Solving Percent Problems
Lesson 3 of 5
Objective: SWBAT solve percent problems.
The Do Now is a review of previous topics. Since students should be familiar with these topics, they will work independently on the problems.
1) Ciara planned to walk her dog for 2/5 of a mile. After it started to rain, she decided to walk only 1/3 of the distance. What fraction of a mile did Ciara walk her dog?
2) Find the difference 28 - 19.7182
3) Write 4 3/7 as a decimal. Round to the nearest hundredths place.
After 10 minutes, students will discuss the problems with their group.
Problem 1 - Students should understand that the wording "1/3 of the distance" means they need to multiply.
Problem 2 - Students should remember that 28 is equivalent to 28.0000. They may not line up the decimal points and borrow correctly.
Problem 3 - Students can change the mixed number to an improper fraction and divide or they can divide the fractional part and add the 4 wholes to their answer.
For this lesson, students will learn an organized approach to solving percent problems. We will use a Part Total Ratio Table strategy. Students are familiar with ratio tables and we will use this concept to solve percent problems.
Example 1 - What is 40% of 50?
What is this question asking?
It is important that students understand what the question is asking for, because it will help them verify if their answer makes sense. Students should realize that the question is asking for a portion of 50.
If I had 50 pencils, what is this question asking?
Students should understand that their answer should be less than 50 pencils.
Can we estimate what our answer should be close to?
Students should understand that 50% of 50 is 25. Therefore they can estimate that the answer will be close to but less than 25.
Let's start with the 40%. How can we break 40% into a part and total?
Students should recall that 40% can be written as a ratio out of 100. This will lead us to fill in the percent column of the table.
In this question, does 50 represent the part or the total?
In understanding what the question is asking, students have determined that we're missing the part and 50 is the total. We will complete the table.
Students should recognize this set up as a proportion.
How can we solve this proportion?
Students should use their previous knowledge and find a multiplicative relationship between the denominators to find the unknown value.
Does our answer make sense?
Students should verify that their answer fits their estimation.
We will continue on to more examples. Although each question is worded differently, I will use the same line of questioning so students can understand that ratio tables can work for all percent problems.
Example 2 - What percent is 12 out of 25?
Example 3 - 20% of what number is 80?
Example 4 - Lola was walking down Greene Ave. She found a wallet with $400 in it. When she returned the wallet to the owner he gave her $80. What percent of the money did she receive as a reward?
The Independent Practice is an opportunity for students to solve percent problems independently. I will encourage them to use their notes to help them. As students work I will circulate throughout the classroom to monitor and help students. Students have the most difficulty with filling in the table correctly.
1) 12 is what percent of 120?
2) 16 is what percent of 200?
3) 60% of what number is 90?
After 10 minutes, students will discuss and compare their work with their group. Students should agree on their ratio tables first and then check their mathwork. If there are any unresolved questions we will discuss the problems as a class.
To apply the concept of solving percent problems to topics that will be useful for students, I will ask the following question.
How can we apply percent problems to real world situations?
- shopping with coupons
- calculating tip
- sales tax