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!

Happy Blog Hoppin!

Cheers!

Comments

  1. Love it, Jamie!! Tips I can use when I tutor the MS again in the spring.

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    Replies
    1. Barbara!

      Thanks! It is funny that you called me Jamie...My mom is the only one that does that! haha. I am glad that I helped you with your tutoring. Let me know if I can help you in any other way.

      Cheers

      Delete
  2. This is such a great post! Your description of teaching decimals really reinforces the work I am doing with my younger students in terms of being sure they understand place value... not just how to use tricks! It is so important to support your future instruction! I also loved your line about connecting place value to their own lives and schema. Money seems to be a great hook that students inherently understand!

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    Replies
    1. I think that we would all be doing our children and students a bettr favor if we looked at the contenuity of our own teaching practices. How is what I am doing relate tos omething they did in earlier grades and what is it that I am doing now that is going to be reinforsed in higher grades. Unfortunently there is a divide from elementary to middle and then again from middle to highschool.

      I think it is one of my favorite things about being a blogger is I get that to have all of these amazing educators that I can coninue to reflect on my own practice by looking at what everyone else is doing.

      Thanks for stopping by!
      Cheers!

      Delete
  3. It is so important for all students to have hands on opportunities to build understanding. Thanks for showing that it's possible in 6th grade too.

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  4. First, I am thrilled to find a new upper grade blogger (I had taken a step away from blogging... your post is motivating me to come back!)

    Second, I do something similar with my kids--but you have organized it SO much better, I am excited to give this activity another try. My students are really struggling with number sense this year, so I always looking for new ideas.

    AND a freebie! WooHoo! Oh Happy Day!

    Thanks for the great post.

    Kim
    Finding JOY in 6th Grade

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  5. LOVE your place value ideas for decimals! It is so interesting to me when kids have just memorized rules like add a zero when you multiply by 10. I think we do a huge disservice to kids when we try to give them more than they are ready for.

    Tara
    The Math Maniac

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  6. I enjoyed reading your post, as it brought back memories of teaching fifth graders. Great explanation and ideas!

    Smiles,
    Sarah

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