Ten Times Greater

I’m new to the blogosphere…shoved here ever so gently by my brilliant math coach Sarah Caban (mathontheedge.wordpress.com)! I’ve decided she is the only person in the district who could add one more thing to my teaching life and make me feel good about it. She bribed me to join this crazy awesome PD adventure with chocolate and wine (which I have yet to receive) and then, before I knew it, she had me hopping and skipping through the halls of school musing to myself about the wonderful world of Twitter and the blogosphere. This is what makes her so brilliant…she is a very clever and subtle math attack-er.

So, here goes my first attempt at finding my blog voice 🙂

Testing is done, routines and procedures have been taught, a math community has been built and it’s time to get down to the nitty gritty. I always start a new math unit (or any unit for that matter) with mixed feelings. I am always excited, but almost certainly nervous and anxious as well. There is pre-test data to sort through and planning to be done.  I want to find the perfect entry point, target my small groups just so and plan jaw-dropping, aha-moment inspiring lessons for each day! These expectations and, let’s face it, my control issues, tend to delay the start of any unit, but eventually I convince myself to just jump in.

Enter 4.NBT.1, my entry point into unit 1. It’s a cool standard, but a difficult one for sure. For those unfamiliar, it requires that my fourth grade students understand the relationships between digits in a number, in particular that they recognize that as you move left on the place value chart, the number will become ten times greater and if you move back, it will become ten times less.  Now, all of my students came to me knowing how to multiply a number by ten. “That’s easy Ms. Miner!” They all knew how to expand numbers using their place values and they even had a conceptual understanding of regrouping, though they have not been taught the addition/subtraction algorithms yet (yay!). They have been primed for success.

So off we went! Diving deep into this standard. We counted around the circle by tens, hundreds, thousands, etc. I recorded patterns and they talked about what they noticed. Really, I was blown away when they discovered on their own that the value was growing by ten times. They practiced and I reflected. Some students started adding ten to numbers rather then multiplying by ten. So we compared and contrasted ten times and ten more. We practiced some more, counted some more! We  worked on the place value chart, used the place value disks, busted out the pennies, dimes and dollars. We worked with the language frame “______ is ten times greater than ______.” It was awesome! I felt like they had it. They were excited and using the terms and answering questions and explaining their thinking. Time for a little formative assessment…

 

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A quick exit slip that asked students to consider the value of a collection of 826 coins. What is the value if they are pennies? Dimes? Dollars? Ten dollars? What is happening to the value of the collection? Explain with words, pictures or numbers. “This will be easy,” I thought, “We’ve been using money like this.” I just needed to document their understanding, and then off to the next concept we would go!

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I’m sure you know what’s coming. I reviewed the exit slips and I was stunned. 2 of my 17 got it. TWO! So of course I looked more closely at the exit slips. I asked myself “what do they know?” (Thanks to Sarah). They almost all got the value correct when the collection was of pennies and of dollars. But when it came time think about the value in terms of dimes and ten dollar bills, they almost all got the value incorrect. Okay… “Do I see any patterns in their work?” AND THERE IT WAS! Nearly every student in the class took the value of the pennies and doubled it to get the value of the collection if it were dimes. Then they took the value of the collection of dollars and doubled it to get the value of the collection as ten dollar bills. It was strange, and I don’t know where it came from and I still can’t figure it out. When does “ten times greater” become “two times greater” in a kiddo’s head? What connection are they making that makes this make sense to them? I encountered this same issue last year and when it showed up again I was baffled. I had definitely done a better job teaching “ten times greater” this year but there it was again.

So now I ask you, Blogosphere, for some help! Has anyone else noticed this misunderstanding with their own students? Do you have any suggestions for next steps? And rather than send you an email, Sarah, I wrote a blog post…just like you asked 🙂

 

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