# Finding Percent of a Number with Diagrams

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## Objective

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.

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

## 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?

• How did you create your double number line?
• How did you determine the value of the part?
• 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.