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.

World of Math

On the first day my new math group met, I asked the students to think of all the things they could that were part of math. As they suggested things, I made a “map” of the World of Math. If we think of more things to add as the year goes on, we will put them on the map as well. I was happy to see that they were able to think of a lot of things to add in addition to arithmetic. Patterns, problem solving, and fun all had their place in the map we created.

Counting

On Thursday Tom took the old-timers and the new second year students to the multi, which gave me some time with our first year students. One of the students had repeatedly asked if we were going to do another scavenger hunt. (There was a Lower School scavenger hunt at our Open House for new students on Monday.) I came up with a number scavenger hunt that involved counting various things in the classroom. As the students went about counting and recording, it was a great chance for me to see how different ones took on the task. I observed how they went about counting the objects and how much confidence they showed in the counting. One student proudly shared that he counted by 3’s. I also watched as they recorded the results. A student asked if 8 was the number with “two balls.” Two girls consulted together about whether the 1 in 12 should go first or not. They had fun with the activity and seemed satisfied as they turned in their recording sheets.

Math Games Online

I have been working on assembling links to some good online math games to put on the computers that the students use at Centers time. We already have KidPix, Logo, and a couple of installed math games on the computers. The links will expand the choices.

As I evaluate which games to use, I found an online article that has been helpful. It was posted by NCTM (National Council of Teachers of Mathematics) and discusses math games and how to evaluate the many online games to finds ones that support students’ learning of math concepts in an interactive way. Here is a link to the article, which includes links to some games that they recommend:  http://www.nctm.org/resources/content.aspx?id=27612

I follow the Free Technology for Teachers blog which features a wealth of resources for teachers available online. Richard Byrne, who writes the blog, periodically includes math resources, including games, in his post.

Turtle Fun

Catching up on activities from November and December:
One focus was learning about a simple computer programming language called LOGO that was developed at MIT as an educational aid for children. In Logo the cursor is a “turtle” who moves across the screen creating graphics based on the commands given by the children. We learned some basic Logo commands, and students then worked on writing out programs (a series of commands) which they could type into the computer to see the results. This project has generated a good deal of excitement in our group. Initially the students worked in partnerships, helping each other as they learned. Then each student had an opportunity to work on a laptop solo. Logo helps students develop their spatial/geometric sense as well as providing good problem solving experience, as they try to figure out how to make the turtle create the drawings they want.

Dreidel Probability

In December we did a probability study with dreidels. We talked about the tops used for the traditional Hanukkah game of dreidel and what we would expect with a fair dreidel. Students said that each of the four sides should have an equal chance of coming up. A few talked about how they want gimel to come up the most. Then we speculated about why one side might come up more than the others. Students thought about how they were made, about whether the letters were painted on or were on the side in relief, and about how the dreidel behaves when it is spun. I shared that to get an accurate picture we needed to have a lot of spins. In our study we compared plastic and wooden dreidels to see if one kind was more consistently fair than the other. Students spun the dreidels in class and at home for homework. Then each student recorded the results in a spreadsheet. Here are our results:

Correcting Math Misconceptions

Our Head Teacher has recently shared some new books with us on the topic of math. Two that have piqued my interest are Math Misconceptions: From Misunderstanding to Deep Understanding by Honi J. Bamberger, Christine Oberdorf, and Karren Schultz-Ferrell and the related book, Activities to Undo Math Misconceptions by Honi J. Bamberger and Karren Schultz-Ferrell.

I have been reading the section on two digit addition and subtraction. The writers share this from research:
 “When children focus on following the steps taught traditionally, they usually pay no attention to the quantities and don’t even consider whether or not their answers make sense.” (Richardson, 1999,100)
and they add that“an understanding of place value is critical to computing efficiently and effectively.”

It gives me good feedback to see that a number of activities they suggest to counter the misconceptions are ones that are part of our curriculum. We include activities such as noticing patterns on a 100s chart, representing two-digit numbers using different sets of tens and ones with cubes and blocks, and having students verbalize and share the strategies they use for two-digit addition. I also have found some new activities to add to our explorations. In one, Make 100, students roll two dice and get that number of Unifix cubes. They place them on a mat with a place for ones and tens. When they get enough cubes, they can snap them together to make a ten and move that group of ten to the other column. They keep going, recording each turn, until they reach 12 turns or 100. For students who need additional challenge, they can work to mentally compute how many more they need to reach 100 at each turn. This game is similar to a game I usually have the students play with base 10 blocks, in which students trade in 10 cubes for a 10 stick. I like the version with Unifix cubes as a lead-in to the other game, because the students are constructing the tens themselves. Later we will play a game that takes away cubes, so that they can deconstruct tens as they subtract.