Area and Perimeter Relationships & Problem Solving, part 5

Area and Perimeter are difficult math concepts that kids usualy learn in upper elementary. As teachers, it can feel overwhelming to tackle all of that content. I’m breaking down the perimeter and area standards into manageable chunks in this blog post series.

Part 1:Teaching Area Concepts

Part 2: Measuring Area & Multiplication

3: Composing & Decomposing Area and The Distributive Property (coming soon!)

Part 4: Teaching Perimeter

This is Part 5: Area & Perimeter Relationships and Problem Solving

Standard:

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

8. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters

I’ve broken perimeter down into two sections here. Part 4 was understanding perimeter and solving problems with perimeter on its own. In this part, we’ll tackle the relationship with area and perimeter. But it’s much easier to understand the relationship between area and perimeter if you’re familiar with both of those things first, of course!

This is another fun one, in my opinion! It’s time to make lots of rectangles and explore and figure things out, and that’s my favorite kind of math.

Overwhelmed?? I’ve spent hours and hours (like soooo many hours) thinking about this and creating a math unit so you don’t have to. Get my Perimeter & Area Math Unit here.

Concept: distinguish between linear and area measures.

If you’ve been playing along at home, this one should be pretty much done at this point! I always introduced this in the beginning, before even teaching area. That seems important to me because up until this point, kids have only really worked with linear measurement. I like to make it clear to them at the beginning of the unit that we’re now in uncharted waters and learning a new way of measuring. (They’ll learn a third way in 5th grade, when they tackle volume.)

Concept: rectangles with the same perimeter and different areas and vice versa.

The goal here is for kids to look for the relationship and to make generalizations about the relationship between area and perimeter.

This is a fun concept that gives kids a chance to explore and come up with their own ideas and understandings.

If you need an idea for how to manage all of this exploration, here’s what I did:

-break the kids up into groups of 2-4.

-assign each group an area or perimeter to investigate. (Definitely do these on two different days!!)

-give them scissors, crayons, and lots and lots of grid paper.

-let them see how many different rectangles they can make with their assigned perimeter or area.

-give them a chance to present their findings to the group. If you have a class that large or you’re short on time, they can make a display on a desk or bulletin board and the other students can circulate, museum-style.

-lead a conversation about how they figured out the rectangles, how do they know they have them all, what did they find, etc.

-Kids can write exit tickets with their ideas for accountability & assessment.

-After you’ve had one day with same perimeters and one day with same areas, have the kids compare the two and discuss if they see any relationships.

**the question will inevitably come up of whether 5×8 and 8×5 are the same rectangle or not, and that will lead to plenty of good discussions. The answer doesn’t really matter, in my opinion, but it’s a great way for kids to think critically and develop deeper concepts.

Overwhelmed?? I’ve spent hours and hours (like soooo many hours) thinking about this and creating a math unit so you don’t have to. Get my Perimeter & Area Math Unit here.