James Tanton’s candy dividing exercise

Yesterday we watched the “tie folding” part of James Tanton’s latest video:

The video led to a great project with the boys last night:

James Tanton’s tie folding problem

The boys knew from the video that the method could also be applied to sharing candy. Since we didn’t watch that part of the video I was wondering if the boys could figure out the connection on their own. Here’s the start:

Next we tried an example to see what would happen if our initial guess was a big over estimate of 1/3 of the Skittles:

Since we were struggling with our second time through the procedure in the last video, I thought it would be fun to try to be more precise in how we split the piles. That extra precision did lead to slightly better results.

So, a really nice math activity. It was really fun to see the procedure work when we couldn’t be totally sure we were actually dividing the piles in half. Such a great project for kids.

James Tanton’s tie folding problem

Saw a great new video from James Tanton today about folding a tie. The kids had spent yesterday hiking in New Hampshire and were a little tired, but Tanton’s project made for a perfect little afternoon project.

I’ll present the videos in the order that we did them, so Tanton’s video is the third one below. Showing his video later in the project will also give you a chance to think through the problem without spoilers.

Anyway, here’s how we started -> what do you have to do to fold a tie in half?

I was super happy with how the introductory problem went because at the end of the last video my older son said that he thought folding the tie into thirds would be hard. Well . . . that’s exactly what we are going to try to figure out!

Next we watched Tanton’s video. He talks about both folding ties and sharing candy, but for today at least we are just focused on the tie folding part:

Now we tried to replicate Tanton’s procedure. My 5th grader had a little bit harder of a time understanding the procedure than my 7th grader did, but they both eventually got it.

At the end we talked about why they thought the procedure worked.

So, a super fun project and a really easy one to implement, too. So many potential extensions, too – might be neat to see how kids approached folding into 5 parts after seeing Tanton’s video, for example.

Thanks for another great project, James!

What I was hoping for with the boys and math

When I started making math movies with the boys my goal was to show other kids what kids doing math can look like. There are examples everywhere of adults doing math, so kids can see those examples with no problem. There aren’t nearly as many examples of what it looks like when kids work through problems, though.

So, 5 years into it we are all pretty comfortable in front of the camera and my younger son – just by luck – is making exactly the videos that I was dreaming about in the beginning.

Below are the last two ones we’ve made. They show him working through algebra problems. Nothing fancy, nothing speedy, but really nice work through the problems. I love the way he thinks through problems and think that other kids might enjoy these examples showing what a kid doing math can look like.

 

 

A fun project from Art Benjamin and the Museum of Math

Yesterday Art Benjamin gave a talk at the Museum of Math. One neat tweet from from the talk was this one:

It is a pretty neat problem and I thought it would make a fun project for the boys today. I didn’t show them the tweet, though, because I wanted to start by exploring the numbers with increasing digits:

 

Next we tried to figure out what was going on. My older son wanted to try to study the problem in general, but then my younger son noticed a few things that at least helped us understand why the sum should be divisible by 9.

 

For the third video we started looking at the problem in general. The computations here tripped up the boys a bit at first, but these computations are really important not just for this problem but for getting a full understanding of arithmetic in general.

 

For the last part of the project we looked at two things. First was returning to a specific example to make sure that we understood how borrowing and carrying worked. Next we applied what we learned to the slightly different way of multiplying by 9 -> multiplying by 10 first and then subtracting the number.

 

After the project I quickly explored Dave Radcliffe’s response to MoMath’s tweet:

It took a bit of thinking for the boys to see what “works in any base” meant, but they did figure it out.

I love this Benjamin’s problem – it makes a great project for kids!

Returning to Patty Paper Geometry

I had a busy week at work last week and didn’t plan ahead for today’s Family Math. Luckily we’ve got plenty of math books laying around and the boys grabbed Patty Paper Geometry off the shelf. My younger son thought that the project exploring the interior angles of polygons would be fun, so we jumped in:

The thing I love about this geometry book is that you really can just jump right in. The methods of folding and tracing in the book really are an incredible way to introduce kids to geometry.

With the introduction out of the way, here’s how the book shows kids that angles in a triangle add up to a straight line angle:

The last topic we did today was an exploration of the angles in a quadrilateral. The approach was the same as for the angles in a triangle and gives an easy demonstration that the angles add up to 360 degrees:

The projects in this book are great – can’t recommend it enough!