Ratios and Percents

Students work in pairs on the Think About It problem. Students are familiar with the idea of 50%, and know that it means the price of the shirt will be 1/2 off.  

Part B, with the 25%, is more foreign to students.  It is okay here if kids are not sure how to find how much Jose will save on the jeans.  Some students guess that 25% means Jose will save $25.  There are students who will share that 25% is equivalent to 1/4, and that 1/4 of 40 is $10.

I frame the lesson by letting students know this is the last part of our Unit Rates and Percents unit.  This is the first of several percents lessons.  In this lesson, we'll use double number lines to find a percent of a number.

After I fill in the quick notes in the Intro to New Material section, I model how to create the double number line for the first example.  You can watch and listen to me create the model for the first example here.

For the second problem, I ask for students to help me with the steps.  I'll use guiding questions, like, "What do we need to divide 200 by?" This form of question tells students what the next step is, but asks for their help in executing it.  By the third example, I am cold calling students, asking simply, "What's next?"  The class completes the third example without my help.

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

• Are students using the correct intervals for the percentages?
• Are students using the correct intervals for the part/totals?
• Are students writing their work in the work space, when arithmetic is needed?
• Are students answering the asked question(s)?
• Are students working systematically/designing appropriate diagrams?

I'm asking:

• Explain the percentage found. 
• How did you begin looking for a percentage?
• Why did you set up your double line diagram like that?
• What quantity represents 100%?
• How did you know what to count by for each number line?
• Why did you divide by ___? 

After 10 minutes of partner work time, students complete the Check for Understanding problem on their own.  I circulate as they work, and look for a double number line that is accurate and well-spaced.  I show the work on the document camera and highlight the strengths of the model.

Students work on the Independent Practice problem set.  

Problem number 4 can be tricky for kids, as they create their model.  There is no need to partition the percents into further intervals; the number line can have 0, 50%, and 100%.  Some students will want to break the number line into 10s or 25s.  This is okay.  As they work, though, I will show them how the model can work with just 50% and 100% shown.

Some students will ask to use scale factor, rather than list out all of the relationships.  For this lesson, I want students practicing finding each piece.  We'l need fluency with the percents and double number lines for our upcoming lessons.  

 An Independent Practice sample is included here, from a mid-level student.

After independent work time, I bring the class back together for a discussion around Problem 10.  I pick this problem for two reasons:

1. There are multiple ways students could construct the double number line (partitioned into 10%, 25% or 50%), and I want to talk about all of these methods.
2. We're working as a class on giving really strong evidence to prove or disprove someone's work.  

Once we've discussed the options for the double number line, we construct an exemplar written response for this problem.  Students then complete the Exit Ticket to end the lesson.  An exit ticket sample is included here.