Building Understanding of Perimeter and Area

Using six squares...
How many different shapes can you make?

Back in the old days of 3rd grade math we would teach kids the rule for perimeter; the distance around.  Then we would teach the rule for area; the number of squares that cover it.  After that we would teach a couple cute ways to remember the difference between the two and move on to another topic.



Instead of using math to solve problems in a book, we REALLY want kids to DO math.  The goal is to build a conceptual knowledge of perimeter and area; so they will be able to solve real life problems.  For this type of knowledge to be fostered, it's important for young kids to play with and figure out these concepts on their own and with others.

So the challenge began with each partnership having the same number of square units and needing to find all the different shapes they can create; the squares must be joined on at least one side.  Records are kept on grid paper with notes taken in their math notebooks.  I love listening in on the interesting discussions about whether certain shapes were the same if they were turned a different direction or not.  Of course I wouldn't tell them yes or no; but as a group we came to the conclusion that  just turning a shape doesn't make it different, with lots of examples demonstrated to prove their point.

Next we will dig into the difference between area and perimeter.  I'll pose this problem:

• If you needed to figure out how many toothpicks would go around your shape, how could you do it?  Do all the shapes need the same number of toothpicks?

I'll let you know what they discovered soon.