Finding the Total Using Percentage Equations

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SWBAT find the total given the part and percent by writing and solving an equation.

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 to solve the Think About It problem.  The problem does not ask students to use a specific model, so some pairs will use a double number line while others may attempt to use equivalent ratios.  

After 2 minutes of work time, I ask the class how this problem is different from the problems we solved in the previous lesson.  Students will name that we're given a part of the number, and not the whole.  

I frame the lesson by letting students know that in this lesson we will continue our work with using equations to solve percent problems, but today we will be using them to find the total given the part instead of finding the part like we did yesterday. We are going to continue using equations as this is the more efficient way to solve.

Guided Practice

15 minutes

Because students are using the same steps from the previous lesson, there is no Introduction of new material in this section.  Instead, I facilitate a Guided Practice with the class, before they work without my support. 

As we work through the two problems together, I use this opportunity to ask students about the reasonableness of their answers.  I want them thinking about benchmark percents and reasoning about how much larger the total should be, when given a specific part. 

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 writing the percent as a fraction, and then simplifying?
  • Are students correctly creating equivalent fractions?
  • Are students determining the correct answer?
  • Are students clearly labeling their units?
  • Are students answering the question(s) asked? 


I'm asking:

  • How did you know to use that ratio to represent that percent?
  • What did you do to simplify this ratio?
  • How did you create your equation?
  • What does the numerator of each ratio represent? The denominator?
  • How did you solve the equation to find the information the question is asking for?


After partner work time, I bring the class back together to discuss Problem 3, and focus on part B.  In Part A, students are generally able to determine that the performer earns $100 a day.  In Part B, students are asked how much the performer earns in 2 weeks at the Barclays Station.  There are two things here that students must do:  (1) convert 2 weeks into 14 days and (2) realize that they are working with the $40 a day that the performer earns at Barclays and not the $100 daily sum they figured out in Part A.     



Independent Practice

20 minutes

Students work on the Independent Practice problem set.  A student work sample is included here. 

Problem 5 gives students the whole, and not a part.  If students are not reading carefully, they may set 50 as the numerator, rather than the denominator.  They'll then find that there isn't a whole number multiplier they can use.  If I see students making this mistake, I will let them continue - I want them to hit a roadblock and then come back to the problem so that they can figure out their own mistakes. 

Problem 12 requires students to access their number sense and mental math skills.  If I see students trying to set up equations and solve for the values, I'll underline the words 'without solving' in the problem without saying anything.  

Closing and Exit Ticket

8 minutes

After independent work time, I bring the class together for a discussion about Problem 9.  First, I have students clap out their responses.  I then ask students if there were any answer choices they were able to eliminate right away.  We talk about why choices A and D cannot be correct.  I then ask students if, given choices B and C, they can determine the correct answer before creating an equation.  I then show the work from a student on the document camera, as an example of what the equation should look like.

Students work independently on the Exit Ticket to close the lesson.