Working with Percents

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Objective

• Define percent • Use diagrams and benchmarks to make sense of percents • Use ratio reasoning to solve real-world problems • Solve problems including finding the whole when given a part and a percent

Big Idea

What is a percent discount? Students apply their knowledge of ratios and percents to figure out which store has the better deal.

Do Now

5 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to review the benchmark fractions and translate them into decimals and percents.  From our work during the College Project, students should be able to quickly identify the missing amounts. 

I ask for a student to define percent.  I want students to remember that a percent represents an amount out of 100.  I declare that 0.1 is 1%.  I want students to realize that 0.1 is one-tenth.  When we create an equivalent percent, it must be out of 100.  I ask for volunteers to critique my reasoning. Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.  

Trash-ketball Challenge

7 minutes

Notes:

  • To play this game I have 3 baskets (trashcan, recycling bin, etc.) set up on one side of the room.  I place painter’s tape on the floor to show the spot where students must stand to shoot.
  • I collect scrap paper and put a stack by each group.
  • Each group needs two whiteboards and two whiteboard markers for the group recorders.

I arrange my class into three groups.  I ask for 2 volunteers in each group to be recorders.  One recorder will use tally marks and the whiteboard to track the total number of shots taken by their group.  The other recorder will use tally marks and the whiteboard to track the total number of shots that make it into the basket by their group members.    I explain that members that are shooting the paper balls will need to be behind the tape line.  If a group member does not follow the directions, he/she will be told to sit out.

I set the timer for one minute and tell the students to begin.  When the minute is up, we clean up and come back to our seats.  I ask the group recorders to share out their data.  Each student records the data in their table.  I ask students, “How can we find out which group won?”  Some students may say that the team who made the highest number of baskets is the winner.  Other students may create a fraction comparing the number of shots made to the total shots taken. 

I record the ideas and tell students that I want them to think about how we could determine the winner while we work on today’s lesson.  We will return to this question during the closure.

Percent Practice

10 minutes

I have students participate in a Think Pair Share about the meaning of percent.  I want students to remember that percent means an amount of out 100.

I tell students that a typical way they will have to use percents is to calculate sale prices when they are shopping.  Being able to find sale prices will help you get the best deal.  Introduce the formula as a way for students to understand the relationship between the original price and a discount.  The percent discount is the percentage subtracted from the original amount.

We go through problem 2 together.  I show student the percent bar diagram as a way to visually represent the information in the problem.  I ask students:

  • What fraction is equivalent to 50%?
  • What is 50% of $60?
  • If the headphones where 50%, how much would you pay?  How much money would you save?
  • What fraction is equivalent to 25%?  Where would 25% go on our diagram?
  • What is 25% of $60?
  • If the headphones were 25%, how much would you pay?

 

A common mistake is that students calculate 25% of $60 and list that as the sale price.  If I see this happening, I ask what it means for an item to be 25% off.   I want students to realize that they must first find the dollar amount that is equal to 25% and then subtract that from the original price.

I have students work on problem 3 in partners.  I walk around and monitor student work.  I call on a student to show his/her work under the document camera and explain his/her thinking.  I ask the class for comments or questions for that student.  I bring up any common mistakes or struggles that I observed while students were working.

Sale, Sale, Sale!

20 minutes

Notes:

  • Before this lesson, I use data from the pretest and/or the previous lesson’s ticket to go to Create Homogeneous GroupsStudents work in groups of 2-3.
  • I give each group a Group Work RubricThis way I can silently give them feedback on their cooperation throughout the work time.  This will be their citizenship grade for the day.

Students move into their groups.  I call on a student to read the situation.  I call on a different student to read question 1.  I tell students they have 2 minutes to talk with their group members and make a prediction.  Before they move on, they must write down their prediction.

As students work, I walk around and monitor student progress and behavior.  Students are engaging in MP1: Make sense of problems and persevere in solving them, MP2: Reason abstractly and quantitatively, MP4: Model with mathematics, and MP5: Use tools strategically.

If students are struggling, I may ask one or more of the following questions:

  • What is this problem about?
  • How many games do they want to buy?
  • Which games will be discounted 20%? Which games will be discounted 30%?
  • What is the deal at Games For You?
  • Does the coupon apply to the original price or the discounted price?
  • How can you find 10% of a price?
  • How can knowing 10% help you find 20% and 30%?

If students are struggling to draw a visual, I will have them look at the visual for problem 3 in percent practice.  They can use this as a reference.

If students need extension, I may ask them one or more of the following questions:

  • At Games For You, does it make a difference if you apply the coupon first and then apply the store discount?  Why or why not?
  • Let’s say you wanted to by a $10 game.  Would taking 25% off, then 30% off the game be the same as taking 55% off of the game?  Show and explain your thinking.
  • You buy a game at Games For You and you pay $15 before taxes.  What was the original price of the game?  Show and explain your work.

Closure

7 minutes

 For Closure I have students return to the question about the trash-ketball challenge.  I ask for students to share their thinking about how we can determine the winner.  I want students to realize that they could find the percent of shots made for each group.  The group with the highest shooting percentage is the winner.  This will be an opportunity for students to work with numbers that may not translate nicely into a percentage.  I ask students to share their strategies and their findings. Students are engaging in MP2: Reason abstractly and quantitatively.

Instead of a ticket to go, I collect student work and pass out the Homework.