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Session name: Sweet Tooth Fractions
Description of session
This session used two childrens literature books to teach about fractions: The Doorbell Rang by Pat Hutchens (which is about friends who share their 12 cookies with an increasing number of guests) and Full House by Dayle Ann Dodds (about a boardinghouse with more and more visitors). We learned how to make two, three, four, etc., fair shares of 12 cookies. After listening to the books, we practiced story problems related to sharing cookies, and eventually we discussed dividing a single cookie into equal parts. Rubberbands and geoboards in the shapes of squares and circles were provided so that we could practice dividing a whole into equal parts.
Critique of content
This was my second favorite session. The books were engaging and tied in well with the material. I liked how the story problems related to the books. The geoboards were handson and made understanding fractions more concrete.
Comparison to NCTM / SOL standards
The NCTM Standard is Number and Operations for grades 35: understanding fractions as parts of unit wholes, parts of a collection, locations on number lines, and divisions of whole numbers. The Va. SOL Standard is 3.5, The student will divide regions and sets to represent a fraction, and name and write fractions represented by a given model.
Applications to future teaching
I found the geoboards very useful, and I hope to incorporate them into my future lessons on fractions. Fractions can be challenging for students and the geoboards made the concepts more concrete. The circular geoboard can be especially helpful for problems in which a circular whole is divided into parts, such as pieces of a pie or pieces of a cookie. The presenter who read the book about sharing 12 cookies brought in homemade cookies for us to sample. This definitely made us more enthusiastic about the lesson, so I may think about bringing in food for my students when applicable!
***
Session name: Conversion Immersion: Decimals to Fractions
Description of session
This session used childrens literature and a card game to teach conversion between decimals and fractions. They started with money since that can serve as a prelude to decimals. The presenters had us keep track of the money that the pig family found around the house in the book Pigs Will Be Pigs: Fun with Math and Money by Amy Axelrod. Then they passed out charts with money amounts in the left hand column, and guided us in filling in the decimal version, fraction version, and word form on the right. We colored in square grids cut into tenths or hundredths. They closed with a game of interconnected cards in which each person has two values on their card, one listed under I have
and another listed under Who has
? For example, if I have 0.2, I will stand up when another card holder asks Who has two tenths? and if I have a grid with 40 hundredths colored in, I will ask who has that amount.
Critique of content
The chart was fairly useful and the game was interesting, but overall this was my least favorite session. In my opinion there were not enough handson manipulatives. The game had potential, but the version they gave us was too confusing even for adults, so a much simpler version would need to be designed for children.
Comparison to NCTM / SOL standards
The NCTM Standard is Numbers and Operations for Grades 35: recognize and generate equivalent forms of commonly used fractions, decimals, and percents; and recognize equivalent representations for the same number and generate them by decomposing and composing numbers. The Va. SOL Standard is 3.7, The student will read and write decimals expressed as tenths and hundredths, using concrete materials and models, and 4.2, The student will
relate fractions to decimals, using concrete objects.
Applications to future teaching
As a teacher, I plan to tie literature connections into math class because this can make math come alive and also make it less intimidating for people who are more languageoriented. I also like the use of games in math since it can motivate students. Although the game during the session didnt work very well, I can appreciate the goal of showing students that there are different ways of representing the same number (e.g., 0.4, 0.40, four tenths, forty hundredths, etc.), and as a teacher I would be interested in incorporating a similar game with connected cards.
***
Session name: TANGRAMS: So Much More Than Puzzle Pieces!
Description of session
There were tangram materials available at each table, and the presenters took us step by step through the process of making our own set of tangrams as we followed along individually with square pieces of paper. Then we made tangram quilts by arranging multicolored tangram pieces into a square, which is actually more challenging than it sounds. We each glued tangram pieces onto 8x8 inch construction paper, and then the presenters explained that in the classroom we could combine all the tangram squares into a class quilt. They held up an example. This class quilt could be used to teach concepts such as area and fractions. For example, students could calculate the total area of all red tangram pieces, all blue tangram pieces, etc. They could also calculate what percentage of the total quilt different colors of tangrams take up. Students working with a traditional tangram square could be guided into discovering that two of the pieces take up 1/4th of the square, three of the pieces take up 1/8th of the square, and two of the pieces take up 1/16th of the square. Then you could have students calculate the area of each of those pieces if the total area of the square is 2 feet squared, versus 4 feet squared, versus 8 feet squared, etc.
Critique of content
This was by far my favorite session, and I based one of my math lesson plans on tangrams. The session was very well organized and it was hands on the entire time. It was fun to design my own tangram square. The application of concepts like area and fractions to a tangram quilt was quite ingenious. I especially liked the use of tangrams because I think that some students who struggle with traditional math can excel with more spatial, geometric activities like these.
Comparison to NCTM / SOL standards
The NCTM Standard was Measurement for Grades 35: Apply appropriate techniques, tools, and formulas to determine measurements. Another relevant NCTM Standard was Number and Operations for Grades 35: develop understanding of fractions as parts of unit wholes [and] as parts of a collection. There were two relevant Va. SOLs. SOL 3.5 is The student will
name and write the fractions represented by a given model (area/region, length/measurement, and set). Fractions (including mixed numbers) will include halves, thirds, fourths, eighths, and tenths. SOL 5.8 is The student will describe and determine the perimeter of a polygon and the area of a square, rectangle, and right triangle, given the appropriate measures.
Applications to future teaching
I would like to make tangram quilts in my future class. If I am working with young children instead of asking detailed questions about area I might ask them Which color takes up the most space? and Which color takes up the least space? Instead of asking them for specific fractions, I might guide them to see that one piece is exactly half of another piece, or that one piece is twice the size of another piece. Online I found holiday tangram models, such as tangrams arranged in shapes such as cats and witches for Halloween, and these would be fun to incorporate in the classroom.
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