#TMWYK – The Return of the Sand Pool

It’s a tough time of year for teachers, and I don’t say that to garner any sympathy.  But I’m going to take a moment to deviate from the regular musings of my classroom and write about my favorite topic:  my daughter.  The discussion won’t be completely unrelated as I have learned a great deal about my students’ development of mathematical literacy while watching my daughter make sense of numbers, quantities and shape.  And of course, Christopher Danielson’s development and facilitation of Talking Math with Your Kids has encouraged me to continue the conversation with my own child.  Specifically, I appreciate that his daughter is a few years older that Maria so that I know what I’m looking for and what to look forward to.

Maria (3.5 years old) loves to be outside.  As soon as the snow melted, she insisted that it was now summer and hence every activity from that moment forward must be done in the great outdoors.  A personal favorite is the sandbox, with water.  I’m not opposed to the sandbox overall, but mixed with water, it becomes more like a swamp.  Plus, let’s face it.  It’s Minnesota. It’s Spring, not Summer, and taking out the hose just isn’t in the cards just yet.

So we made a deal that when the temperature on my weather app reached 70 or above, we could take out the hose.  In the mind of my three year-old, this meant that the first of the two digits needed to be a seven.  On Saturday, this lucky girl got to take out the hose.

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Results as expected.

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Sunday, I decided to test Maria’s understanding of these numbers.  She again asked “is it seven on the phone?”  I instead showed her Chicago’s temperature which was a balmy 82 degrees.    As expected, her response was “Aww, it’s not seven so we can’t do water.”   I know she knows 8 is bigger than 7, but hasn’t yet connected that a temperature that begins with an 8 represents something warmer than a temperature that begins with a 7.

 

 

Nrich’s Digit Doozy

If you are a math teacher who hasn’t taken some time to get lost in the problems on Nrich, stop reading this and go there  right now.  You’ll need to finish reading this post tomorrow because that’s how long you will be immersed in its seemingly endless array of engaging problems.

Today, my intention was to do a little starter activity with my 9th graders to help support their number sense.

Here’s the basis of the problem:

american billions C

For two out of three of my classes, it turned into a whole-class period problem-solving extravaganza.  Seriously.  30 minutes later, the brain sweat is still palpable in the room.  There were so many calculators in use, I think the smartphones were starting to get jelous.

Some chose to use whiteboards, some choose numbered cards 0 – 9 while some wanted to use paper.  It was so interesting to me to see them figure things out that must be true about the different number places.  A few remembered the divisibility rules for 3 and shared them.  Then they were able to put the divisibility rules for 2 and 3 together to get divisibility for 6.  I didn’t even know that there was a divisibility rule for 4 and 8!

Some student observations:

  • The 2nd, 4th, 6th, and 8th numbers need to be even.
  • The last number must be 0.
  • The 5th number must be five, since the last number must be 0.
  • The first three numbers have to add up to a multiple of 3.
  • The first 9 numbers need to add up to a multiple of 9.

I even had a student say, “How much longer do we get to play this game?”  Music to my ears.

It’s difficult to give students a task that you know most of them won’t solve which is why I’ve shied away from this one in the past.  I made sure to praise the efforts of those that were able to get their numbers to work for all except one of the digits.   (For example, their 2, 3, 4, 5, 6, 8, 9, and 10 digit numbers worked, but their 7 digit number didn’t).

Nrich gives another variation on this task by making it a game.  Basically, students take turns creating 1, 2, 3…digit numbers by choosing from the 0 – 9 digit cards until someone can’t use any more of the cards.  I think having them play this activity as a game would help alleviate some of the discontent of feeling like this problem was too difficult to solve.