Fold and Punch

I’ve been spending a little time over the last week getting ready to run the Family Math nights at my younger son’s school. There are 5 nights – one for each of the grades K-5 (with the grade 4 and 5 night combined for some reason).

The way the nights run is that there are a bunch of intro activities for kids (and parents!) to do as they arrive and then 2 or 3 longer projects over the next hour. Three boxes filled with the intro activities from prior years were handed to me when I agreed to run Family Math night this year – and some of these activities are really great. For instance, there was this amazing coincidence when Anna Weltman tweeted the “H puzzle” this past weekend:

There was also a great activity called “Fold and Punch”:

I’m extra excited about this activity because one of the longer activities that I’m doing with the 2nd and 3rd graders uses Katie Steckles’ amazing video about the Fold and Cut theorem:

 

Here’s a link that has the 3 projects that we after watching Steckles’s video:

Our 3 fold and cut projects

Today I tried out the fold and punch activity with my 4th grade son. Here’s how it went:

 

Also, he kept working and finished the remaining 4 patterns when the camera was off. The way he did the last pattern was pretty clever. Hopefully you can see the folds he used, especially the one down the diagonal of the paper:

  

How did he get only 3 holes with those three folds? Well . . . half a punch 🙂

  

I can’t wait to see how both the fold and punch and fold and cut activities go with the 2nd and 3rd graders – such fun projects 🙂

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First root problems

My son had bit of a struggle with problem #18 from the 2007 AMC 10 b today. Here’s a link to the problem:

http://www.artofproblemsolving.com/wiki/index.php?title=2007_AMC_10B_Problems#Problem_18

and here’s the problem itself:

Screen Shot 2016-01-12 at 8.10.53 PM

Tonight we took a closer look at this problem.  He was able to solve it, but during the solution we had an interesting detour caused by the square root of 2.

Here are his introductory thoughts about the problem as well has his first steps toward the solution:

 

Next we went on to solve the equation he came up with in the last video:

\sqrt{2} x = x + 2

His idea for how to solve this equation is to square both sides:

 

After finding the answer to the equation, we went back to the original linear equation and found other ways to solve it. My son’s solution starting around 1:05 and going for maybe 45 seconds was fascinating to me. I hope that after this short little additional talk that he is more comfortable solving linear equations.

 

So, a challenging problem for sure, but it was nice to stumble on the little algebra trouble, too. Hopefully a little extra practice here and there will help him gain a better understanding of both algebra and geometry.