Finding Percent of a Number with Diagrams

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SWBAT find percent of a number by drawing a double line diagram.

Big Idea

Percents are special ratios written as a comparison of a number out of 100.

Think About It

7 minutes

As today's class begins, students work independently on the Think About It problem.  I expect that students will be able to create a double number line and figure out how many chocolate bars Nathaniel ate, based on our work in the previous lesson.  

After 3 minutes of work time, I have a student share his/her work on the document camera.  As a class, we check to be sure that the model:

  1. has units labeled for each number line
  2. shows the 0 candy bars/0% relationship
  3. shows the 40 candy bars/100% relationship
  4. has evenly spaced hatch marks
  5. has partitioned the percents by multiples of 25%
  6. has correctly partitioned the candy bar numbers
  7. has answered the question

Intro to New Material

15 minutes

This lesson is an extension of the previous lesson.  Students will use double number lines to find the percent of a number.

In this lesson, students will need to partition their number lines using 10%, 20%, or 25% and will then need to use the number line to find a percentage that is a multiple of the benchmark percent (40% or 75%, for example).

In the Intro to New Material section, we walk through two examples as a class.  My focus here is two-fold:  

  1. to give students the opportunity to practice using double number lines with percents with immediate feedback from me
  2. to have a whole-class conversation about which percentages to pick when partitioning the bottom number line

Partner Practice

15 minutes

Students work in pairs on the Partner Practice problem set.  As they work, I circulate around the classroom. I am looking for:

  • Are students explaining their thinking to their partner?
  • Are students showing all of the appropriate work in the work space?
  • Are students working systematically/ designing accurate diagrams?
  • Are students using benchmark percents effectively to determine the value of the part?

I am asking:

  • How did you create your double number line?
  • How did you determine the value of the part?
  • How do you know that your answer makes sense?
  • Ask clarifying questions if there are disparities between both number lines; check to see if computation is performed correctly.

After 10 minutes of work time, we come back together as a class to discuss the first problem in this section.  First, I ask students how they chose to partition the number line.  Some students will have chosen to use multiples of 10, while others will have used multiples of 20.  I want students to see that either choice leads them to the correct answer.  

Students then work on the Check for Understanding independently.  After 2 minutes of work time, students turn and compare answers with their partners. 

Independent Practice

20 minutes

For Independent Practice, I ask my students to work on the problem set.  A sample of student work is included, to give you an idea of what my students work will look like.  Hear and see me complete a problem from the Independent Practice problem set here. 

As my students are working, I am making sure that their models have all of the components listed in the Think About It section of this lesson. 

There is a challenge question at the end of Independent Practice which can be used as enrichment for higher-level students.  It can also be used whole-class, to build problem-solving strategies and perseverance will all students.  

Closing and Exit Ticket

8 minutes

After independent work time, I bring the class together for a discussion about Problem 3.  I like Problem 3 because it requires students to analyze someone else's response.  Students need to not only compare their answer with Keith's, but then also supply a strong written response for why Keith is incorrect.  

Students then work on the Exit Ticket to close the lesson.  An exit ticket sample is included here.