Fly On a Math Teachers Wall - Place Value

Even good math students enter my room with a misunderstanding of place value. I honestly have still not found out what ALL the misconseptions are.  Often times I find that the littlest explaination is all they need.

"hey the numbers to the right of the decimal represent the parts, to the left you will find the whole"

Sometimes students need for it to connect to thier own understanding of the place values...

"Hey, having $0.34 is a lot different than having $3.40 right?"

Students may be able to correctly name the place-value columns, but they often do not understand the significance the name, the value or the operation that is done to get to that value.  For-example, they can not give amathematical explanatino fo why regrouping works....or why we "add the zero" when multiplying larger numbers. 

Unfortunently with the MANY standards we are all faced with, when I start talking about conversions of rational numbers, or manipulating them...I can not spend a whole lot of time "going back" to a 2-4th grade standard.  I wish that I could but in my state...if you are in 6th grade, you are taught 6th grade standards. 

I think the best way to go about doing "grade level content" while still trying to get a concrete understanding of placevalue is to provide them with , hands-on experiences with the concept of place value and provide them the opportuinity to express the concepts at grade level.  In the process the difference between the digit and number are clarified and then number snese is enhanced.  I choose enhanced because even as a math teacher I am not sure I fully have a supurb understanding of the topic myself. I know lots of "tricks" to help me but sometimes the actual math behind it is still alittle "fuzzy."

Becuase my students typically have the same fuzzy notions of place value and it's role in conversion.  One reason may be because they rarely receive a mathematical explaination.  I am in no way saying that students are not getting good educations in lower grades,  I am saying that we as a society are pushing kids too much too early.

Many times the explanatinos may be chock full of numbers and theory yet still have no connection to the way numbers work.  A great example of this is the standard method for converting a decimal to a percent and to a fraction: just move the decimal place two digitis to the left or the right!  The method is nothing but a trick, and our children learn to mistake "tricks" for understanding "math."

Students need help in constructing mathematical explanations.

Here is a great activity that is hands on that allows for students to see the representations of the numbers, the importance of place value and what the dang difference between 2.3 and .23 is!

So here is my freebie! {You will need base ten blocks!}

I will explain each peice.  First I have my students practice with the place value mat pg, one.  This mat looks similar to some others that you might have seen in earlier grades.  However we count a flat as a ONE rather than a 100, a long as a TENTHS and a unit as a HUNDREDTHS.  This can be confusing to some students so make sure you have a converstaion with them about the flat being a decimal square and not a flat, it now becomes a ONE because 100 hundredths are there. 

Spend some tme for about 7-12 minutes just practicing making different decimals with the place value mat.  I give them some decimals like thirty-two hundredths, or one and sixty-nine hundredths. or two hundredths.

After students look as though they have a firm grasp on how to use the manipulatives I have them open up the packet of explorations and start using the base ten blocks to build the different fractions decimals and percents.

The most important part of this is the reflection questions on the bottom!

I have students work in pairs for this activity!  Click here to get this activity for FREE!

So there you have it!  One great activity that really sparks some Ah Ha! Moments!  

Now, go check out my friend Ms. Math Dork and what she has to say on the topic!

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Cheers!