I've Learned To Use Manipulatives To Clarify Misunderstandings.

 

Over this past year, I've discovered how useful manipulative are in helping to clarify missing information in a students knowledge base. As you know, I am currently teaching grades 6 to 12 in a two room school house (yes they still exist in Alaska) and I've resorted to manipulative to help clarify student misunderstanding.

I had study hall this past weekend and one of my Algebra I students was having difficulty distinguishing between tens and tenths.  Apparently, she thought they were the same so I used a place value chart (borrowed from the elementary classroom) to help clarify this topic.  I showed her the ones place and then pointed to the column on either side after which I identified the tens and tenths, emphasizing the whole numbers end only in s while the decimal value ends in ths.  I then went to the hundreds and hundredths followed by thousands and thousandths.  She said this is the first time she understood the difference.

Since the elementary teacher is out on medical leave,  the sub in there just turned 21 and doesn't have a strong math background so she sends students to me.  I had one who pretty much understood when fractions were different as to which was larger but equivalent fractions he struggled with so I pulled out those fraction strips and used them to show him.  He could see using fractions strips better on how certain equivalents were the same rather than just coloring in sections of printed squares or rectangles.

In addition, he could see why you would need the same denominator to compare different fractions.  He was also able to connect to why you multiply the denominator and numerator by the same number from "playing" with these strips.

For my 7th graders, we hit multiplying and dividing decimal numbers, so out come the base 10 manipulative so that we could use as we worked through questions.  I found that using these for division was easier for them then for multiplication. They did understand that if the number was 3.4 divided by 6, they had to change some of the larger pieces into equivalent smaller ones.  Out of my 3 students students in that class, one cannot multiply anything but one digit by one digit numbers so he is struggling to show his work.  

Then there is the Algebra I group who had trouble adding like terms so again, I pulled out the base 10 pieces because I can use the ones as ones, the tens as x, the 100's as x^2 and the 1000 block as x^3.  I used these pieces to represent the terms in the equation so they could see what could be combined.  It worked so well and helped them see by x^3 doesn't get combined  with x^2.

In the meantime, I look for other possibilities of using the limited supply of manipulative to clarify mathematical concepts and understanding.  Let me know what you think, I'd love to hear.  Have a great weekend.