Digging Math

MATHS:  I'm still plugging away on my 8-week "How to Learn Math" class via Stanford and EdX. It's really about how to teach math. Professor Jo Boaler leads the class. She's British, and there, math = maths.  However you say it, the course is fantastic.  The lectures I listened to today were about number sense (looking at problems and thinking about ways to change or 'deconstruct' them to make them easier to solve) and having "math talks," where problems are solved via group discussion and comparing how students in a classroom got the answer - it's interesting hearing how many ways there are to get from A to Z.  And what it really demonstrates is how creative and dynamic math can be. It's not just about formulas and flash cards!

Part of my homework was figuring out three fun math problems. Of course, I employed the kids' in the process.  They were:

1) A man is on a diet and goes into a shop to buy some turkey slices. He is given 3 slices which together weigh 1/3 of a pound, but his diet allows ¼ of a pound. How much of the 3 slices can he eat while staying true to his diet? Give an answer and briefly explain your reasoning.
2) Charmaine and Tesha each have a number of cards, in the ratio 2:3. Tesha and Holly have a number of cards in the ratio 2:1. If Tesha has 4 more cards than Charmaine, how many cards does Holly have? Give an answer and briefly explain your reasoning.
3) If Jo takes 3 hours to paint a house and Sam takes 5 hours, how long do they take if they paint it together? Give an answer and briefly explain your reasoning.

We had fun solving them, drawing pictures and talking about potential answers, and made fairly short work of them. Then we watched professor Jo Boaler's explanation of each and instantly realized before she gave us the right answer that we completely, stupidly blew question number 3! Doh! But it was a 'good' mistake. Dr. Boaler would be the first to say that when you make mistakes, you're learning (atop the blog today is a graphic I designed as homework for the class a couple weeks back).  Anyway, on #3, we made the completely lame error of having our answer be more than 3 (I know, right?! LAME!). But after talking about it, I bet it's a mistake that none of us would make again (at least not anytime soon).
A couple of days ago I read a story in the Seattle Times that instantly made me think, "Fun math problem!"
The headline read: "Huge tunneling machine off to painfully slow start" and the subhead reported the Highway 99 tunnel machine has traveled only 24 feet since the drilling began a month ago.
http://seattletimes.com/html/localnews/2021696892_99tunnelxml.html


I had the kids read the story on the Times' site, and then asked them, "At the current progress rate that Bertha is digging, how long would it take the tunnel to be completed?"


They first gleaned numbers from the story they could use to solve the problem, such as what day Bertha started digging, what the date of the story was, and how much progress she's made over that time span.  They could then calculate the number of feet per day.

They also gleaned that when done, the tunnel is 1.7 miles long, and converted that into feet.  Then, since they knew how many feet (or fraction of a foot) Bertha digs each day on average, they were able to calculate when she'd be done.


Prior to starting the dig, Bertha was projected to be done digging by fall of 2014. That is significantly shorter than the 30.7 years they calculated she'll take. ;)


Of course, as the story says, they expected this first part to be slow going. Only time will tell how this turns out.  In the meantime, it's a mess down there.

Here's CJ's solution.

Annabelle had more illustrations, so she took up two pages.

UPHILL BATTLE: It's one week until we leave for NYC, and we are in Serious Training for our Statue of Liberty climb. Today, we trekked from our house straight up the 'face' of 'mount' Magnolia (our steep neighborhood). It's a vertical gain of about 213 feet, so it's a good challenge. (The climb we'll make in the Statue of Liberty is 354 stairs, and about 20 stories, so about 240 feet, so that's good training.)

There was a little moaning on the kids' part, but I told them they were wasting their precious oxygen and that made them button their lips. ;)

It was a lovely morning for a walk. We saw some pretty flowers ...

and stopped at the park on our way home.