Distinguishing the Whole when working with Fractions

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.

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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.

About stamp36

Instructional Leader for Trillium Lakelands District School Board
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9 Responses to Distinguishing the Whole when working with Fractions

  1. Tanya says:

    I love math

    Liked by 1 person

  2. Renee says:

    I love math

    Liked by 1 person

  3. Sarah Bell says:

    I live math! And it’s so great to see teachers like you so passionate. I was not lucky as a student.

    Like

  4. Sarah Bell says:

    Typo in the last comment! I love math!! It’s so great to see teachers like you so passionate. I wish I was as lucky as a student.

    Liked by 1 person

  5. Julie says:

    I think my mom is laughing out loud right now as I type the words,”I love math”.” It was so hard for me, but I don’t want to give my boys a bad attitude about it. Maybe your blog will help me help them.

    Liked by 1 person

    • stamp36 says:

      It is one of most important things we can do as parents, that is to not to tell your children (especially girls) that you were bad at math. The research clearly shows that parental math anxiety passes on to their kids. If homework comes home and it is different than how you learned it don’t say you don’t understand this new math or don’t worry I was bad at math too. A simple mindset change has show to make a huge difference. Tell your child. I am not sure how to do this but we will try together! If we make a mistake that is OK, we need to make mistakes to learn. This goes for teachers too, teachers who are not confident in teaching math often pass their math anxiety to the students. It’s often simple language, the way they say things. For example if a teacher says. “We have to do math now” as if its a bad thing or a hard thing totally changes the message to their students. Or if they say they were not good at math but we need to get through it together. All these types of messages contribute to math anxiety and to kids not enjoying math. The research is proven now, there is no math mind, or math brain, everyone can learn math and learn math well. It comes down to mindsets and the way it is taught.

      Like

  6. gardenkinder says:

    Wow, your blog is fabulous! I love math! I didn’t always feel that way though. I’m learning to develop a renewed relationship with math so I can impart a fresh mathematical mine in my students. I’ll follow your blog, thanks for sharing your insight with all of us.

    Liked by 1 person

  7. gardenkinder says:

    Mindset autocorrected to mine 😉

    Liked by 1 person

  8. Tricia says:

    I Love math especially with ideas and props like this!!!!

    Liked by 1 person

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