Area or Perimeter Hands-on Learning

Area vs. Perimeter

This lesson is a custom lesson designed by me.  Please give credit where credit is due when sharing.

     I have taught area and perimeter for years and students seem to always have trouble telling me the difference no matter how many examples we talk discuss so I have created this assignment.  It starts off pretty vague at first so that students will have to think and figure things out.  I do not tell them the real purpose of the assignment until they have completed it.  

1.  First have a classroom discussion on what is the difference between area and perimeter.
1. Have several students give their explanations.
2. Have several students give examples.
1. perimeter
1. picture frame
2. boarder around a room
3. fence around your property
4. window frame
2.  area
1. The carpet covering a floor
2. The amount of grass covering a yard
3. The concrete slab for the basketball court
4. All the land covering a piece of property
2. Once that is done hand out a piece of graph paper to each students.

Sheet of Graph Paper
I prefer 1 cm Size for this assignment

1. Tell the students that for this assignment they will only be concerned with perimeter.  You want them to draw as many polygons as they can that have a perimeter of EXACTLY 20 cm (equivalent to 20 ft in real life).  Remind them that they are NOT counting boxes,a as this would be area, but are counting each cm line as 1 unit and in real life we are going to consider that 1 cm = 1 ft.  There is a good chance many students are confused at this point so I give an example.  The example I give is the easiest one so they will have time to think and figure out others by themselves. 

Make sure that they label they units.

2.  Now tell them do draw as many as they can in 10 minutes.  If you have students that quickly get several done you can quietly tell them to try and draw irregular polygon shapes.  If you have students that are stuck (I usually ask them to try for a couple minutes before I give a hint) ask them to tell you the different ways you can use two numbers to make ten. Often you will find these students DID NOT participate and copy the example that you already gave.  Encourage them to do the example first so they may understand better.

1 + 9, 2 + 8. 3 - 7 and 4+6. They should have  already did 5 + 5, if not encourage them to do it now.

3.  At this point I like to walk around the room and make sure students have at least 4 or 5 drawings.  I also encourage students who rushed through or are quick workers to try and figure out a few more.  Most papers should look like below.

I would have this student ad the cm to all of the polygons that he left it off from.  I also would  express an interest in the fact he drew an irregular shape polygon.

4.  At this point, after making sure all the students have draw their 20 cm polygons, you can proceed to the next step.  Ask what the measurement of the perimeter of each polygon the students drew is (everyone should have 20 cm polygons).  At this point I would let tell them now we are going to focus on area.  I want you to find the area of each shape.  Each square is 1 sq cm (or in real life 1 sq foot).  I explain to the they can write the area as 5 x 5, but when we are discussing construction we would verbally says 5 by 5.  The formula for rectangles and squares is length times width or side times side.  For the irregular shapes they will need to divide them into smaller rectangles to figure out the area.  Depending on your time and level of your students, you may just have them count the squares.  I also point out at this time that although the perimeter was 20 cm, the area for the 5 by 5 square is 25 sq cm.  Just as they multiply  5 x 5, the are also multiplying cm x cm which results in sq cm.

When this step is completed their papers should look like the example below.

Again make sure that they have labeled the area as sq cm or cm squared.

5.  At this point start a discussion on what students noticed.  Hopefully you will find that students noticed that a 20 cm perimeter can have different areas.  Talk about what if you hired them to put up a dog run in your yard.  The only thing they knew was that you wanted it to be 20 cm perimeter and they did not confirm area and built a 9 x 1 dog run.  You own a Great Dane, how happy are you going to be?  They have to make another trip out to fix the dog run, how happy will their boss be? What are the advantages and disadvantages of each one?  The irregular one could put a dog house in the tiny part or their food and water.  Give each student about 5 minutes to decide which type of dog (or any pet if you like) they would put in which dog runs.  Why did they pick the one that they did?  What breed of do do they plan to put in their dog run?  Let them draw a pet in their enclosure and share with their shoulder buddies are come up and put it under your Elmo so they have a chance to explain their pet and design to their classmates.

  Rescued Tiger

Enrichment Activity

Design an enclosure for an animal sanctuary (a place that takes sick or injured animals and makes them better).  Do the research on how big an enclosure that endangered animal you pick needs to get enough exercise each day. What type of things does your animal need?  A bear may need a swimming pool, a tiger may need something to play with, and a monkey might need something to swing from for fun.  You choose your animal and do research on it.  Then design a proper habitat for the animal that the sanctuary will be satisfied.  Be very detailed and take your time. 

Resources:  Graph Paper from Worksheetsworks  or waterproofpaper

Ducksters Polygons Definition