Percent Problems in Context
Lesson 13 of 20
Objective: SWBAT solve different types of problems involving percentages in real world context.
To start off today's lesson, my students will complete 3 problems reviewing the concept of equivalency between fractions, decimals, and percentages. They will also complete two simple percentage problems. One will require that they find the percent of a number the other will require that they find what number a given quantity is a percentage of.
This curriculum reinforcer is designed to transition smoothly into today's engagement activity as well as today's exploration piece. Both of which involve the concept of percentages.
Please see the PowerPoint attached to this section for the problems for the Curriculum Reinforcer.
During the engagement piece of this lesson, we will discuss the meaning of the word percent. This discussion is for the purpose of transitioning into today's instruction where students will actually use the meaning of the word "percent" to solve problems mentally.
What I mean by, "use the meaning of the word percent." is, after students come to the conclusion that percent means "per one hundred" or "for every one hundred." Then we will go into some scenarios where they will have to use this concept of per every one hundred to figure out a given percentage when presented with a specific quantity.
This portion of the lesson is very brief and is a simple and easy way to prep students for what is to come next.
For the instructional piece, I will first inform students of my expectations for today. To do this, we will go over the objective for today as well as the assignment that they must complete to sho understanding of the concept that will be taught during this lesson. Next, if necessary, I will teach students prerequisite skills necessary to fully understanding today's lesson. To do so, I will present a mini lesson on the following skills and concepts.
- Changing fractions to decimals and vice versa (use 4/5 for this example)
- Changing percentages to decimals and vice versa (use 35% for this example)
- Changing percentages to fractions & vice versa (use 60% for this example)
While I am presenting 3 mini lesson (if necessary), I must keep in mind that my focus for this lesson is to help my students gain the ability to change percentages to fractions. This is the skill that is necessary for the successful completion of this lesson
After presenting the mini lessons (if necessary), I will then, present students with a type of percent problem that they have previously encountered. I will use this problem to highlight mathematical truths surrounding the concept. The problem that I will use to do this is as follows:
- Jerry bought a jacket, a sweater, and a pair of shoes which came to a subtotal of $250. If Jerry has to pay 10% in tax, how much will Jerry pay in tax?
Using this problem, I will have students use the concept of ratio relationships to discover why it is possible to simply multiply $250 by 10% and arrive at the solution to the problem.
I will then present the same problem in a different way. See below:
What if the problem said this instead…
- Jerry bought a jacket, a sweater, and a pair of shoes. If, when purchasing these items, Jerry paid $25 in tax at a rate of 10%, what was the total cost of the items before tax?
I will ask students, "Can we solve this problem in the same manner as we solved the previous problem (i.e. by simply multiplying the quantity presented by the percentage presented)?" Why or Why not? To answer these questions, the students and I will do the following:
- Multiply the two quantities to see what we get ($2.50). We will discuss whether or not this solution makes sense (which it doesn't) and why it doesn't make sense.
- We will then set up a proportion to find the solution. During this time, I want students to raise their hand and tell me the differences they observe when setting up the proportion for this problem versus setting up the proportion for the previous problem.
- Students should notice that the given parts of the proportion are different and therefore require division rather than multiplication.
In completing these problems, I am looking for students to gain the understanding that finding the percent OF a quantity requires a different solution plan than finding the quantity when given the percent and the part of the quantity.
Try It Out
Earlier during this unit, I taught students how to use a 4-Step flow map to solve problems involving ratio relationships. Today, we are going to use that same flow map to solve problems involving percentages, as percentages are ratios and therefore the 4-Step flow map is applicable.
First, I will complete the following 2 problems to provide examples.
- 10 is 25% of what number?
- Country music makes up 75% of Landon's music library. If he has downloaded 90 country music songs. How many songs does Landon have in his music library?
Then, I will allow students to complete the next 2 problems, indicated below, on their own. After they have been provided with 4 minutes to complete those 2 problems, I will immediately provide them with the solutions to the problems so that they can check their work for accuracy and ask any questions to clear up misconceptions.
- 60 is 20% of what number?
- Peyton spent 60% of her money to buy a new television. If the television costs $300 how much money did she have?
To explore the concept of percentages, my students will complete a worksheet that presents this concept using simple problems as well as more authentic real-world problem solving questions.
I will provide my student swith 20 minutes to complete this worksheet. After the 20 minutes, the students will receive 5 - 10 minutes to confer with a partner about their work before students are chosen to close out the lesson with presentations of the problems.
The class will go over the worksheet as a whole. I will select a different student for each problem. Each student will come to the document camera and present their solution to the class. I will ask questions to ensure that they were deliberate in the manner in which they solve each problem. The types of questions that I will ask are as follows:
- How did you know that ____ was the ratio that needed to be used to find a solution to this problem?
- Explain why you set up your proportion in that manner?
- What method did you decide to use to solve your proportion?
- Did you provide a complete answer?
- Does your solution answer the question asked in the problem?
To explore the concept of percentages, I will have my students complete a task where they go, "shopping." The will be required to do the following in order to be successful:
- Choose at least 4 items but no more than 8 items
- Calculate the cost of your items after you are given a coupon and take into account the sale going on in the store at the time. Don't forget that you must include a 7% tax in your grand total
- Create a poster that features the items purchased as well as a receipt that you will create to show your calculations.
**NOTE: The document attached to this section contains the purchase items and the coupons that need to be passed out to the students. However, you will need to assign prices to the purchase items. It is good practice to assign the prices yourself based upon the ability of your students. Some students may need percentages and prices that are more easily calculated, such as prices with 5's or 0's at the end and no change... For example: $30.00. Other students may need a challenge. For this reason, you may give them prices that have numbers other than 0 and 5 and you might include change... For example: $23.97.
Closing This Lesson:
To close out this lesson, I chose three students to simply presented their posters to the class and talked about what pathways they utilized to arrive to their solution. I chose my students strategically based upon what I noticed during the time they spent solving the problem. I wanted each student to have something different to add to the overall understanding of the concept. For this reason, I chose students who did something different in arriving to their solution.
Using these presentations, the students had a thought provoking conversation that deepened their understanding of percentages and their application to the real world. I facilitated this conversation with strategic questioning and well placed comments.