On Wednesday and Friday last week, I had the group serve as "testers" for the riddles the partners had written on Monday. (See the post "Math Riddles.") Each worked with his/her partner from Monday. We took a riddle and went through the clues one by one. Each clue narrowed down the possibilities of which frog counters were in the bag. Once we had gone over all of the clues, we determined if we were left with only one possible solution. Two of the riddles succeeded in revealing the solutions. Three needed one or two more clues. Usually the partners who wrote the riddle were able to come up with additional clues that would work. Where help was needed, members of the group suggested ideas. It was a great example of collaboration.
We enjoyed all of the riddles. Each set of partners had set about the task in their own way, yet all found success in the end.
Sunday, September 28, 2008
Friday Math Homework Review
On Fridays we take time to review the math homework for the week. For the daily homework, I often draw on Primary Math Problems of the Day from Creative Publications and Marcy Cook. Problems include estimation problems, as well as ones that direct students to make a drawing that shows the solution and to write an equation for the problem.
When we review the problems, I ask students not only to share their answers but to share the strategies they use to get those answers. It helps them learn to put their math thinking into words and lets them see that there are often different approaches/ strategies that can work. For example the estimation problem this week was to estimate how many students in our class have a piano. Several students articulated (each in his/her own way) that they thought of particular students in the class who they knew had a piano and then added some more, thinking that if these students had one that there were probably some others they did not know about. Another simply said he knew some had pianos and some did not, so he just guessed a number that he thought was not too big and not too small. Interestingly, I thought that students who had a piano at home would be more likely to give a higher estimate, but this was not always true.
When we review the problems, I ask students not only to share their answers but to share the strategies they use to get those answers. It helps them learn to put their math thinking into words and lets them see that there are often different approaches/ strategies that can work. For example the estimation problem this week was to estimate how many students in our class have a piano. Several students articulated (each in his/her own way) that they thought of particular students in the class who they knew had a piano and then added some more, thinking that if these students had one that there were probably some others they did not know about. Another simply said he knew some had pianos and some did not, so he just guessed a number that he thought was not too big and not too small. Interestingly, I thought that students who had a piano at home would be more likely to give a higher estimate, but this was not always true.
Monday, September 22, 2008
Math Riddles
Today I did one of my favorite Marilyn Burns activities: Riddles with Color Tiles. I use frog counters which have the same colors as the tiles. We started with a riddle I had prepared, showing them a paper bag in which I had put some frogs. They worked with partners determined by drawing cubes out of a box. I gave out the clues one at a time, having the partners talking together and agreeing on a guess to display. By the end every group had correctly guessed what was in the bag (4 blue and 2 red frogs.) Now came the more challenging part. Each group was to choose some frog counters (10 or less and no more than 2 colors) to put in a bag. Then they had to write a series of clues that would by the end reveal what was in the bag. It was fascinating to watch the partners work. Some needed reminders to include their partners in the work. Others settled right down and cooperated well.
Next time we will test out the riddles to see if they work!
Next time we will test out the riddles to see if they work!
Sunday, September 21, 2008
Exploring Geometry
Math learning follows a spiral. Children revisit topics over time, hopefully learning more and deepening understanding with each visit. All of the seven and eight year olds in my math group have had experience with shapes in general and pattern blocks in particular. Last week I pulled out the pattern blocks and had my group examine each piece. An activity like this is an opportunity for me to see where different group members are in terms of their math understanding of a topic. It also allows me to work with children at different levels of understanding as I am covering both basic information as well as some more advanced concepts.
Everyone could identify the name for triangle. Then I asked them what made a triangle a triangle. All knew it had 3 sides. Anything else? Do they know what the word triangle means? How about the prefix tri-? After several guesses, someone made the connection with tricycle. Then we looked at angle. Several had a sense of what an angle is, but could not quite put it into words. Once we got a better sense of angle, and I provided some words for the term, I asked about the "Triangle Area" that we live in. Several were able to identify the points of our geographic triangle (Durham, Raleigh, and Chapel Hill.) We went on and identified, described, and explored the other shapes: square, rhombus, trapezoid, and hexagon. Hexagon was identified by several as either a pentagon or an octagon, so we got to talk some more about prefixes as well as stop signs. Children this age love to play with shapes, so before we went on to do some of Marcy Cook's Young Geometry problem solving tasks, I gave them a chance to make their own shapes. As always the Marcy Cook activity was fun for them, and as I watched them work, I learned more about how each of them approaches such tasks.
Everyone could identify the name for triangle. Then I asked them what made a triangle a triangle. All knew it had 3 sides. Anything else? Do they know what the word triangle means? How about the prefix tri-? After several guesses, someone made the connection with tricycle. Then we looked at angle. Several had a sense of what an angle is, but could not quite put it into words. Once we got a better sense of angle, and I provided some words for the term, I asked about the "Triangle Area" that we live in. Several were able to identify the points of our geographic triangle (Durham, Raleigh, and Chapel Hill.) We went on and identified, described, and explored the other shapes: square, rhombus, trapezoid, and hexagon. Hexagon was identified by several as either a pentagon or an octagon, so we got to talk some more about prefixes as well as stop signs. Children this age love to play with shapes, so before we went on to do some of Marcy Cook's Young Geometry problem solving tasks, I gave them a chance to make their own shapes. As always the Marcy Cook activity was fun for them, and as I watched them work, I learned more about how each of them approaches such tasks.
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