### 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!

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!

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

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

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!

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!

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.

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

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

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

Smiles,
Sarah

Oh Em Gee. I love seeing some love! Thanks for leaving some or asking for some!

### Creating Ratio Posters

This was a really fun project that I did with my 7th graders when we were working on ratios, Rates and proportions that I never got a chance to post this past year, and I will not be teaching 7th grade again! (sort of sad...but not really.)
To introduce the topic we started with a review of ratios.  Below you will find the worksheet that went along with the project.  You can see this student was using her worksheet to help her think of a topic idea!!  LOVE!

She also was not very careful with her worksheet.  Sorry for the wrinkles.  As you can see the students had to pick a topic, draw or represent (i told them they could use stickers or glue objects to their poster) 20 objects, then on a second sheet of paper complete 10 questions relating to ratios from their poster and reflect.  Here is what this student came up with!

If you have had any questions about using art or projects in a math class here it is, Directly from the mouth (er, hand) of a student.  STUDENTS LOVE VISUAL PROJECTS …

### Multiplication is for White People Chapter 1

Part One: Inherent Ability
1. There Is No Achievement Gap At Birth

### Back To School First Day Activity Idea

Hi there!  I have been slacking on the blogging lately.  When summer started I was upset that I was not going to be teaching summer school, and that I had to drop out of Grad School for a while (Due to some REALLY ridiculous issues at a different school not allowing my transcripts to get set over...Long story really.), but I have actually been INCREDIBLY busy this whole summer.

I wanted to do a quick share for an activity that you can do on the first day of school and how I used it last year! (I wish I had pictures!!! That is going to be one of my goals this upcoming school year is to take more pictures in my room, of my products.  I think it is actually going to become a classroom job!!!)
So here it is I posted this last year about this time but it works so well.  I have it as a freebie in my TPT store. You can click the picture or HERE to download.
This is what I did last year and will do again this year on the first day of school.  I took pictures of all of my students on the fi…