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.

Math Journals and the 0-99 chart

I use math journals in a lot of ways. Often I ask children to record their math thinking about a group problem solving session in their journals. They also record math explorations and math game results. Recently we have been working to place numbers on the 0-99 chart.

The first day I presented the chart, I had already placed 0-16. I asked how many number cards were placed on the chart. Some students thought 16, but then someone pointed out that 0 was a number, too, so there were 17 cards on the chart. That day we placed 17 more numbers. At our next math group I turned the chart around so that they could not see it. I reminded them that there had been 17 cards on the chart to start with and that we had then added 17 more cards. How many cards were on the chart now? I asked each student to figure out the answer to the question and to show how they figured it out in their journal. Some students found a way to represent the cards in a drawing or by marks and added them up. Some used grouping by tens to help with that. Others worked with equations. Some needed a little help to talk through their process before writing it down. Some came up with the correct answer and some did not, but all were able in the end to represent the math process. The next math group we counted the cards to check our work. Those who came up with an incorrect answer were able to see what tripped them up. I told them that my goal was that everyone be able to show their math process in their journal. Everyone met that goal.

Birthday Graph

Our new school year is well underway. The first week, as we are getting to know each other, we do a graphing activity with the whole class. First we place the names of the months of the year in a row along the rug. Then we call out the months, one at a time, as the students sit behind the name of the month in which they were born. Once our "people graph" is complete, we ask the students questions based on our graph. Which month has the most birthdays? Which has the least? Is there a month with no birthdays? and so forth.

Next each child chooses a birthday cake picture to color in. These are labeled with the children's names and birthdates. Then each is placed above the correct month on a poster board chart. Now our birthday graph poster is prominently displayed in the classroom. The children refer to it on a regular basis to check on birthday's coming up and what cakes each child chose.

My Math Explorations

Today as we settled back into our routines after Spring Break, I took a little time to share with my math group about some math related explorations I did over break. For the first part of the break I took time off entirely: time to play with my granddaughters, time to watch the Final Four, time to hike and look for wildflowers. But the last few days of break I began to look through some math materials and think more about math and the rest of the year.

Math Solutions has a new book that looks interesting, Faster Isn't Smarter. Several chapters of the book are available online (http://www.mathsolutions.com/index.cfm?page=wp18&contentid=994&crid=294&mcrid=107) and that gave me a chance to read through them and mull them over. I shared with my students the name of the book and the idea that sometimes thinking deeper and taking time to process yields a broader understanding than coming up with a quick answer. Being fast in math doesn't necessarily mean you are smarter than others who take more time. I told my students that what is important is to learn what strategies work for you.

I also shared an activity from the latest edition of Teaching Children Mathematics, published by the National Council of Teachers of Mathematics. The activity I read about was for kindergarten students so I upgraded it some for my students. It involved tossing some 2 sided counters (red and white) and recording how many of each color turned up. Students were asked how they figured the totals (recognized the number, counted, knew the number fact, grouped the counters in their mind, etc.) They got practice in explaining their math strategies to the group or to a partner. Some students took on the additional challenge of explaining what they heard another student share as a strategy. We will do this activity again soon, working with a different total number of counters.

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.

Fraction Games

We have several board games in our classroom that focus on fractions: Frog Pond Fractions (by Trend Enterprises, Inc.,) Auntie Pasta's Fraction Game (by Learning Resources,) and Pie in the Sky (by Learning Resources.) Now that we are working on fractions in math group, the games are on our math group shelves and are one of the choices that students may make at "math choice" time, when they have finished their group work for the day.