Thursday, May 19, 2011

carrying -- the math sort

For the past two weeks, I've been working on introducing the concept of carrying in addition to the boys. We started our work last week by reading the Enki Math story "Tricky Mischief Save the Day." The story is not about carrying per se, but is about our friends in the Land of Jewel having to add together large numbers of jewels, so it set the stage for some discovery of adding larger numbers. This is J's drawing of the castle, with the King of Jewel and the King of Other visiting up in the throne room while the King of Other's spies try to steal Tricky Mischief's counting secret.

Zoo Boy's drawing, of the King of Other in one frame, with his bag of jewels, and the spies in the other frame, sneaking up on the door where Tricky is counting her jewels.

The kids were very excited to read yet another installment about the kingdom and characters they've become fond of.

After working thoroughly with the story last week (and taking an entire day off to watch a ewe have a lamb -- the advantages of homeschooling!), this week I introduced the concept of carrying with our counting boxes from our previous place value work. The boys (particularly Zoo Boy) were super happy to see the counting boxes again, and I set up the activity so that our 1, 419 jewels needed to be added to the King of Other's 897 jewels. We combined the boxes, and discovered that there were enough jewels in the wooden boxes to make up a new china box, and there were enough china boxes to make up a new silver box, and there were enough silver boxes to make up a new gold box. As we "carried" (physically) each new box to the top of the column, the kids got the physical experience of carrying in addition. Then we counted up the new total.

Then we sat down and wrote out the equation. Zoo Boy was SO excited to "carry" the ones to their new column. It's amazing how quickly he was able to apply the newly discovered concept to paper output -- without me saying a word or guiding him at all!

J was a bit slower figuring it out -- he was already naturally "carrying" in his head, and it took him a few minutes to put together what we did with what he was already doing. But once he reconciled it in his own mind, he was equally excited as his brother.

Then I left them with the boxes to play. For about an hour I could hear them out there creating different equations and explaining the carrying process to each other.

Today I pulled out the base 10 blocks (singles, rods of 10, flats of 100, and cubes of 1000s) and we repeated the activity (with different numbers). I had prepared cardstock in coordinating colors to represent the boxes they were already familiar with in our previous work. The kids quickly transferred their knew knowledge to the new manipulatives, and were able to immediately produce written output for the equations.

Then, of course, I left them with the cubes, and addition continued for another hour.

Tomorrow we'll play a few games with the base 10 blocks and carrying, and then I'll either go on to borrowing (in subtraction) next week, or I may just let it sit while we work on our next cultural unit and touch on borrowing at the end of the year. Waiting is probably better, but that means I'll have to write a new story as a tie in. We'll see how energetic I'm feeling! Either way, I definitely want to introduce it before the year's end so they can work on their practice with it over the summer.