Adding a Dimension To Fractions.

I am teaching a pre-algebra class this year.  I've discovered most of them struggle when adding or subtracting integers. The see the - sign as subtraction rather than a negative number.

I always spend the first semester building their skills before introducing the algebraic element.  This year, I am going to do something a bit different.

Instead of teaching fractions using only positive quantities, I want the students to learn fractions are not always positive.

If I find a piece of material, a remnant, that is 1/4 inch short of the length I need, that would indicate a negative value.  On the other hand, if the material is 1/4th of a foot over, that would be a positive value.

My students entered high school with certain ideas such as you cannot subtract a larger value from a smaller value so you have a negative result.  Like if you write a check for more than you have in your checking account.  They also see -4 -6 and do not recognize it as -4 + -6.  Even after spending two months on it, they still struggle.  I've used chips, number lines, everything I can think of and they still struggle.

I already know they are going to struggle when I write 5 1/4 +(- 1 1/3) instead of 5 1/4 - 1 1/3.  I suspect even having them draw pictures and  using number lines when they begin working with simple fractions, they will still struggle.

When we start the topic, I plan to have them go onto the internet to find ways in which fractions are used in real life.  They'll have to use their own words to describe each situation and provide a picture to illustrate the use.  Too often, they do not connect what they learn about fractions in school with their use in real life.   

Once this activity is out of the way, I plan to use some activities from Texas Instruments with a bit of modification for my students.  The activities range from the general question of "What is a fraction?" to discovering that fractions are equivalent if they are found at the same place on a number line, to mixed numbers.  There are 15 different activities in this unit.

When it comes time to discuss common denominators, I've found graph paper is wonderful for creating models designed to show students why any fraction must have the same denominator to combine.  Years ago, one of my students admitted they didn't know the boxes had to be subdivided into equal parts.

I also have a couple of games on my ipads for students to play so they can practice using fractions in a more fun way. Towards the end of the unit, I plan to break the students up into groups to create a game using fractions.  Once the games are completed, I'll have other groups test the games based on a rubric. 

I hope they have an easier time learning this topic than they did learning integers.  Let me know what you think.  I'd love to hear.