27 is 20% of what? Huh?... Bar Models Save the Day

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Objective

SWBAT compare quantities using percents.

Big Idea

students work independently and in groups to draw bar models and set up proportions to compare percents.

Do Now

10 minutes

Students enter silently according to the Daily Entrance Routine.  Their Do Now assignments are already on their desk and they begin working silently. They are turned over to the blank side and as students file in they are asked NOT to turn the papers over. There is a timer displayed on the SmartBoard with 2 minutes set. Once all students are seated with pencils in hand, I say “ready, set, go!” and students race to complete each percent fluency question on their paper.

At the end of 2 minutes, I ask all students to raise their pencils in the air and gracefully put them down on the floor between their feet. Then they are asked to take out a pen. I review the answers to the first ten and then switch over to cold calling for the rest of the answers. I stop reviewing answers after #28, the furthest question a student in class reached.

Paycheck points will be awarded to students who completed at least #1 – 22. Those who got all of these problems correct will earn 2 points, and those who made some mistakes will earn 1 point. Students are asked to submit their papers for paycheck points at a table in the back of the room. 

*Note: These materials were created using resources on the NY State Education website www.engageny.org

Guided Practice

15 minutes

Most of the material used in this lesson includes samples and word problems from engageny.org. To access the teacher materials uploaded on this site, click here. We transition to class work by opening to the class work section of our binders. I distribute the worksheet and instruct students to read the first problem. They are asked to come up with at least one question if they do not understand how to do the problem. If they think they do know how to solve, they are asked to try it. This gives me time to distribute all class work, ensure that students are staying organized, and not allow students to sit by idly. Most students do not understand what this question is asking them to find. I introduce the bar model visual strategy:

Step 1: Draw a bar

Step 2: Label 0% and 100%

Step 3: Label the percent in question and any known quantity(ies)

Step 4: Label the unknown with a variable.

Step 5: Use proportions to find the unknown.

I explain to students that they must be constantly thinking about the percent, the whole, and the piece. That whole’s can be represented as quantities and as 100%. Other questions to ask during a check for understanding include:

  • What does 100% represent in this problem?
  • What does the piece represent in this problem?
  • What is the “whole” in this problem?
  • How do you know you need to find the percent in the problem?
  • What proportion could I write to solve this problem? Is there another way to write a similar proportion?

I model the first question, guide students through the second question and ask them to complete the third question independently. During independent work, I walk around to ensure students are drawing bar models and using them correctly to write and solve proportions. 

 

Task

15 minutes

Once students have correctly completed the third problem they are welcomed into booths to work in groups of 2 to help each other through the questions on the "Task". The expectations set are the following:

  • Students must work independently for most of the work
  • Students may ask their partners for help; interactions should remain at about 30 seconds to no more than one minute. A timer will be displayed on the board to help students keep time.
  • Volume should be no higher than a whisper.
  • Students may raise their hands to ask questions about the problems.

 

After working this way for 10 minutes, individual students will be asked to come to the front to display their work. I ask other students to copy their proportions on the board next to each problem if they showed a different proportion.

Closing

10 minutes

During the last 10 minutes of class I will ask those students to explain their work on the board, or to explain how they arrived at a different proportion. The following lists questions I use to push students to analyze and evaluate the work on the board, MP3:

  • What does the variable in [student name]’s proportion represent?
  • What is the “whole” visualized in the bar model?
  • What is the “piece” visualized in the bar model?
  • Which quantity corresponds with x%?
  • Which quantity corresponds with 100%?

 

Once there are 5 minutes of class left I ask students to pack up and I distribute homework.