Algebra and the Skiing Cat Who Helps you with Negative Fractions

 

Algebra uses fractions a LOT.  You need a fraction in the slope equation to graph an equation.  In a previous post on slope that you can see  at Treasure Maps and Graphing Slope     the skiing cat above will help, I hope, in helping kids use negative fractions while graphing. 
      I explained that in the equation y = mx + b, or y = 2/3x + 8 for example,  that the +8 (or b value) represents the point on the graph (treasure map) where the pirates parked their boat. B is for boat I tell the kids. I tell the kids that it is a banana boat which is yellow. I always had them color their y axis yellow when graphing.  It helped reinforce which axis is the y,  which left-handed kids seemed to be confused about.  I had them color the x axis brown, like the ground.
     Once they had parked the boat at the b point, they used the fraction in front of the x (the m) to go looking for the treasure.  So, they went up two and over three in the example above to find the second point.
    
     But, what happens if there is a negative number in front of the fraction. We left-brained people can't seem to remember whether it goes with the numerator or with the denominator.  This makes a big difference as to what direction the pirates go searching.  They could be going south or down if it is a negative numerator.  They could be going left is it is in the denominator.  
     So, since I had already used a ski slope to explain using two sets of points to find slope here
I thought we could build on this idea.  If the students could be taught to recognize the negative sign as "catski," then they would recognize also that it doesn't matter if the negative sign goes with the numerator or the denominator because....

-a  = a

b    -b

The explanation could be that the negative sign is really a skiing cat's tail.  Tell the kids he uses it like a map to tell him which way to turn on the slope (like the pirates do while looking for treasure).  If he uses it to help him go down the mountain (-a value) or he uses it to go left on the mountain (-b value), he still always ends up on the same slope at the bottom of the mountain. 

Once you've done several slope equations with negative fractions, and the kids realize the points on the slope might change, but that it is still the same slope, they will relax when they see the negative fractions.  They might even want to go skiing.