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Fraction Models

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“Fraction Models” representation on the Illuminations website provides number sense through visual experiences with irrational  fractions. The site also allows children to see that different representations of fractions may be written with different numbers and operations and still mean the same proportion of the whole.  The experience with equivalent fractions will build schema for algebraic equations that require reducing rational numbers.

 The ability to change the squares to show area, length, and width removes the mystery of irrational numbers. Children may see that larger numerators simply means complete wholes and part of a whole. At this time, fourth-grade class is working on multiplication of tens, hundreds and thousands. The wide range option on scale would allow children to explore the concept of decimal places. Seeing the area representations change in proportion to the number line slide would allow my children who are still counting on their fingers to multiply make a connection to skip counting. Playing with the pie models would allow my children to build visual understanding of simple rational fractions. The screen is somewhat busy. I predict that some guidance on looking at different parts of the screen to make comparisons would be required. Also, it was fun to enlarge the pie with the scale and not look at the corresponding percentage and decimals algorithms. (I have trouble focusing sometimes also.)

Our training has taught us that playing with models such as this is an excellent way to build experience before introducing new concepts. The experience also would allow children to make discoveries themselves, without having to teach them directly. We may reinforce their ideas through explanation and scaffold their understanding with questions. As I’ve already mentioned, I also see opportunity for reviewing concepts and clearing errors in thinking with the models.


Written by autumnsfall2

November 4, 2010 at 5:17 pm

Posted in Math games

Experience Fractions Game

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The Fractions Game on the Illuminations web site had decent instructions. The goal is to slide all the rulers to one by matching the fraction on the card. Individuals may play themselves by beating the previous time required to finish. The sound has to be turned on, which my be best in a classroom.  I was not clear that I had the correct equivalent by the popping sound. A card is turned over and the player has options on how to slide the markers along tracks to reach one. Six tracks are marked with fractions of halves, thirds, fourth, fifths, sixths, and 10ths of one. Players may count one part at a time to reach one, using the same denominator.  As the game progresses,  a player is forced to find an equivalent fraction as the option for using the exact denominator is no longer available. A player may reduce the fraction or multiply by one in the form of a fraction to match an available denominator. When no exact option is not available, the marker may be slid to one if the fraction on the card is larger than the space required to reach one. A weakness is that the tracks became illegible near the end faded and froze up after three rounds. Positive reinforcement was given at the end of each round.

The game builds experience with concepts about fractions. Fractions of different numbers may be equivalent. Different fractions may be added to make one. Fractions are part of one. Larger numbers in fractions do not mean they are larger parts. Numerators tell how many pieces of one. Larger denominators mean smaller pieces of one.

The game may be used with partners or individuals at the computer center. The game may be used in fourth grade after an introduction using concrete manipulative models. The teacher may model using the game on a SMART board. Students may use the representations to practice or extend their understanding about fractions. Fifth graders may need review and practice. with fractions.

Written by autumnsfall2

October 31, 2010 at 5:35 pm

Posted in Math games, Technology

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NCCTM conference awesome!

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The North Carolina Council of Teachers of Mathematics 40th Annual State Conference in Greensboro Friday, Oct. 29, was awesome! Presenters gave evidence that constructivist instruction is happening in elementary schools in the mountains, from the piedmont, and to the coast.

Leigh Hutchins and LaShay Jennings of Buncombe County Schools , which uses the Pearson Investigations curriculum, challenged teachers to differentiate for students’ strengths and weaknesses by modifying games. They had developed involving dominoes and money chips. They suggested send concept modifications to Chutes and Ladders home with students to make a home-school connection with parents. They stressed giving children experience with numbers to build concepts of their relationships and operations.

Amy Scrinzi of the NC Department of Public Instruction, Office of Early Learning, set up centers of games for players to internalize facts. She gave a thumbs down to flash cards and timed tests. She said that as a child she thought there were hundreds of facts to be learned and that she would never memorize them.  Instead, help children internalize facts and number relationships by playing games in centers. She offered inexpensive games made of discount store pieces, like pompoms, cups, paper plates and markers. Players focus on one number at a time. Place the number of pompoms under focus in a cup. Spill the pieces on the plate halved with a marker line. Children record the number of pieces that fall on the  left half of the line and the number on the right side. They continue spilling and recording to build hands-on experience with ways to build a concept of that one number. Then, children discuss what they noticed about the number and how many ways to show it. Building number knowledge with games using one-to-one, hands-on objects like connecting cubes, plastic jewels, dice, and counters. The pieces were used to correspond to numbers on number lines, spinners, dice and balances.  Try “Grab Bag Subtraction” for two players. One player fills the bag with pieces of the number under focus. The other pulls out some counters and shows them. They work together to predict how many are still in the bag. The exchange may be, “I put in 6 and you took out 3.” How many left? They record a number sentence and guess before counting the pieces left in the bag.

Sonya Gregory of Charlotte-Mecklenburg Schools challenged teachers to offer experience solving problems and using reasoning skills. She recommended identifying a child’s strategies for solving a problem and building upon their models. Teach children to ask themselves, “What do I know? What do I need to find out?  Are there any roadblocks?” She provided these mind hooks for steps to solve problems: “Do it,” concrete; “Explain it,” verbal reasoning; “Picture it,” visual representation; and “Write it,” number sentence or expression.  She also shared “Box the Operator,” a strategy for solving word problems. Highlight operation words with a box. Underline numbers needed to solve. Circle unknown references. Draw arrows around equality words. Then put the highlighted data in an equation.

Tammy VanCleef, also of Charlotte-Mecklenburg Schools, showed card games can be used to differentiate among students in the classroom. Pose problems of comparing numbers with cards. Whoever has the larger or smaller number takes the cards. The player with the most cards has the greater number. Ramp it up by challenging to compare pairs of cards, which will build understanding for addition.  Add a third player for even more comparisons She showed video of two girls who challenged themselves without prompting. She also suggested making video, with proper permission, for observation, assessment and documentation.

From Cumberland County, the district math resource coordinator  Dawne Coker showed how to turn textbook problems into higher-order thinking exercises. Replace the numbers in a word problem with blanks. Scramble answers in boxes to be filled into the blanks. Challenge players to replace the numbers in the proper order. The method can be used from first to fifth grades. Another game, “Error Detectives,” makes the classroom a safe place to learn from errors. In teams with captains, players receive problems with errors. They are challenged to find the error and then show the others. They solve the problem correctly and show the others. Teachers often see students making the same error repeatedly. Ms. Coker suggested going home to write a problem and make the same error while modeling the next day.  See how quickly students catch the error. Students will learn to feel safe to engage, even if a mistake is made.

Written by autumnsfall2

October 30, 2010 at 1:24 am

Posted in Math games

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