Michelle Schade INDIAN TRAIL MIDDLE , PLAINFIELD, IL
6th Grade Math : Unit #3 - Ratios and Proportions : Lesson #21

Percents and double line diagrams and tape diagrams (Day 1)

Objective: SWBAT to visually represent a percent to solve problems.
Standards: 6.RP.A.3c MP1 MP2 MP3 MP4 MP6 MP7 MP8
Subject(s): Math
60 minutes
1 DO NOW - 15 minutes

The worksheet for this section has students looking at numbers out of 100 and making a direct correlation to percents.  This is a great review of yesterday’s learning and will set them up for today very nicely.  When students complete their worksheet, be sure to have them compare answers with a partner so they have time to talk mathematically about their solutions. (SMP 3)

2 Using tape diagrams, grids, and double number lines - 30 minutes

Ask students to discuss with a partner how a 10 x 10 grid could represent 200 people? 1 square = 2 people ) (student may have difficulty understanding that the whole can be more than 100 when representing a percent). If students are having trouble, back up the discussion and ask them how a 10 x 10 grid can represent 100 people? (1 square = 1 person) Bring them forward and ask them again the initial question again.

Next, show them a tape diagram and have them discuss with a partner how could a tape diagram represent 200 people? I will be giving them a model in their notes that is already made because some students may have difficulty determining accurate and appropriate segments on a tape diagram.

 The tape diagram is familiar to some students as they have used this before, but called them fraction bars. The tape diagram gets seperated in to parts.  Each part represents part of the whole.  Since a whole is equal to 100%, then the tape diagram would equal whatever whole we were dealing with.  In this example, the whole represents 200.  I'm asking students to use their benchmarks (25,50,75%) of the whole.

Finally, show them a double number line (already made) and have them discuss with a partner how a double number line could represent 200 people?

The double number line is going to be new to students and they will be reluctant to use it on their own.  Explain to students that the double number line represents comparisons of two different quantities.  Each part of the number line shows one of the quantities.  I like to draw one number line with one quantity on top and the other on the bottom.  If students have difficulty using the double number line, draw a rectangle around it to show them that it works the same way as a ratio table. 

How to videos
Developing a Conceptual Understanding

I've created some videos to show how to use the tools for Ratios and Proportions.

 

Videos:  Tape diagrams, double number lines, and ratio tables.

3 Finding 25% of a number - 20 minutes

During this part, I’m going to have students find 25% of 100, 200, 60, 20 and 500.  Students can use the tape diagram, ratio table or a double number line.  I want them to answer the following questions: 

Record the fraction represented by your diagram

What pattern can you see

What conclusion can be drawn

(SMP 4,6,7,8)

Students should be able to say that all fractions represented are equal to ¼ = 25% and depending on the whole amount 25% could represent a different quantity.

Next, students will need help with this part, have them write the following number sentence

25% of _____________ = ___________________.  They will write this for each of the scenarios.  (25% of 100 = 25 and so on)

During this part, point out that when we find 25% of a number, that number is the whole amount.  The result is the part. 

4 Closure - 20 minutes

Have students find 10% of the numbers (100, 200, 60, 20, and 500).  I chose 10% because it is a commonly used percentage and helps us find other percentages very easily.  Students can use their diagram of choice, however, I would remind them that when finding 10% of a number it may be helpful to divide the segments into 10 equal parts.  Before letting them loose, I would ask them why I say that.  (10 x 10 = 100)  To check further, ask them how many equal parts would be needed to find 20% of a number? (5).  Have students work on finding 10% of each number.  When they are finished working, I'm going to have the students partner up with someone that used a different strategy.  They can discuss how the strategy worked, what they found out and say “I know that 10% of ____________ = _______________.” To offer an extension, for students who need it, I would have them find the percent of more challenging numbers (240 or 175).  The students working at a higher level can partner up to check their work.