Lesson Plan: Venn Diagrams & Word Problems
Grade Level: 7-8
Massachusetts Frameworks Addressed:
- Compare, order, estimate, and translate among integers, fractions and mixed numbers (i.e., rational numbers), decimals, and percents.
- Use ratios and proportions in the solution of problems, in particular, problems involving unit rates, scale factors, and rate of change.
- Use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems, e.g. multiplying by 1/2 or 0.5 is the same as dividing by 2.
- Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1).
- Select and use appropriate operations—addition, subtraction, multiplication, division, and positive integer exponents—to solve problems with rational numbers (including negatives).
Problem #1: Web Browsing Habits
A poll of 2,000 students revealed:
- 554 respondents only watch TV. They do not browse the Web while they watch.
- 1,200 respondents only use the Internet. The TV is not on while they're browsing.
Use the Venn diagram (below) to answer the following question:
- How many people watch TV and browse the Web at the same time?
Problem #2: Social Media
A survey of 1,200 college students reveals that 3/4 have a profile on MySpace, 3/4 have a profile on Facebook, and 1/2 have a profile on both sites. Using the Venn diagram below, answer the following questions:
- How many students have a profile on MySpace? (Whole number, not a percentage).
- How many students have a profile on Facebook? (Whole number, not a percentage).
- How many students have a profile on both sites? (Whole number, not a percentage).
Problem #3: Political Affiliations
In a recent poll of 400 registered voters, 40% said they have always been a Republican, 42% said they have always been a Democrat, and the remaining respondents said they have switched from one party to another at some point in their lives.
Answer the following questions:
- How many people said they have always been a Republican? (This must be a whole number, not a percentage).
- How many people said they have always been a Democrat? (Whole number, not a percentage).
- How many people have switched parties? (Show both the percentage and the whole number).
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