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.

How Much IS 1,000? Do 3rd grade kids know?

Kids are always intrigued by the measuring tape, but this
group took it a bit further, stretching them all out to see
how many TOTAL CMs.  It was easier counting than some
of the groups, but stretched out further.

Our current focus in math is place value; actually reading, writing and representing numbers to 1,000.  Yep that's right out of the CORE.  Over the years, I've discovered that kids learn to put numbers into the right "places" and read these numbers quite easily.  The tricky part comes with understanding what these number REALLY represent.  How much is 1,000?

How much is 1,000?

Naturally our class had an EXPLORATION of the number 1,000.  I started the ball rolling by setting out our money bin and a recording sheet with different currency (bill) amounts.  I DIDN'T include 100 dollar bills.  Kids took some time with the money and figured out a way to make $1,000.  Some industrious kiddos took on the task of figuring this out for each currency.  They did lots of counting, sorting and discussing related to 1,000…hee, hee, her!!  Don't you love it when they're doing great math thinking and don't even know it?

All of our meter sticks, plus the discovery
of a RARE yard stick that threw off the
easy counting!!!!

The day before we LOOKED for and CREATED a chart of things that we had MORE THAN 1,000 of in the classroom.  I taught some quick estimation strategies, but it was hard to know if they really knew what 1,000 was…so...of course, we dug even deeper.

This partnership did some awesome counting, sorting
and even recorded their data on sticky notes so they
wouldn't forget.  Just so you know, these are a couple
boys who tend to get off task and have been know to
cause a bit of trouble.  Nice to know that ACADEMIC
ENGAGEMENT works better than BEHAVIOR CHARTS!

Small groups or pairs of kids started to explore different areas in the room.  Each group was given or chose a set of objects to count; so they could prove it was more than 1,000.  I must admit that THE TEACHER was even surprised that some of these collections weren't even 1,000.

Cooperative counting, putting together large numbers;
yet it is still not 1,000 Rainbow Tiles:0)

We had MORE than 1,000 words, of course my groups of
words are no longer organized for word work…sigh.

Once again digging into the numbers helps to build a solid conceptual base.  Next we'll look at the number line and how these big numbers fit together.

Good to know that we have MORE than 1,000 books in our
classroom library.

Math Strategies: But do I HAVE to think?

How do we get children to the next level in their learning?  Is it possible to take them from learning steps and procedures to thinking, REALLY thinking?  In math we've been exploring strategies for adding numbers.  One strategy was to use a number line, they could break the numbers apart into different jumps, but needed to show their thinking.

With the whole community together, we explored a few different methods.  It seemed as though the kids were getting the idea; so I had them do one on their whiteboard to see their individual thinking.  The results were quite interesting for a few kids...I wish I had pictures, but I'll show you what they did.

This was their "thinking" or "lack of" related to putting together  two numbers.  

Since they HAD to use a number line these kiddos decided to put one number to start and make hops to the end.  Funny enough when I asked, "How much money would you have if you had $38 in the bank and got $49 more dollars?"  After a bit of thought they came up with the the exact dollar amount.

Fast forward to today's math lesson - thinking!!!  We had a great discussion about how the most important part of math is thinking about what you're doing and why.  I reminded the kids that our strategies are there to help us figure out and understand what we are doing, but we NEED to THINK if what we are doing makes sense.  So we rolled up our sleeves and approached addition strategies again.  I'm happy to say lightbulbs went on and they were really thinking through different ways to put together numbers.

Don't let number lines get to you and your kids.  They are an amazing way to get kids discussing and thinking about numbers.  I'm getting ready to dive into finding the difference on a number line, wish me luck!!!

I've put together some problems for math notebooks involving number lines, number sense and place value.  Adding and subtracting on a number line is "IN PROGRESS".

Digging into Learning (Teacher's Pay Teachers Store)