Reply To: Teaching fractions to students who know the algorithms but do not understand the

[Charity Kitsyuk]

Wow I am really surprised how day 1 went. I have 2 math classes.They are leveled into two groups by the choice of administrators and other teachers. First 5th grade math top 50th percentile in the school. These are the kids who were not taught adding and subtracting with unlike denominators yet. And Second, 6th graders bottom 50% percentile for the school. They learned the standard algorithm for adding and subtracting fractions last year. 

I did task 1 and 2 of Gimmie a Break. Adding 1/2 + 1/4 when looking at them as a kit kat bar. The 5th graders totally got it right away and were almost bored. They could clearly see that 1/2 of a kit kat was 2/4. They all came up with 3/4. They are the top kids of 4 years of a very conceptually based elementary curriculum. This class gets concepts  but struggles more with algorithms. 

The 6th graders who I was hoping to just review were all over the board. 75-% of them got the wrong answer, but coming up with the right answer was work even for the rest. Some had 4/6 or 1/3 They for the most part have all forgotten the algorithm. They have very little understanding of the concept and try to add the denominator and the numerator. I was shocked that they did not even see what was right in front of them. As soon as they saw the equation they stopped seeing the chocolate bar and tried remembering the “steps”. 

Here is the question. How much time do I spend developing their understanding of adding and subtracting fractions when in 6th grade they should be fluent in that and moving to dividing fractions?  

Note: I have found that they like to have a memorized algorithm but in everything we have covered so far they remember last year’s algorithm wrong, or in pieces.