Perimeter vs. Area

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to review what they know about perimeter and area.  One misconception that students may have is that if two figures have the same area, then the figures will automatically have the same perimeter.  I’m looking for students to calculate the perimeter and area to prove that although all three designs have the same area (6 square yards), they have different perimeters.

I call on a student to share one idea.  That student then calls on the next student to share his/her idea.  I encourage students to build on what their classmates have said by using sentence starters like, “I agree/disagree with __________ because…” and “My idea connects with ____________’s idea…”  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

My students are familiar with perimeter and area of squares and rectangles from earlier this year.  We can quickly review the definitions and formulas.  Massachusetts give students a formula sheet on the state test, so I have students use it in class to get comfortable with using it as a resource.

 I ask students, “Why are area and perimeter important? How could we use these skills in our lives outside of school?” Students participate in a Think Pair Share.  Students can usually connect perimeter and area to designing and constructing rooms/yards/buildings/etc.  

I have students work independently the problems about the pool and then have them share out.  A common struggle for students is determining when to calculate perimeter and when to calculate area.  I continue to return to the definitions: when we find area we are covering a figure, when we find perimeter we are finding the distance around a figure.  Another common struggle is that students falter when the dimensions include fractions and decimals.  

I look to see whether students are accurately calculating with the decimals.  I draw pictures for each problem to show what is going on.  For #1 I will draw an arrow around the outside of the pool to imitate someone walking around.  For #2 I will shade in the pool to show what a cover would do.  I push students to explain why their answer is correct and I make sure that they are using the correct units.  Students are engaging in MP6: Attend to precision.

Note:

• Before this lesson I Post  A Key.

I have a student read over the directions.  I review expectations and students start working independently.  Students are engaging in MP2: Reason abstractly and quantitatively and MP6: Attend to precision.

As students work I walk around to monitor student progress and behavior.  I look to see how students work with the problems that involve decimals and fractions.  I take note of particular problems that many students are struggling with.  If students are struggling, I may ask them one or more of the following questions:

• How can you use a picture to show what is going on?
• What are you trying to figure out?
• Do you need to calculate the perimeter or the area?  Why?
• What strategies do you have for adding/multiplying fractions/decimals?
• Why did you use those units?

When students complete their work, they raise their hands.  I quickly scan their work.  If they are on track, I send them to check with the key.  If there are problems, I tell students what they need to revise.  If students successfully complete the chart they can work on the challenge questions. 

In order for students to be prepared for this unit, they need to be familiar with vocabulary about angles.  We watch the Angle video and take notes.  My students don’t need to know about supplementary and complementary angles, so I stop the video early.  

After the video I will have students model the various angles using their arms.  During the geometry unit I have my students model angles and lines with their arms, which can turn into a quick, fun game of Simon Says.  Brain Pop videos have other resources, one being quizzes.  My students enjoy taking the quizzes as a way to review the material they just saw and gain confidence about the vocabulary.

For the Closure, I have students flip to a problem that I noticed students struggled with.  For instance, I may have students look at problem 3 because one of the dimensions is 20 ½ feet.  I ask for students to share their strategies for solving this problem.  Students participate in a Think Write Pair Share.  I call on one student to start and then that student will share his/her idea and call on another student.  I encourage students to make specific connections to each other by saying “I agree with __________” , “I want to build on what __________ said”, or “I disagree with ________________ because”.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.      

I pass out the Ticket to Go and the HW Perimeter vs. Area..