Last week when we were transitioning from models to formulas for adding and subtracting mixed numbers one of my struggling students showed me some absolutely amazing thinking and reasoning. My intervention group was doing such a great job with this topic that they started to get a little bit bored.

My instruction included the use of manipulatives and drawings. We did not go over any procedures except to combine the whole numbers with whole numbers and fractions with fractions, all had common units denominators, and then combine the fractional parts and make wholes as needed. We did not change from mixed number to improper numbers and then add the numerators… etc. These problems were fairly simple.

My student who has struggled all year is doing a great job with fractions. Like I said above, they were getting a little bit bored of the problems. So, I gave them a subtraction problem where you would need to break apart the whole number to regroup in fractional portion of the number in the minuend. I did not help them along the way on this problem. I was going to have them draw it out or use manipulatives to model the situation. This student looked at it, and said, “you can’t do that”. The other students subtracted incorrectly and then said oh year it won’t work. They were all curious about solving this problem. Side note, these students have continuously score under the tenth percentile on standardized assessments and don’t like math.

It did not take long for the student, who did not solve the problem on her paper but knew something wouldn’t work, to figure it out. she said, “Oh, it’s just like when you subtract regular numbers. You have to regroup!”

Now, they did not know how to regroup in this situation. Their experiences with subtracting with regrouping are in base ten, they wanted to add 10 to the numerator. The denominator was 4. It will be interesting next week to see how else they are understanding this. I was really excited when this conversation happened. Math Interventions work!