Finding Percent of a Number with Diagrams
Lesson 5 of 8
Objective: SWBAT find percent of a number by drawing a double line diagram.
Think About It
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:
- has units labeled for each number line
- shows the 0 candy bars/0% relationship
- shows the 40 candy bars/100% relationship
- has evenly spaced hatch marks
- has partitioned the percents by multiples of 25%
- has correctly partitioned the candy bar numbers
- has answered the question
Intro to New Material
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:
- to give students the opportunity to practice using double number lines with percents with immediate feedback from me
- to have a whole-class conversation about which percentages to pick when partitioning the bottom number line
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.
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
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.