One of my all-time favorite (and most versatle) math manipulatives is the 1 inch color cube! I specifically have the foam version…. why you ask? Well, multiple reasons….
1) They are QUIET! A day full of manipulatives can lead to a head ache with repeated clicking and clacking!
2) They cannot be used as a weapon! If they are thrown, they may go about 2 feet because they are so light AND it’s foam people! If they do manage to hit a head, or other body part it just won’t hurt!
3) If you step on it, you won’t twist an ankle, or want to scream in agony (what? we’ve ALL stepped on a lego before… it HURTS!)
4) If you get one of the sides wet, you can push that same side against a white board and it will stick! Yep, no need for the “overhead” version or a document camera!!
Regardless, if you don’t have any, click on the link below and grab a set for your classroom. You won’t be disappointed!
Anyway, I was going somewhere with this! A few weeks ago (yeah, yeah…. spring got busy and I’m just now getting time to post this one… sorry!!) my 5th graders were working on Area and Perimeter in their math class. I had a bunch of kiddos who were really struggling seeing that Area and Perimeter were DIFFERENT but that one of the measures COULD have an effect on the other.
Enter, the foam cubes….
The class revolved around one relatively simple task…
Using ONLY 24 cubes, create as many different figures with DIFFERENT perimeters as you can.
What follows is a progression of pictures showing the thinking of my students.
The most common first creation around the table was the 4×6 array.
|4×6 array. Area = 24 square units. Perimeter = 20 units.|
Once the first array was made… others soon followed.
|2×12 array. Area = 24 square units. Perimeter = 28 units.|
And some more arrays…
|3×8 array. Area = 24 square units. Perimeter = 22 units.|
And another…. or is it? We had to stop and have a quick conversation about the 6×4 array. As a class we decided that while this array looked different, and the representation was different, that the perimeter stayed the same as the 4×6. We decided because we were not worried about representations but more so perimeters that we would considered a 4×6 and a 6×4 the same in this instance.
|6×4 array. Area = 24 square units. Perimeter = 20 units.|
and then finally two of my ladies came up with the last array…
|1×24 array. Area = 24 square units. Perimeter = 50 units.|
At this point, we took a moment and created an organized chart of what we had discovered (I confess that I forgot to take a picture of this , so here is my recreation…)
We had a really nice discussion about how the area remained 24 and the perimeters changed. AND THEN… one of the students noticed that if one side grew longer the other side had to shrink. This comment lead to someone noticing that the longer the longest side grew, the bigger the perimeter of the array was.
This seems so obvious to most people, but was a real ‘AH-HA’ moment for my kiddos.
After we had time to process this crazy new idea, I through them for another loop. I told them they weren’t finished finding ALL the figures. I mentioned that sometimes all the pieces don’t have to make a nice looking rectangle. And at the point, some were baffled…. then one kiddo built the below picture. And a discussion started…. did this figure follow the rules? was the perimeter the outside ‘fence’ OR was it the inside ‘fence’ OR was it both?!!?
|8×6 “frame”. Area = 24 square units. Perimeter = 28 exterior, 20 interior, 48 total.|
Then a student made a triangle-ish figure. We had to decide that this figure was one in which we didn’t know how to calculate the side length but we would learn in a few years once we understood square roots.
After about 5 minutes of trying to think outside the box (but still NOT quite getting there) one student suggested an idea. What if…. what if we started with an array and then just moved one block…. hmmmm…. so they all made a 4×6 or 6×4 and moved one block.
|4×6 or 6×4 with one block moved. Area = 24 square units. Perimeter = 22 units (for ALL figures where an exterior block was moved to another exterior position)|
Another student asked, “can you do that with more than one block?” I smiled…. and they went to work.
And they just kept creating….
And creating… Then someone said “the possibilities are endless!” I giggled and said, “maybe they are! but maybe they aren’t” and we decided to save that discussion for another day.
The next day, the students took their hands on (concrete) learning from the day before and turned it into a representational activity. Same task – Area of 24 different perimeters… the twist – all 10 kiddos had to have DIFFERENT perimeters. Whoever “found” a unique perimeter first, got to claim it for themselves.
They used pencil and paper.
And I used the smartboard to show how to count perimeter on a square coordinate grid.
And they started creating….
We had a blast creating and they thought VERY outside the box. Most of them decided to “write” letters with their blocks and quickly realized they were all getting the same perimeter.
We ended up spending 2 class periods creating our drawings and decorating them. Unfortunately, I cannot find the final product pictures 🙁 Bummer! Oh well, guess you’ll just have to try it out with your own kiddos! An easy, very inexpensive lesson that can be recreated year after year with amazing Ah-ha moment results!! Not too shabby, eh?
Super excited for how this lesson turned out! AND I’m even more excited to be apart of Meg Anderson’s new monthly link-up: LOVED THAT LESSON! I definitely LOVED this lesson! Make sure to click on the link below to go find other lessons people loved!
In case you mised LOVED THAT LESSON last month, you can find that link ups HERE