### Playing with Math

Report cards are looming on the horizon. I came in early and sat down at my computer, turned on some Bach, and began typing. I got into what some scientists call flow (the mental state of operation in which a person in an activity is fully immersed in a feeling of energized focus, full involvement, and success in the process of the activity), and the time flew by (I also got lost in the garden for awhile!). Before I knew it, it was time to start class for the day. Unfortunately, I hadn't planned a thing, and I realized this I was walking outside to bring the kids in.

They arrived in the classroom and got their bags unpacked and put away in their lockers. I looked around the room for some kind of inspiration. Luckily for me, I had just received a box full of math manipulative the day before. I grabbed a box of fraction circles and just as everybody was sitting down to the communal table, I dumped them all on the table and walked away.

I'd like to say I was surprised at what happened next, but I really am not. Play is a powerful learning tool, and when given creative freedom over a tangible item, kids will come up with amazing things. Kids need to play (adults too). One of the girls made a circles out of two halves. Then, four quarters. Soon, the rest of the class was trying to see how many ways they could make a whole. I interjected for a moment, asked them to get their math journals, and then we got back to playing. As they played I gave them challenges, and asked them that must do the following for each challenge; a) show it with the tiles, b) draw a picture of it, and c) show it mathematically.

With those simple rules, we started off on the challenges, which I will list below. It is important to note though that these challenges were not being done as a list to get through. Each student was working on something different. Since I hadn't planned a thing, I was creating these challenges based on what I witnessed in their play. I tried to let their natural play flow into a lesson. By taking what they were playing with, and harmonizing it to the math we were studying, I think we provided a great deal of depth into this lesson (which lasted about an hour and half). As we came up with new ideas and activities, I wrote them down on the white board, and as they finished one, they would go to another.

How many different ways can you make a whole? Write down all the different ways, draw picture of your circle, and show how the pieces add up mathematically.

How many different ways can you make a third? Write down all the different ways, draw picture of your third, and show how the pieces add up mathematically.

- only 3 pieces; none of them are the same

- only 6 pieces; none of them are the same

- using a fifth and an eighth piece

- Using eight pieces, only 2 of which can be the same

- And so on.... (the kids came up with some good ones which I can't remember nor did I write down)

Joy and Takumi walk into a pizza shop. Joy orders 3/4 of a pizza, and Takumi orders 2/3.

Who ordered more? How much more? (show with pictures, tiles and symbolically)

How do we make it equal, so each of them get an equal amount of pizza? (make a poster for the Pizza cook informing of him of how to make 2/3 equal to 3/4, just is case this situation happens again, he can refer to it for help)

Take a piece to act as your base, preferably something large (half, third, quarter etc.). How many equivalent fractions can you make? Stack them on top of the base and see how high your tower goes. Keep track of your progress by listing each layer and showing how it works mathematically.

Having them play, and then allowing them the lesson to emerge out of that play..... I could have easily planned a lesson like this and then had them work through all the problems one by one. But, this was more fun. It was directed by them and even if I changed their activity, they could still see their original idea in the final activity. They owned it.

It is interesting that my role as a teacher in this morning was just to dump a bucket of tiles on the table. After that, they came up with the activities, and I simply oriented their attention to how this applied to their mathematical study (and altered the activities to make them more challenging in some cases, or to make them easier in others). It required, from my part, an understanding of the pedagogy of learning, but also I had to have a sound working knowledge of fractions, and the myriad of ways they can be represented. It is not just a matter of playing, but rather, orienting play in a purposeful direction that promotes growth and increased understanding, conceptually, and from a computational perspective.

They arrived in the classroom and got their bags unpacked and put away in their lockers. I looked around the room for some kind of inspiration. Luckily for me, I had just received a box full of math manipulative the day before. I grabbed a box of fraction circles and just as everybody was sitting down to the communal table, I dumped them all on the table and walked away.

I'd like to say I was surprised at what happened next, but I really am not. Play is a powerful learning tool, and when given creative freedom over a tangible item, kids will come up with amazing things. Kids need to play (adults too). One of the girls made a circles out of two halves. Then, four quarters. Soon, the rest of the class was trying to see how many ways they could make a whole. I interjected for a moment, asked them to get their math journals, and then we got back to playing. As they played I gave them challenges, and asked them that must do the following for each challenge; a) show it with the tiles, b) draw a picture of it, and c) show it mathematically.

With those simple rules, we started off on the challenges, which I will list below. It is important to note though that these challenges were not being done as a list to get through. Each student was working on something different. Since I hadn't planned a thing, I was creating these challenges based on what I witnessed in their play. I tried to let their natural play flow into a lesson. By taking what they were playing with, and harmonizing it to the math we were studying, I think we provided a great deal of depth into this lesson (which lasted about an hour and half). As we came up with new ideas and activities, I wrote them down on the white board, and as they finished one, they would go to another.

**Make Wholes**How many different ways can you make a whole? Write down all the different ways, draw picture of your circle, and show how the pieces add up mathematically.

**Make Thirds**How many different ways can you make a third? Write down all the different ways, draw picture of your third, and show how the pieces add up mathematically.

**Make Wholes with.....**- only 3 pieces; none of them are the same

- only 6 pieces; none of them are the same

- using a fifth and an eighth piece

- Using eight pieces, only 2 of which can be the same

- And so on.... (the kids came up with some good ones which I can't remember nor did I write down)

**Pizza Problem**Joy and Takumi walk into a pizza shop. Joy orders 3/4 of a pizza, and Takumi orders 2/3.

Who ordered more? How much more? (show with pictures, tiles and symbolically)

How do we make it equal, so each of them get an equal amount of pizza? (make a poster for the Pizza cook informing of him of how to make 2/3 equal to 3/4, just is case this situation happens again, he can refer to it for help)

**Stack it**Take a piece to act as your base, preferably something large (half, third, quarter etc.). How many equivalent fractions can you make? Stack them on top of the base and see how high your tower goes. Keep track of your progress by listing each layer and showing how it works mathematically.

Having them play, and then allowing them the lesson to emerge out of that play..... I could have easily planned a lesson like this and then had them work through all the problems one by one. But, this was more fun. It was directed by them and even if I changed their activity, they could still see their original idea in the final activity. They owned it.

It is interesting that my role as a teacher in this morning was just to dump a bucket of tiles on the table. After that, they came up with the activities, and I simply oriented their attention to how this applied to their mathematical study (and altered the activities to make them more challenging in some cases, or to make them easier in others). It required, from my part, an understanding of the pedagogy of learning, but also I had to have a sound working knowledge of fractions, and the myriad of ways they can be represented. It is not just a matter of playing, but rather, orienting play in a purposeful direction that promotes growth and increased understanding, conceptually, and from a computational perspective.

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