Equivalent Fractions

Almost a half century ago, my teacher taught a math lesson that I still remember today. We were learning how to add and subtract fractions, and she explained how to make equivalent fractions in order to have a common denominator. She started by asking us to multiply 1/2 by 1, 3/4 by 1, 5/6 by 1, etc. Then she wrote several names for 1 on the board - 2/2, 6/6, 10/10, etc. She explained that we could multiply the numerator and denominator by the same number without changing the value of the fraction because we were really multiplying by 1. I realize now that she was teaching us both the how and why in math, and I think that is why I still remember the lesson and have been able to manipulate fractions ever since.

Whenever I help students learn to make equivalent fractions, I always try to replicate my teacher's lesson. This week, I came across a great visual in a Wikiversity article and decided to make a laminated version on 4 x 6 cards, so students could use them with dry erase markers. I think this will help them understand what they are doing and why they are doing it.

February 2011 - Last week I started making the cards reversible by changing from multiplication to division, so they can also be used to reduce fractions to lowest terms by dividing by a form of one. Students have had very positive responses to these cards.

Adding Meaning to Mean

I had the opportunity to observe a 6th grade math teacher add relevance and meaning to the study of mean, median, mode, and range. She compiled formative assessment data from her four math sections to determine specific concepts to focus on prior to the summative assessment. She used the results to design further instruction, but she also presented and discussed the results with the classes, which helped them better understand the meaning and uses of what they were learning. It also allowed them to analyze the data. The assessment contained twelve questions - three for each concept. The data was organized by listing the percentage of students who correctly answered each question under the concept heading. The class discussed their interpretations of what they saw and were able to accurately infer which questions in each section resulted in the lower scores. For example, they decided that the question involving median that had the most incorrect answers involved an even quantity of numbers in the list. Following the lesson, the teacher displayed business websites containing statistical data and talked about how they use statistics to make business decisions.

This was one great way to answer the most often asked question in math classes - "When am I ever going to use this stuff outside of school?"

Playing with Words and Numbers

I got to teach 2nd grade today and enjoyed watching one of the Word Journey groups type the words into Wordle - http://www.wordle.net/ - and print them out. They loved it and enjoyed looking at those created by their classmates. Practicing spelling words can be fun.

Their feedback during my math lesson also gave me something to smile about. We were working on double digit addition. I love helping kids use what they know to figure out what they don't, so I used think-alouds to talk through the relationships between numbers. When I needed to add 7+6, I said that I know that 6+6=12, and 7 is one more than 6, so 7+6 must be one more than 12. Pretty soon I had the class talking through the problems with me. I felt good about the lesson and even better when one girl said, "I like the way you teach math", and several classmates agreed. Before becoming a teacher, I enjoyed playing with numbers on the job for 30 years. It is really exciting when I see kids enjoying playing with numbers too.

Tell Me and I Forget ... Involve Me and I Understand

As a 3rd grade associate this week, I watched a veteran teacher guide students to an understanding of the use of a coordinate grid. Prior to this lesson, they had used a map with letters on the horizontal axis and numbers on the vertical axis to locate cities. This time numbers were on both axes. The class discussed if this would cause any problems. About half thought it might. One student plotted the point (3,2). The teacher asked if anyone had a different location in mind. Another student placed a point in another location. The class discussed the problem. Next, the teacher explained the rule that solves the problem and results in each set of coordinates identifying only one point. I thoroughly enjoyed watching the students discuss their ideas with their shoulder partners and with the whole class. This lesson is an excellent example of involving kids in their learning.

Thinking About Mummies

After an extended weekend due to two snow days, I was back in the classroom. One of my favorite activities this year is volunteering with the homework help group at the middle school. The one-to-one aspect allows me to help students really understand the why, so they can consistently implement the how, especially in math. This week, I also had the opportunity to observe how peer discussion can get the brain's wheels spinning.

I was sitting with a 5th and 6th grader, and the 6th grader was working with the BBC's Mummy Maker at Discovery Kids - http://kids.discovery.com/fansites/tutenstein/mummymaker/mummymaker.html . He commented about using a hook to stir up the brains, and the 5th grader was hooked as well. The next step was to remove vital organs. The instructions said that one must remain to help the person reach the afterlife. A clue revealed that the conscience lived in that organ. The boys expressed their thoughts in conversation. The 5th grader said he thought it was the heart because it is the source of feelings about right and wrong. The 6th grader added that it might be the stomach because of the feeling you get in your stomach when you do something wrong. He opted to try the stomach and discovered heart was the correct answer. I was again reminded of the importance of letting students learn by sharing thoughts with peers.

It Doesn't Get Any Better Than This!

     I don't think I've felt this good since I found out from a group of third graders that I rock the world. This week I have had three amazing days in classrooms. The first two were in 7th grade math. On Monday, I got the impression that some of the students couldn't do the math because they didn't believe they could, so Tuesday morning I wrote one of my favorite sayings on the board. If you think you can't, you're right! I told them that the first step in accomplishing anything is to believe you can do it; if you don't believe in yourself, you will fail. I told them I believed I could become a distance runner at age 40, and I did. I believed I could take my first college class at age 50 and become a teacher, and I did. I believed I could run a half-marathon at age 55, and I did. I urged them to look at things that challenged them and say, "I think I can!" I don't know the exact words I heard from one girl in the back because I was so overwhelmed by the meaning. She said something to the effect that starting today she was going to have a whole new attitude about life and she was adopting my saying as her motto. Wow! I have had a lot of positive responses to my Can Do spiel but never one that touched me so profoundly.
     Today I got a call to teach in a 3rd grade class where I have subbed before. Before school started, I walked out of the classroom and down the hall. I said hello to a boy I passed, and he responded, "Hello, Mrs. Downing." He continued down the hall, and I thought I heard my name again, so I turned around. He was excitedly telling his classmates, "We get to have Mrs. Downing today!" I knew right then it would be a very good day. It was.
     I don't have my own classroom yet, so until I do I am going to continue enjoying every day I have the opportunity to positively impact the lives of children. Teachers can change the world, one student at a time.

Look at This!

     Yesterday I experienced another example of students taking pride in their products when the audience is greatly expanded by publishing their work on the web. (See The Purpose and the Audience.) I was volunteering at the after-school homework program when a student opened the school's website on his computer. I heard him exclaim, "Look at this!" He turned his screen toward me and, pointing to a video, he excitedly explained that it was a math project his classmates made. He hadn't even worked on the published project, yet he was thrilled that it was on the web for all to see.