## Wednesday, February 12, 2014

### Fractions, First Grade and the Common Core

My first graders have been busy with our geometry unit the last few weeks.  As we are bringing the geometry unit to a close, we have shifted our focus to fractions.  Yes, you read that right.  Fractions our in our geometry unit.

When I first read the Common Core standards, I was surprised to see early fraction standards included under the geometry heading.  After thinking about it, it really does make perfect sense.  Here is the standard for first grade.

• CCSS.Math.Content.1.G.A.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halvesfourths, and quarters, and use the phrases half of,fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
Our district wide math program does include some instruction around fractions in the geometry unit,  However, it relies heavily on teaching the symbolic notation of fractions. (writing 1/2, 1/4 etc)  From my own experience, and from what I have read about this Common Core standard, introducing fraction notation to early can lead to improper whole number reasoning.  Kids need a lot of experience creating equal shares and using the words halves, fourths and quarters before they ever see the symbols.

Because of this, last year I created a lot of my own materials to work on fractions with first and second graders.  We are using these ideas again this year and I wanted to share with you some of the great conversations and discoveries we have been having in first grade this week.

#### Partitioning Squares

We started the week out with partitioning squares.  I made a big pile of squares out of scrap paper using the paper slicer.  We spent some time trying to cut a square in half and it is quite amazing how fast first graders pick up on how to do this.

I started by telling a story about one of my own children making a sandwich and trying to cut it in half.  I demonstrated the cut he made (which was way off center).  I then told them he said he cut the sandwich in half and many kids were quick to notice that this was not true.

They had a big problem with the pieces not being equal.  We had a great discussion about halves always being the same size.

Then I turned kids lose with scissors and paper squares and had them try cutting the sandwich in half.

 This was by far the most popular way to cut the sandwich in half.  Notice we labeled it with the word half and did not introduce the symbols for one half (1/2)
We then had a great discussion about other ways to cut a sandwich.  Many kids brought up the idea of cutting it into fourths.

I again turned kids lose with the scissors and paper squares and had them try to make fourths.  We did stop briefly and one student shared how folding the paper before cutting it made him more accurate.

 One student's idea about how to make halves and fourths
 Another students' idea about cutting a square into halves and fourths
 Another way to make fourths

We finished up by creating a quick anchor chart/poster to show the different ways we made half and fourths.  I did this by simply gluing down some of the students' squares onto a piece of card stock.

 The different ways my students cut a square in half
 Here are the three different ways my students cut squares into fourths or quarters

These different ideas also inspired some great discussions and review of names of shapes and words like equal and congruent.

#### Partitioning Circles

The next day, we again explored halves and quarters this time in the context of circles.  I began the class by having two students come up and show me how to cut a circle in half.  Predictably, we learned a lot about how not to cut a circle in half.  Also when a student misjudges where half is and creates two pieces that are not equal, it gives the opportunity for a great discussion to come up.

The funniest thing happened when one of the students cut the circle into two pieces that were not the same size.  One of the young ladies in the class said, "my sister always cuts our pizza like this and says that she gets the bigger half."

The student who sits next to her jumped in with, "if one piece is bigger than it can't be half so I guess your sister doesn't know about fractions."

Wow.  Do you know how many adults I have heard say the bigger half or the smaller half.  I hope this sunk in with the other kids in the class but I am not sure we are there yet.

I then sent kids out to create halves and fourths on their circles.  I made sure I had plenty of paper circles cut out because there were a lot of students who needed more than one try to make halves or fourths.
 Most kids partitioned their circles into halves and fourths like this.

I was hoping someone would try another idea and after some encouragement to try another way, a student came up with this.

 A students attempt at creating fourths
This caused a small uproar at the table when I asked if they thought it was fourths or not fourths.  We ended up calling over the rest of the class, all gathered around the table and tried to prove to the other kids if they created fourths or not.  The class was split about 50-50 on this matter and there were some great attempts at trying to convince kids.  Finally a student was able to prove that the pieces were not equal by stacking two of them together and showing that one was larger than the other.
 The picture is not very clear but this is how a student finally convinced the others that this circle was not partitioned into fourths.
We finished by adding our ideas to our fourths and halves poster we made when we partitioned squares.

#### Partitioning Rectangles

We finished our work with paper shapes by partitioning rectangles.  The process worked very similar to the previous days but this time we got even more creative ideas and had some really good discussions about what is partitioned into fourths and what is not.

 Here are the ways my students found to cut rectangles in half

Here are some of the ways kids created (or tried to create) fourths.  Imagine what kind of discussions you could have about these ideas.

#### Playing Fourths and Not Fourths

The following day we played this game:
This gave students the opportunity to review and practice what they had learned over the past three days.  We played it as a scoot game and the kids loved it!

I followed this up with some formative assessment to see who needs more help and who is ready to move forward.

 This formative assessment is from my fraction unit

We will be moving onto other activities from my fraction unit next week.

 Looking for some great activities to help your first and second graders with fractions?  Check out my full unit plan.  On sale now!

1. This is perfect. I'll pin it for when we tackle geometry towards the end of the year. Thank you!
❀ Tammy
Forever in First

1. You are welcome! This was simple and easy to prep and the kids got a lot out of it.

2. Great article. We generally get the kids to play math games like Math Blaster or Math Playground to help them enjoy math. We will definitely try out your way to have fun with fractions. It's a more hands on approach. Thanks!