Sunday, March 9, 2014

Expanded Form Activity

Expanded form, also known as expanded notation, is one way students need to be able understand and write numbers.  The other forms being standard form and word form. When teaching place value, students must be able to see and understand the value of each individual digit in a number, which of course would be expanded form.  For some kids, this concept can be a bit difficult to fully understand.

A few years back, I picked up a student calculator ... you know, the ones that we all have sets of,  but they get stashed in the back of the closet or workroom because we often times don't see them as a tool for helping kids understand. Trust me, I have seen many dusty calculators :-)    I think mine is designed for the 3-5 classroom. It looks like this:


Anyway, when I picked it up and I started punching in some numbers to add, it dawned on me that it was bumping the addition problem to the top of the screen, basically showing the values I was keying in.  I had this 'ah-ha' moment that this would be a great tool to use to help kids see the values of digits when working with expanded form.  At the time, I actually had a small group struggling with expanded form, so I tried it out with that group the next day.  

The first thing I did was give them an addition problem (basically just an expanded form problem), such as 5,000+600+50+9, but I didn't tell them what it equaled.  I had them write the problem out horizontally and vertically, so they could see that it was basically just an addition problem like they were accustomed to adding.  I then had them key the addition problem into the calculator, and they could see their problem across the top of the screen as they entered each number, which was pretty much seeing the expanded form or values of the digits in the numbers.  I then had them hit the equal button to get the standard form of the number.   Once they had the answer, or standard form, of the number, we looked at the number on their calculator screen, which of course was 5,659.  We compared it to the addition problem on their paper and discussed that what they had done was given each digit in the number a value and that is what they added up to find the total value of the number.  We continued this process several times to gain understanding.  

Then I transitioned to giving them the standard form number first, such as saying," If I gave you the number 9,876, what values would you give each number (starting with the 9) that you could then key into the calculator as an addition problem that would get you an answer of 9,876?"  They would then start by saying, "Well, I think we would enter 9,000 for the 9." So, I would tell them to hit a 9,000 and then the plus sign.  Then they would say, "Next I think we would add 800 for the value of the 8." They would key that in.  Remember, all along the addition problem they are typing will be popping up at the top of their calculator screen.  ...... They would continue with the process until they key in all of the values.  At the end, when they hit the equals sign, it's like magic to them because if they did it right, they will end up with the number I told them to start with.  Sometimes they will give me a little , "YEAH!" when it is right.... they came up with that part on their own. (Don't you just love it when they do that!)

By the way, the calculator on my computer will represent expanded form too.  I used it to type some pictures out to show you the process used in the problem mentioned above. 
Click on the image to enlarge. .... not on t he 'p' that will pop up. :-)
For the last few years I have incorporated this expanded form activity into my teachings of expanded form and place value.  The kids LOVE using the calculators!  I hope you will have fun trying out this bright idea in your classroom.
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1 comment:

  1. Great tip! Most classrooms do have those sets of calculators - this is an excellent way to use them to actually learn with! Thanks for sharing this post!

    Buzzing with Ms. B

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