Sunday, July 7, 2013

The Three Part Problem: Part 2 (Student Examples)

As we put together our action research, we included a few of the simple problems that we tried this year in our appendix. Thought it may be helpful to "see" some of it in action.
My goal for next year is to keep problems more closely connected to the children and their experiences/interests. The level of engagement was so much higher when they were an active part of creating the problem.
My fear is that problems don't always "come up" naturally in play. However, if I continue to strive for 1-2 rich problems each month I can always supplement with teacher created problems that I feel are engaging. I wonder if I am keenly observing and thinking about opportunities for rich problems, if I will notice more opportunities to capitalize on?
Problem #1:
The children had really been enjoying songs and action games that included numbers. We had been singing 10 in the Bed during music and movement often. We decided to read the story “10 in the Bed”.  To extend their thinking we posed the problem,

How many different ways might the dogs be in and out of the bed?

Various materials were set out as a provocation. We set out teddy bear counters, 10 frames, blank paper and pencils, and an abacus.

Children used the 10 frame to show their thinking. Most children chose to use 2 different colours to represent on and off. Alternatively, some children filled some squares and left some blank.

Some children recorded their thinking on paper right away. Other children recorded their thinking on paper as a way to preserve the answers that they came up with on their 10 frames.

Some children found the 10 frame overwhelming and instead turned it over to create a whiteboard. Some children acted it out using the picture of the bed and the snap cubes.

Some children acted the problem out using their bodies. They sang the song that accompanied the book one at a time to determine the different combinations.

Problem #2:
The children had been noticing and exploring patterns in the classroom, outdoors, and on their clothing. In our building area, we noticed one of the students had created a structure which he explained to be a “booby trap”. In order to get into the trap, the other children had to guess his pattern code from a panel that he had created. To extend this experience further, we saved the structure over the next few days and provided materials for children to explore this challenge even further. Together with the children we developed the problem:
How many different patterns could there be to crack the secret code?

Various materials were added closer to the building area. The structure was saved and the panel was visible for children while solving the problem. We provided blank paper, geometric shapes, stickers, and stamps.

Some children recorded their thinking on paper right away. Other children recorded their thinking on paper as a way to preserve the answers that they came up with on their 10 frames.

Most children used the stickers to represent their ideas for different patterns. Some children created 1 pattern, some created up to 6.
Problem 3:
The children had enjoyed reading the book “The Mitten” by Jan Brett. They were fascinated by the animals fitting into the mitten. We discussed as a class what materials we should add to the provocation to help them in thinking about the problems. Together with the children we developed the problem:
How many different ways can the animals be in and out of the mitten?
Some children used the animals to act out their answer. Many children recorded their thinking with pictures on blank paper. They used circles, mittens, dots, and lines to record their thinking.

Some children set the animals on top of the mitten as a visual for the number that were in or out. Some of the children began to write the algorithm for addition down as well (e.g., 4+4=8)
Problem #4:When our school was gearing up for Spring Fair the interest began to rise in Kindergarten. The children talked a lot about the activities that would be at the fair and we began to talk about the different amounts of money that events cost.
To extend this thinking, we talked about what the children could do if they brought $10 to the Spring Fair. The problem solving was incredible and the children were so connected to thinking about this problem because of their excitement.
What could you buy with $10 at the Spring Fair? What might your family buy?

The children used snap cubes, 10 frames, and Pic Collage to capture their learning. The children proudly tweeted our results out to parents.

1 comment:

  1. Hi Tracy,
    I absolutely LOVE reading your blog and your last two posts in particular. Math has been a big area of inquiry for our school and in particular with our FDK teams. Seeing you elaborate on your journey with the 3-part Math Lesson was intriguing and you documented it beautifully! I love how you brought in their interests when coming up with the math problem while at the same time, documenting their thinking and learning through the use of technology (e.g. photos/pic collages, etc). Moreover, I also loved how you highlighted the challenges you faced. As teachers, it's so important to reflect upon what worked and didn't work and I'm so glad you shed light on the "difficulties" that you faced throughout the learning process. This is wonderful for other educators so that we can take what you've learned and apply it in our own settings.
    Thank you for continuing to share your experiences, passions and student learning on your blog! I can't wait to share with my colleagues!
    Jocelyn Schmidt