Fractions Concept Lesson

On Thursday, I did  a fractions concept lesson in my class that was tricky, but REALLY sunk in once the idea clicked.  I thought it was worth while to share, so here it is.

Let me preface this by saying that I did not write this lesson.  My district did about 6 years ago.  Because of that, I am not going to attach any of the documents I used.  

First day, they were given a piece of paper with 3 number lines, and 3 strips of paper that were the same size as the number lines. (remember that...it becomes important for Day 2)  I told them that those 3 pieces of paper were candy bars and they needed to show how much of the candy bar 3 different people would get


Sue got 3/4 of the candy bar.
Jose got 1/2 of the candy bar.
You got 4/6 of the candy bar.
.
They could use the paper bars to help them, but the ultimate goal was to get the numbers on the numberline. 

Just folding the paper was eye opening for me. So many students didn't have that concept...especially when the were working on the 4/6. Some kids ended up with more spaces (folded it wrong) and just ripped off the excess! I was walking around guiding them, doing a lot of modeling and helping, and they all seemed to get it by the end of the math block.




Here are some examples of what was going on during this part of the concept lesson.

 You can see that the person above really understood where everything went on the numberline (with a minor exception for 4/6...which was quickly corrected after I took this picture!).  They connected the two fractional representations and understood the concept.  The person on the bottom though did NOT understand.  With her (and her partner) I had to spend a lot of time guiding them towards the understanding of how to create fractions and what they meant.  This group was confused all around, but asking them questions like, "What is the whole?", "How can you show parts of a whole?" "Fold the paper for me to show me that someone will only get 1/2"  "How do we know how many pieces to fold the paper in/break the numberline into if we want fourths?"  etc...

It was all I could do NOT to just take the papers out of their hands and do it for them.  Took a lot of restraint on my part ;)  But by the end of Day 1, with all of the guiding questions, the kids eventually were all able to put the fractions on the number line and understand the concept of fractions being less than a whole.

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Day 2, they got "gum" this time that was longer than the number line itself. They had instructions that were the basically the same as the day before, with slight changes in the fractions.

Tim would get 3/4 of the gum
Sally would get 5/6 of the gum
Mark would get 4/8 of the gum
You would get 3/5 of the gum.
Who will receive the biggest piece of gum?  Show your answer in two different ways.

What was also different on Day 2, than on Day 1 was that the pieces of "gum" were BIGGER than the number line.

While they got the folding this time, putting it on the number line was difficult.  Most of them immediately folded the 3/4 piece, then went to place it on the number line.  When they held the paper up to the line, it was the same size as the whole. They put the mark indicating 3/4 on the 1 and moved on.  They then folded 5/6, noticed it was longer than the whole, extended the number line, and were fine with that.

I asked some of them to just put the numbers on the number line, without the paper. They could do that (the lesson from the day before on putting numbers on a number line sunk in!!). Then I showed them how the paper gum was one way to represent 3/4 and the number line was another. I used an example of 100 miles.  In the car, it is far.  But on a freeway sign, the 100 miles takes up about 6 inches in writing.  They mean the same thing, but aren't exactly the same size.  That is the same with the paper and number line.  The whole is a different size, but the idea behind what they represent is the same.  I know...not a perfect analogy, but I would say 90% of my kids GOT it! They are really good with number lines and fractions now because they have the CONCEPT of it.

This was SUPER frustrating for me as a teacher. I wanted to jump in and just tell them the answers. But I stuck to the guiding questions, and it really paid off in the end. 2 days of mindnumbing, want to beat my head on the desk feeling was worth it because now, they have the CONCEPT of fractions, not just some abstract meaningless idea of them.

(So sorry for the lack of pictures on Day 2...I forgot my camera :( )