Percentage Equations

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SWBAT find percent of a number by writing and solving an equation.

Big Idea

To find the percent of a number, you can set up an equation to find an equivalent ratio to the part out of one hundred.

Think About It

8 minutes

Students work independently to complete the Think About It problem.  If I notice that students are spending a long time on the simplest form column in the organizer, I will give the whole class a cue to move on to prompts below the chart.

After student work time, I show a completed table on the document camera.  Most students will have been able to fill in all of the boxes, and I am simply giving them a way to check their responses.  

I then ask for a student to show his/her double number line on the document camera and explain the work.

Finally, I ask for ideas on the last question.  Some students may name using scale factor, which is a more efficient way to solve.  Some students will see the relationship between 25% and dividing by 4.  I take 2-3 hands for this question.

I then frame the lesson by letting students know that we'll continue our work with ratios and percents.  In this lesson, we'll use equations to model the problems, which are more efficient than double number lines and tape diagrams.  

Intro to New Material

15 minutes

To begin the Intro to New Material section, I create a double number line for the first problem.  I do this quickly, as students are proficient with this model.  I create the double number line because I want students to see that the relationships we'll use in our equation are also found on the double number line.  The equation is a different way to organize our work, but the end result is the same.

Because of our previous lessons, students know that percents are always out of 100, and that percents can be expressed as ratios that display the part over the whole.  I ask students what we know in the first problem, and whether this is the total number of serves or a portion of the serves.

I have students organize their work in 2 lines.  The first line is where students write the percent as a fraction, and then simplify.  In this problem, students do not have to simplify in order to create equivalent fractions.  I have them do it anyway.  I want them to always check to see if they can simplify (and this is a skill that my students can always use reinforcement with).  The second line is where they will create their equivalent ratios.  You can see my work on this notes page.   

I then lead students through the second problem.

Partner Practice

15 minutes

Students work in pairs on the Partner Practice problem set.  A student work sample is included.  As students are working, I circulate around the room.  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 4 in this set.  I ask for hands from people who feel very confident about their work.  Many hands will go up.  I ask for an answer, and almost always, I will get 2 ounces as an answer.  I'll point to a few kids and ask, 'do you agree?'  Students will say yes.  I then will tell the class that I do not, in fact, agree with 2 ounces and suggest they should go back and re-read the problem.  This problem gives students the information about the percent that is radioactive, and asks for the number of ounces that are not radioactive.  It's a great moment that highlights the importance of reading carefully and annotating the problem.

Once the 'oooooh' moment has passed, I tell students that I can think of two strategies to use to solve here.  Pretty quickly, students will raise their hands to suggest we subtract the radioactive ounces from the total.  I then have students turn and talk with their partner about another way we might solve.  I'm looking for students to realize that we can use 90% in our ratio, to find the portion that is not radioactive.

Students then complete the Check for Understanding problem independently. 


Independent Practice

20 minutes

Students work on the Independent Practice problem set. 

For Problem 3, I am looking for students to identify that David put the 80 in the numerator, and not the denominator.  I want students to clearly identify this mistake, and not give a more vague response, like 'he set up his fractions wrong.'

For Problem 9, I want students to access their number sense.  If I see students setting up two equations (to find 75% of 48 and 20% of 100), I will affirm that doing the work is always a great strategy.  I will then ask them to reason through this problem without the equations.  I'll ask, 'is there any way to figure this out before getting to the step of creating equations?'

There are two extension questions in this problem set, which ask students to find percentages over 100.

Closing and Exit Ticket

7 minutes

After independent work time, I bring the class back together to discuss Problem 11 from the Independent Practice set.  I have students share with their partners what Kimani needs to do, in order to solve this problem. 

Students complete the Exit Ticket independently to close the lesson.