I love starting a new math module with an engaging task that gives my students and I valuable insight into what they already "know." The results of this fraction activity was fascinating...and gave us one of the best collaborative conversations we've had so far. It also helped to unearth some very common misconceptions kids have about fractions.
People often ask me, "why this new way of math? The old way works just as well. Why do kids need to be able to understand why the math works, if they can do it?" Well this activity is a perfect example. Only TWO of my 24 students could correctly place these fractions on a number line. I definitely have more than two that can operate with fractions or even could have found a LCD and then renamed them to compare and order...but do they really understand how to REASON about fractions? If they understood the meaning of a denominator (and the numerator respectively) then this activity would have been a cinch...but alas, it was not. Let's recap some of the highlights presented in the same order the students were presented the information.
1st group (two groups had the same answer): (top two strips) compare and order fractions-no problem! We will just put the denominators in order from least to greatest. if they have the same denominator, we will just use the same numerator.
2nd group (single strip second row): "We knew that the smaller the denominator, the larger the parts, so we put the fractions in order from greatest to least using the denominators." That "fraction rule" is absolutely correct, except these students did not take into account the numerator. By this point I am in LOVE with this lesson, and these students.
The next four groups (row three and four) all knew some foundational "rules":
It certainly was nice that we had two groups that had the "right" answer and could explain their thinking, but of course that's not where the most learning occurs. Now, would I love to have an entire group of 5th graders do this activity "right" the first time? Sure I would, because we have a LOT of other 5th grade learning to learn. LOL. But until that day comes (and if we all stay true to the intent of the Common Core State Standards and teach our children with an inquiry approach to math vs. a procedural "here's the way to do it" approach I know that in a few years I will get those students) I will continue to have these brilliant conversations with my kiddos. Conversations where their mistakes are welcome, for the benefit of all, including their teacher.
People often ask me, "why this new way of math? The old way works just as well. Why do kids need to be able to understand why the math works, if they can do it?" Well this activity is a perfect example. Only TWO of my 24 students could correctly place these fractions on a number line. I definitely have more than two that can operate with fractions or even could have found a LCD and then renamed them to compare and order...but do they really understand how to REASON about fractions? If they understood the meaning of a denominator (and the numerator respectively) then this activity would have been a cinch...but alas, it was not. Let's recap some of the highlights presented in the same order the students were presented the information.
1st group (two groups had the same answer): (top two strips) compare and order fractions-no problem! We will just put the denominators in order from least to greatest. if they have the same denominator, we will just use the same numerator.
2nd group (single strip second row): "We knew that the smaller the denominator, the larger the parts, so we put the fractions in order from greatest to least using the denominators." That "fraction rule" is absolutely correct, except these students did not take into account the numerator. By this point I am in LOVE with this lesson, and these students.
The next four groups (row three and four) all knew some foundational "rules":
- Any fraction with a numerator of zero has a value of zero
- If the numerator and denominator are the same, the fraction has a value of one (I especially loved that one group had 9/9, and others had 6/6. Reinforced the "rule" without me having to tell them the rule.)
- If the numerator is larger than the denominator, the value is larger than one
- They understood that 1/2 was in the "middle" (I would love to have seen how they laid out the number line if I had a quantity of two or more...I will save that for next time.)
It certainly was nice that we had two groups that had the "right" answer and could explain their thinking, but of course that's not where the most learning occurs. Now, would I love to have an entire group of 5th graders do this activity "right" the first time? Sure I would, because we have a LOT of other 5th grade learning to learn. LOL. But until that day comes (and if we all stay true to the intent of the Common Core State Standards and teach our children with an inquiry approach to math vs. a procedural "here's the way to do it" approach I know that in a few years I will get those students) I will continue to have these brilliant conversations with my kiddos. Conversations where their mistakes are welcome, for the benefit of all, including their teacher.