Tuesday, November 6, 2012

5th Grade Math Unit: Area, Perimeter, Volume of Prisms and Pyramids, Polygons and Circles

5th grade math unit 3 (which you can see listed in my subject specific page for MATH) is a huge unit. It covers area and perimeter, the volume of rectangular prisms and pyramids, polygons up to ten sides, and circles. The main bits of this unit get down to the vocabulary, practical application of the necessary formulas, and conceptual understanding of each concept.

The unit is available at its own page HERE, and is also posted here in its entirety. So without further delay:

5th Grade Mathematics Unit 3 is all about 3-Dimensional Geometry, including Area, Perimeter, Volume, Attributes of Polygons up to 10 sides, Circles, and Parallel / Perpendicular Lines. It's a big unit, but we always manage to pull it off with pretty good results. So let's get right to it!

Unit 3 is split into three portions:


The first portion of this unit is very simple, it's all about area and perimeter. We spend the majority of the time doing area and perimeter of quadrilaterals (especially area), but it's also a good opportunity to refine measuring skills by going outside, in the hallway, or measuring the classroom.

The assessment that I use for this cycle of instruction is very simple, and can be found HERE.

The PDSA (again, it stands for Plan/Do/Study/Act, and is the current form of lesson planning that my school does) can be found HERE.

Now that the nuts and bolts are out of the way, I'm going to list some great online resources that could help any teacher out in the classroom when teaching area and perimeter:

First off, I have already done a fairly lengthy post on Area & Perimeter, titled Area & Perimeter Teacher Resources: Worksheets, Games, and Activities.

And to repeat some of what I've already posted:
  • Interactive Shape Explorer: A nice interactive where students find the perimeter and area of various, randomly generated regular and non-regular polygons on a grid. Optionally, the teacher can ask students to copy the shapes on graph paper and solve there.
  • The most simple classroom activity is to have students measure the dimensions of the classroom, a chalkboard, the hallways, their desk, etc. Then use those dimensions to find perimeter and area (and later on, volume). 
  • Everything You Wanted to Know About Perimeter and Area: Go to pretty much any resource listing on perimeter and area activities, and you'll probably find a link to this one. There's a reason for it, it's simple and effective. It's Smartboard/projector friendly for whole class, and teaches as it goes.
  • Cyberchase Airline Builder: An online game where students must use the given amount of sticks to create different polygons. 
  • Zoo Designer: I wasn't impressed with this game at first glance, but played it for a few minutes and actually see some value in using this in class. This one is also web based.
  • Real Estate and Perimeter Game: I found that at the blog Homeschool Parent. It's a good idea for a very effective in class perimeter or area game. I'll be using this, my students always enjoy the partner games.

I've always enjoyed teaching volume, because it just makes perfect sense right after teaching area, and it's fun and the students usually enjoy the process.

Let's get started with the assessment, which can be accessed HERE (you'll need to download it to see the attached images, they don't seem to show up in the Google Doc preview), and the PDSA, which can be accessed HERE.

First, I'm going to list some basic volume of rectangular prism (and just general volume) links:
Now, my favorite volume activities include making cubic units. I usually have my class use rulers to make a cubic foot, yard sticks to make a cubic yard, etc. I'm not even going to show a picture here, because all you do is use the given unit to make a cube. It's pretty cool and effective.

It's also important that students know how to use the units. I count off if students don't label units, and don't use them appropriately. I teach my students very simply that for a unit to be squared, it has to involve 2 dimensions, cubed involves 3. Here's a simple visual:

I also think it's important to expand and reinforce these concepts when applicable. My students always enjoy the EXPONENTIAL GROWTH activity, where we build some cubes, starting with a 2x2x2, going to a 4x4x4, then an 8x8x8, it looks like this:

Now on to the more difficult volume of pyramids:

It's actually very simple to find the volume of a rectangular pyramid. First, take the three measurements (length, width, height), and multiply. Now here's the catch: divide your answer by 3. That's it. The majority of the work here is getting students to understanding this 3:1 relationship, and practice it.
In my opinion, these first two sections of the unit go hand in hand, and are fairly simple for 5th graders to get once they grasp the concept. And the concept is important, let them experiment with 3D shapes (make them out of paper and fill them up with sand or rice). These are more or less developmentally appropriate skills for the vast majority of kids at this age level. 

Now, we move on to the final portion of this section on volume of pyramids, where we discuss the attributes of three-dimensional shapes, including vertices, faces, and edges. 

We're basically talking about vocabulary for this final section, so that's how I approach it. Let's move right into it:
So now we come to the finale of this lengthy unit, a set of lessons on polygons (up to 10 sides), and circles. The circles part especially tends to rock the kids around for a bit. 


Here we go, let's get started with the assessment HERE and the PDSA HERE.

First we'll deal with the polygons, because again, it comes down to vocabulary and practice (i.e. memorization and matching):
OK, now we finally come full... circle (haha... nevermind). Anyways, students will learn radius, diameter, circumference (and all applicable formulas), as well as the value of pi to two places. 

The pi part again comes down to repetition and memorization. So, I came up with the now irreverent "PI MONKEY," a mainstay in my classroom. He hangs up near the front door, beckoning to the students each time they walk out the door:

Now that pi monkey has done his job, it's time to teach some circles!:
Remember that circumference is simply pi multiplied by the diameter (or pi multiplied by the radius x 2): It looks like: C= pi x d  OR C= pi x (r x 2). It's fairly straight forward. 

OK, we've reached the end, FINALLY. Now that we're here, it's time for the big unit test. You can grab that HERE.

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