Friday, September 7, 2012

Understanding Place Value

One of the most common concerns I hear from teachers at every grade level is that their students don't understand place value. So every teacher begins the school year with  place value instruction.

Most place value instruction seems to be revolved around the place value model. 

We relate place value to money.

We ask the students to:
  • read, write and compare the numbers 
  • identify the digit in the _____ place 
  • describe the  value of the ____ in this number  
So I ask, if every year students' math instruction starts with place value why don't they get it? 

I wonder, isn't understanding place value more than just knowing the hundreds, tens and ones? 

Yes, place value is so much more. Students need to understand "sets of ten" can be perceived as single entities. Ten "ones" become one "ten." Ten "tens" become one "hundred." The pattern continues forever! 

Isn't it mind blowing that these 10 digits create infinite  quantities?                                                                                          

It's the position of the digit in a number that determines what they represent! 
Large Quantities Build Place Value Understanding:
If we want our students to understand place value shouldn't we get them to work beyond these models?  "Really big" numbers are best understood in real-life situations. It is difficult to conceptualize quantities as large as 1000 or more. However, the number of people that fill a football stadium has a meaningful concept for those who have experienced that crowd! 

Below is a video that helps students explore large quantities. Have the students watch, ask questions, and find the answers!

Here are some other ideas to get them working with large quantities. Remember for larger computations students can use calculators!
Ask how many:
–Counting collections of all sizes

–Candy bars would cover the floor of your classroom

–Steps an ant would take to walk around the school building 

–Grains of rice would fill a cup or gallon jug

–Quarters could be stacked in one stack floor to ceiling

–Pennies can be laid side by side down the entire block

–Pieces of notebook paper would cover the gym floor

–Seconds you have lived 

I love how these ideas relate to measurement.

Building Understanding of Place Value by Exploring Large Numbers.... What a great idea!

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