I have been doing some work on fractions with a 7/8 class at one of my schools. The class as with many classes has some significant learning gaps when it comes to fractions. The teacher and I determined that we had to go all the way back to showing that a fraction is a quantity, representing fractions using models/equipartitioning and determining the whole.
After a well planned sequence of tasks we really feel we have closed some major gaps in terms of representing fractions and they now seem to have solid grasp of equipartitioning. I know you may be thinking that a 7/8 class is in dire straits if we are working on these concepts when they should be ready to add and subtract fractions in grade 7 and multiply and divide fractions in grade 8 (In Ontario). Still we did what we needed to do because you can’t do operations with fractions if you can’t even represent a fraction! The class has made some huge jumps with only a few really precise tasks to help close those gaps.
With this blog I just wanted to share some student work and show one spot where we are still seeing some misconceptions. I see this actually in a lot of classes I am in where students sometimes get confused in determining what is the whole or wholes they need to use to answer the problem.
Here are some examples of the group task that was done on Monday. There is picture of the task below too. I also love that the teacher decided to use the VNPS whiteboards. Makes the math more visible and the students love to work on them.
As you can see with the work samples the groups were able to see that the juice containers each represent a whole. This was also evident in the other 5 groups except for 1. After the group task was complete the students then did some purposeful independent practice. They completed a task similar to the one they did as a group. Here are some work samples.
If you look at the top two on the right and the middle one on the left you will see that all three of these students treated both gatorade bottles as the whole together and came up with an answer of 2/6. There were three other students who also had this misconception. When the teacher and I reviewed the student work we saw that we still have some work to do with determining the whole. Moving forward some guided groups will be created to look at the key understanding of “a fraction should always be interpreted in relation to the specified or understood whole.” Two things I want to highlight. 1) This is one reason why the exit card is so important, judging by the group work it could have been easy to say they all understood that you have to determine the whole first before representing the fraction. 2) Determining the whole is a key understanding of fractions that I think is sometimes overlooked or not as much time spent on it as other key understandings related to fractions. Remember this is my opinion with what I see in many students work with fractions, doesn’t mean it’s right! LOL.