# Magic Vs, Exploring Area vs. Perimeter and Estimation

**Magic Vs**

My 3rd Graders have some issues with general number sense. They have moments of brilliance where the lights are on and everyone’s home, and other moments where the light is off and everyone’s on vacation. That being said, I think that a basic curiosity for math is hidden…DEEP, *DEEP* within them. I’m trying to pull it out…my newest tactic is using Magic Vs. Some people may not be familiar with these, or just not familiar with calling it Magic Vs in particular. If you’re curious, the idea came from here. I’ve decided I need to spend more time exploring NRICH over the weekend to find more post-test activities.

I decided that I’d help guide them through the first example, and we started simple using 1,2,3,4, and 5.

My students are constantly in awe of my artwork…

With some pretty heavy guidance we got through the first one so I decided to challenge them a bit with the next one.

Magic V 7-11

It clicked that they should put the largest number in the middle rather quickly and everything flew from there. They really understood the fact that they couldn’t put 9 and 10 together or 7 and 8 because they’d never be able to balance it out with what they had left.

**Exploring Area vs. Perimeter**

We moved onto exploring area and perimeter. I started them off with 16 tiles each and asked if they could make a square. We played around with the different numbers and figured that since 4 x 4 = 16, we’d be able to make a square because all the sides would be equal. This was really intuitive to them which was great. After asking them to find the perimeter (and getting answers ranging from 12-18) we slowed down to define perimeter. Once we landed on the correct perimeter we wrote down the dimensions and the area/perimeter. We had a brief discussion about how the perimeter could be changed without the area changing. None of them believed me that they could be different. We then made rectangles that were 2 x 8 and 1 x 16 and figured out area and perimeter. The light bulbs were definitely on.

Can perimeter be different when a shape has the same area?

……

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“OOOOOOOH I get it Mr. Jones”

**Our Next Installment of Estimation**

These blocks aren’t going to estimate themselves…

I decided to incorporate some error bounds for the kids this time. They had to pick a “Too Small” number that was bigger than 25, and a “Too Large” number that was smaller than 400. Then they had to make their estimates…So far my range of guesses goes from 27 to 350. I’m concerned about both of those extremes, but I guess with time we’ll get better with our estimation… Any suggestions are welcome. Outside of practice, I don’t know how to get them better at estimating.

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Matt, Interesting idea to provide the kids with the error bounds, especially with the actual blocks. This has been our first year digging into the estimation180 activities, and we’ve struggled at times with communicating the idea of “wrong answers, but not unreasonably wrong”, which is what I think you’re getting at with your concern for their extremes. This is a great scaffold for that.

I hope it will help them to get more comfortable with visualizing and estimating. As time goes on I think I may only show them either the too high or too small and eventually pull both of them entirely.

I think that they are so tentative giving the “wrong” answer after years of focusing so hard on being “right”. I try to get them to understand that the concepts are more important than the answers but I’ve been unsuccessful so far. I think it just comes with time, and I suspect that the work the kids are doing outside of my room could be undermining those efforts.

I just found your blog today-love it! For estimating, I’ve had pretty good results when we practice each week using the same estimation jar. Every week we talk about precision and I find their estimates get progressively less “scary”. Interestingly, as they get better at estimating concrete things, their estimates on abstract problems get better too. Here’s a blog post from early last year that shows what we do: Our Estimation Jar