Tuesday, May 7, 2013

Perimeter Problems and Area Art!

As you may have figured out, math is a true passion of mine as is finding ways to push students' thinking about math (and other things!) and put them in situations where they need to problem solve, cooperate, and persevere!

We are a few days into a mini unit on area and perimeter, and we have been doing a number of "hands on" investigations.  The CCSS states that fourth graders need to:

"Apply the area and perimeter formulas for rectangles in real world and mathematical problems."

It would be very easy to look at this and think, "Man--the area and perimeter formulas are pretty simple . . . I'll teach them those, do a few problems about carpet and grassy fields and we should be good to go!"  The simple fact is, we must remember that true understanding of mathematical concepts involves careful study, a variety of investigations, and applying new learning in a variety of ways.  Over the last week we have built shapes with one inch times, used cheese crackers to find rectangles with certain perimeters, and used grid paper to explore different perimeter and area questions.

Today I decided to ask students to apply some of the learning we have done to moderately open ended task.  Here is the task I gave them:

Students could use the open space at the bottom of the investigation sheet or sheets of grid paper to work on finding the 3 rectangles that would fit the rules.  Students busied themselves guessing and checking, sketching and figuring, and then asking someone to "prove" whether or not the rectangles they found did, indeed, fit the rules.  I walked around asking questions and having students prove to me with numbers and/or drawings that their three rectangles worked.

Some students crossed off efforts that weren't successful.  Others wrote comments like "too small" or "perimeter too large".

Things went along pretty smoothly for most, but we did have some work to improve along the way!  Two students were really struggling with the guess and check method and were having a hard time visualizing the different types of rectangles that can be made with any given perimeter.  I asked, "What do you do when you get stuck?  You've already tried a picture--now what?" and after a short pause . . .

Victory!  We want students to be able to draw from a wide range of strategies to help them get "unstuck" and that's just what happened.  Within a few minutes, the tiles magically arranged themselves into a great solution!

Another student was really struggling keeping track of perimeter as he counted.  He had learned a good strategy . . .

but he kept losing count and was getting a different answer each time.  I asked him how he thought he could better keep track so he didn't keep losing his place.  He really didn't have any ideas, so I gave him a little think time.  Eventually I asked, "What do I do when I am solving a problem that is a little tricky or has lots to remember?"  He lit up and said . . .

"You write stuff down!"

 . . . and so he did!

Success!  This simple strategy helped him see that he did, indeed, have the right answer!  He just couldn't keep track of it in his head.

So here's where it gets fun!  As a few students began to finish, I called a time out and brought the group together to explain the next steps.  (You thought we were finished, right?)  We talked about the measurement unit we just finished, and I explained to them the next step would be for them to BUILD their rectangles with 1/2 inch wide strips of paper.  We reviewed the definition of a rectangle and I asked the students to experiment a little with using the strips to build exact models of the rectangles they had just found.

They measured . . . 

and cut . . .

and arranged in rectangles!
As they built them, I reminded them to ALWAYS check their work with the ruler and lo and behold, many students were finding that their perimeters were no longer correct!  I asked them to brainstorm at their tables and finally someone noticed that they would have to overlap the corners or else it ADDED length to the sides.  It took some convincing for some students--but over time, all students were able to build their three rectangles.  Finished, right?

NO!  I am a HUGE believer in taking pride in one's work, so guess what we did?  We glued those rectangles down to make geometric art and we displayed them proudly in the hall for all to see!  Check out some of our finished work!

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I love to find ways to combine problem solving, art, hands on learning, questioning, and teamwork, and today was a blast!  One of my easily frustrated students said as he hung up his work, "This project was the perfect amount of challenge for me!"  I couldn't agree more!

Want to see all of these resources in one place plus MORE?  I have put them all together in a fun resource that has everything ready at your fingertips!  Also check out the fun area and perimeter task cards below.


  1. What a great activity. It looks like so much fun. I am going to try this with my class.

  2. This is a fabulous activity! I will for sure have to try this next year! I love that it is interactive and the students are creating something that really shows "math". Very cool!
    Middlehood Madness

  3. Thanks! The kids LOVED it--and now all the other fourth grades have decided to do it as well. We will have a bright and cheerful hallway by the end of the week! :)

  4. I LOVE this activity! I think I may need to try this very soon with my kiddos! Thanks for the great inspiration!

    Mathematically yours,
    Jamie aka MissMathDork!

  5. I love this idea!!! I'm filing it away for next year.

  6. This is a great idea! I love it. Some of my students are struggling with area and perimeter, and it makes a nice art project!


  7. This is truly marvelous! I saw it on pinterest! Going to use this with two of my students, who REALLY need a refresher on area and perimeter of rectangles. I wonder if it couldn't be applied to triangles as well? I am going to use the black paper too, but I am going to have them put it in their math notebooks. Thanks so much for this great application of a math concept so important to memorize and understand!

  8. What a wonderful project! I think my kids would really enjoy building and it would challenge even my most proficient students. Thanks for the great idea to apply such an important skill.

  9. On your investigation paper you say "perimeter between" do you make them find a rectangle in between the two numbers or if they come up with a perimeter that is one of those numbers. For example on rectangle #1, could they do a 2X6 rectangle with a perimeter of 16 inches and an area of 12 sq. inches??

  10. Thank you for this post. I am an Art Appreciation parent volunteer for my son's 4th grade class and we did this project. It was a challenge but the kids were able to complete, and we all had fun!

  11. This is fantastic! I am doing research for an interview and this is very inspiring :) Thank you for sharing.

  12. I love this activity! We are doing area and perimeter in math right now and will be trying this out! Thank you!


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