Finding the Whole with Diagrams

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SWBAT find the whole, given the part and the percent 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

Students work in pairs on the Think About It problem. 

After 3 minutes of work time, I bring the class back together.  I ask the class how this problem is different from the problem in the previous lesson.  Students will name that in this problem, we do not know the total amount but are instead given a part.

I then cold call on a student to show his/her double number line on the document camera.  The class gives positive and critical feedback on the number line as we work together to get to the answer.

I frame the lesson by letting students know that we'll continue our work today with percents and double number lines.  In some of the problems in this lesson., we'll be looking for the whole when given the percent and a part.

Intro to New Material

15 minutes

The steps students are taking to solve the problems today are very similar to the steps in the previous lessons.  Therefore, I run the Intro to New Material section more like a guided practice.

For the first problem, we talk about the appropriate benchmark percents to use to split up our number line.  I have students respond to the prompt about Mr. Cerna on their own, and then we share out all of the different ways students chose to explain that there are not enough seats on the bus. 

You can see and hear me talk through Example Two from this section here.  Our class discussion includes time talking about using 10% or 20% as the benchmark fractions

Partner Practice

15 minutes

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

  • Are students explaining their thinking to their partner?
  • Are students writing their work in the work space?
  • Are students working systematically/ designing accurate diagrams?
  • Are students correctly identifying whether or not they are trying to determine the part or the total?
  • Are students answering the question asked?

 I am asking:

  • How did you determine the benchmarks for your number lines?
  • How did you draw your double number line diagram?
  • How did you know that you were given the part or total and were looking for the part or total?
  • How do you know that your answer is reasonable?
  • Ask clarifying questions if there are disparities between both number lines; check to see if computation is performed correctly.

After partner work time, students complete the Check for Understanding problem independently.  A CFU sample shows what student work could look like.  Once students have had 3 minutes to model this problem, I ask the class if anyone tried something that didn't work.  Students may share that they initially partitioned the percent number line by 30s.  Another might share that they placed the 4 as the whole, and not the part.  

Independent Practice

20 minutes

Students work on the Independent Practice problem set.

Students can use multiples to partition their number lines, or they may choose to use scale factors.  The student samples show three different ways my students chose to model problem 1.

In both the Partner Practice and the Independent Practice problem sets, there are a mix of problems - some ask students to find the whole, while some ask students to find the part.  As I circulate, I am watching to be sure that students are correctly identifying what they are given and what they're being asked for. 


Closing and Exit Ticket

8 minutes

After independent work time, I bring the class back together for a conversation about their work.  I ask for two students to name a problem they'd like to hear the entire class talk about.  We then work through each of those problems as a class.  My role in this conversation is to facilitate - I keep the conversation going, but have the students complete the work.  I ask things like 'what's next,' and 'how do you know.'

Students independently complete the Exit Ticket to close the class.