What’s the fastest way to help this 9th grade student?

• I’d bet that a visual model would help this student a tonne. Also, this may be a problem with reading, not necessarily math. They may have just missed the 1/3 “of what you have left” or not understood how this is important.

• I agree. This is a problem that my ELL students have difficulty with. I have them write “now i have $\dfrac {3} {4}$ (or 0.75) remaining” and “I keep $\dfrac {2} {3}$ of that amount.” I got rid of “left” and put in “remains” or “remaining” after I heard about the left angle triangle, and realized that those dual-use words are a nightmare for my kids.

• Units!

I would do some messing around with things like pounds and ounces of chocolate chips, and then cases and individual bars of chocolate, and then point out that you need to be especially careful with units in situations where you have percents or sometimes fractions. What unit is it a fraction of?

• Definitely visual models.

What makes this confusing for students is that the first step of 4/4-1/4 does give the correct answer of 3/4. The student doesn’t understand that it works because they are subtracting 1/4 of 4/4, and that next they need to subtract 1/3 of 3/4. Simple subtraction works with whole numbers (You have 15 candies, your friend takes 3, and then another friend takes 5 more). This student needs to develop the idea that taking away fractional parts is more complicated.