Frog Riddles

Last week we did an activity from Marilyn Burn's and Bonnie Tank's A Collection of Math Lessons from Grades 1 through 3. Basing my lesson on the chapter on "Riddles with Color Tiles," I do frog riddles. First students use frog counters in four colors to come up with solutions to clues I give about what combination of frog counters are in a bag I have. They work in groups of two (generated by drawing a colored cube from a box). After we do a couple of riddles and talk about the process, each group is asked to come up with their own riddle of at least 4 clues. Each clue should move the solver closer to the solution, and the solver should be able to get the solution by the last clue. It takes some thought, logic, and planning to develop a riddle. After each group completed a riddle, we exchanged bags and clues and tested each others' riddles. Some were returned to the pairs that developed them for additional clues or clearer clues. Each partnership ended up with a successful riddle.

More Fractions!

On Monday I got out some play dough and shaped it into squares to represent brownies. Then we worked together to figure out how we could cut each "brownie" into fractions, such as fourths, sixths, and fifths. As students worked, I asked them to put into words the strategies they were using. At the end, the students agreed that it was easier to cut the "brownie" into an even number of pieces, as they could start by cutting it in half. Fifths proved the most difficult.

Then we learned the game Uncover from Marilyn Burn's About Teaching Mathematics: A K-8 Resource. It is the opposite of the game Cover Up which we learned a couple of weeks ago. This time we started with our whole piece covered by the two half pieces. We rolled the fraction cube to see which piece we could remove. Students had a choice on each turn of removing the piece that represented the fraction they rolled, trading one of their pieces in for equivalent pieces (e.g. trading a half in for a fourth and two eighths,) or passing.

Fractions

We have been exploring fractions lately. We started out cutting up an apple and talking about what fraction of the apple the pieces were. The students were able to recognize that two parts needed to be equal for them to be halves, and so forth. We also worked with blackberries to begin talking about fractions of a group of things. The additional value of these materials was that we could eat them when we finished.
We went on to make fraction kits, an activity from Marilyn Burn's About Teaching Mathematics: A K-8 Resource. In the activity, the students cut identically sized and multi-colored strips of paper up different ways. First they cut one in half and label each piece 1/2. The next strip is cut in 4 equal pieces and labeled appropriately. By the time we get to the fifth piece, the children have cut and written a lot. They are worried that they will need to cut this piece into 32 pieces, so they are relieved that this piece stays intact to represent 1 or 1/1.

After we made our fraction kits, we learned the game Cover Up, in which they roll a fraction cube to get pieces to cover the whole piece. On Friday we used the kits to explore equivalent fractions as well as how fractions add together. Later we will learn the game Uncover. It is a great hands on activity.

Measurement Explorations

We have been working on finding items in the classroom that are about as long as the white and orange cuisinaire rods. Once students found 5 items for each, we learned that the white rod is one centimeter long and the orange rod is 10 centimeters or 1 decimeter long. Another day we did the same activity using inch cubes. After these explorations, students had to measure some things at home with rulers or yardsticks for homework. Where possible they were to measure in English and metric units. As we shared the results of their measurements last Friday, we developed a clear sense of the relationship between an inch and a centimeter.

This activity was drawn from Marilyn Burn's work.

Frog Riddles

It's a new year and a new math group. Some of the students were in my language group last year. A couple are new to our class. Others I know as they were in Sky last year, though not in one of my small groups. As I often do, I have chosen an early activity from Marilyn Burn's and Bonnie Tank's A Collection of Math Lessons from Grades 1 through 3. Basing my lesson on the chapter on "Riddles with Color Tiles," I do Frog Riddles. First students use frog counters in four colors to come up with solutions to clues I give about what combination of frog counters are in a bag I have. They work in groups of two (generated by drawing a colored cube from a box). After we do a couple of riddles and talk about the process, each group is asked to come up with their own riddle of at least 4 clues. Each clue should move the solver closer to the solution, and the solver should be able to get the solution by the last clue. It takes some thought, logic, and planning to develop a riddle. After each group completed a riddle, we exchanged bags and clues and tested each others' riddles. Some were returned to the pairs that developed them for additional clues or clearer clues. Each partnership ended up with a successful riddle.

Marilyn Burns and More

One of the highlights of the NCTM Meeting for me was the presentation by Marilyn Burns on the topic of "Using Assessment to Guide Grades K-6 Mathematics Instruction: A Focus on Number and Operations." I have long used books by Marilyn Burns as a resource for my math teaching. She is a wonderful presenter, engaging with a warm sense of humor. Yes, she did use Powerpoint, which she noted was a recent change for her. But it was an outline which she fleshed out in her talk. She also incorporated some engaging video of the kind of assessment she was talking about. I particularly enjoyed seeing her use an assessment that I have used before, taking it from one of her books. Seeing the questions she asked, the way she encouraged the student to verbalize her thinking and reassured the student that the information would help Marlilyn be a better teacher, was quite helpful. All in all an inspriring, productive hour.

Later in the day I attended a session with a colleague of Marilyn Burns at Math Solutions, Lisa Rogers. She was addressing the development of number sense with primary students. By modelling some of the strategies she suggested and drawing in the audience with questions, she kept me alert and involved even though her session was late in the afternoon.
I also enjoyed a presentation on Singapore math, which is creating a buzz right now in this country. A lot of what was presented to us described a central focus on problem solving, the importance of helping students visualize math, and the laying of a foundation with informal experiences before introducing formal treatments. It is also a spiral curriculum that comes back around and revisits and reenforces topics. Other presentations I attended explored the development of algebraic thinking and the development of an understanding of base 10.

More Fractions

One fraction activity that I particularly love with this age is one I take from Marilyn Burn's About Teaching Mathematics: A K-8 Resource. In the activity, the students make fraction kits, cutting identically sized and multi-colored strips of paper up different ways. First they cut one in half and label each piece 1/2. The next strip is cut in 4 equal pieces and labeled appropriately. By the time we get to the fifth piece, the children have cut and written a lot. They are worried that they will need to cut this piece into 32 pieces, so they are relieved that this piece stays intact to represent 1 or 1/1.

Last week we made our fraction kits and learned the game Cover Up, in which they roll a fraction cube to get pieces to cover the whole piece. Later this week we will learn the game Uncover. We will also use the kits to explore how fractions add together and equivalent fractions. It is a great hands on activity.

S'marvelous S'math

We include activities in our curriculum that we call S'math because they use science and math together. One source for ideas is AIMS Education Foundation (http://www.aimsedu.org/). AIMS stands for Activities Integrating Math & Science. We also draw on other sources to "cook" up our plans, drawing in any themes we are pursuing as well as student interests.

This year our whole Lower School theme is "Way to Grow." Some of our early S'math activities focused on plants, using our Sky Class garden at times. We are also studying the human body and learning about its systems and parts. One activity focused on the skeleton as we explored bones and joints. More recently we did an activity (drawn from Marilyn Burns) in which students were asked to estimate how many times a strings equal to their heights would go around their heads at the forehead. We then went on to explore other body ratios (How does your height relate to your wingspan? How does your height relate to the length of your leg?)

Riddle Follow-up

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.

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!