

Exercises

1. Express 9 hours as a percentage of 3 days.
2. Richard works from 11:00 a.m. to 3:00 a.m. His dinner break is 75% of the way through his work shift. What time is Richard’s dinner break?
3. At a playoff basketball game, there were 370 fans cheering for school A and 555 fans cheering for school B.
   a. Express the number of fans cheering for school A as a percent of the number of fans cheering for school B.
   b. Express the number of fans cheering for school B as a percent of the number of fans cheering for school A.
   c. What percent more fans were there for school B than for school A?
4. Rectangle A has a width of 8 cm and a length of 16 cm. Rectangle B has the same area as the first, but its width is 62.5% of the width of the first rectangle. Express the length of Rectangle B as a percent of the length of Rectangle A. What percent more or less is the length of Rectangle B than the length of Rectangle A?
5. A plant in Mikayla’s garden was 40 inches tall one day and was 4 feet tall one week later. By what percent did the plant’s height increase over one week?
6. Loren must obtain a minimum number of signatures on a petition before it can be submitted. She was able to obtain 672 signatures, which is 40% more than she needs. How many signatures does she need?

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Lesson Summary

• Identify the type of percent problem that is being asked as a comparison of quantities or a part of a whole.
• Identify what numbers represent the part, the whole, and the percent, and use the representation
• A strategy to solving percents using mental math is to rewrite a percent using 1%, 5%, or 10%. These percents can be solved mentally. For example: 13% = 10% + 3(1%). To find 13% of 70, find 10% of 70 as 7, 1% of 70 as 0.7, so 13% of 70 is 7 + 3(0.7) = 7 + 2.10 = 9.10.

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