CCB Mathematics pages 236 - 241
Understand ratio concepts and use ratio reasoning to solve problems.
Analyze proportional relationships and use them to solve real-world and mathematical problems.
Write percents as either decimals or fractions to solve Problems
Use proportions to solve percent problems
Decimals, fractions, and proportions can be used to solve percent problems.
In this lesson, students learn how to find the percent of a number, and how to use proportions to solve percent problems. To determine student readiness, write proportions on the board, leaving a numerator or denominator in either fraction empty. Ask students to find the missing values.
Explain to students that they can use proportions to solve problems involving percents. The basic form of a percent proportion is part/whole=%/100. Point out that if someone scores 95 points out of 100 points on a quiz, his or her score can be written as 95/100 or 95%.
- Percent of a Number
- Use Proportions to Solve Percent Problems
Evaluate Reasoning: Ask students to describe an experience in which they purchased something that came with a discount. Have them explain how they determined what their savings were. Ask: What did you do to evaluate the problem? What process did you apply to the problem to find your answer? Was your solution reasonable? Then have students read the text and work with partners to evaluate Silvia’s reasoning. Afterward, ask volunteers to share their reactions to Silvia’s reasoning.
Use Percents: Have students read the sidebar and complete the activity. Then have students list the steps they used to solve the percent problems using the proportion. Have them exchange summaries with another student and discuss any differences they find.
Retell Solutions: Have volunteers retell how to identify the part, whole, and percent in a problem. Provide feedback, giving students time to revise their explanations. Allow other students to retell other parts of the lesson as time allows.
Compare Discounts: Ask students to imagine being in a department store and being confronted by two possible purchase options: A $40 sweater is on sale. What is the better discount: 45% off the original price or 25% off the original price and another 20% off the discounted price? Have students write to explain their answers, and encourage them to share their work.