## Archive for **October 2010**

## Experience Fractions Game

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.

## Foundation for understanding algebra

Reading the article “Children’s Understanding of Equality: Foundation of Algebra, by Falkner, Levl and Carpenter in *Teaching Mathematics*, I was surprised that children see the equal sign as an operation rather than a relationship. I recall hearing the words “is equal to” or “the same as” when reading math problems. Also, I was surprised by that 84 percent of the 145 sixth graders who did not correctly compute 8 + 4 = ? + 5. I found that the small sample of one of three fourth-graders in my clinical class got the addition problem wrong. Two of three got the multiplication problem 9 x 9 = ? + 63 correct; but they did not make the connection that 63 is a multiple of 9. They just finished factoring. The third child is working on the tens number system, and number sense. We can help children build number sense by given the equations context and working with a manipulative like a set of 100s blocks.

## NCCTM conference awesome!

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.

## Addressing Student Errors

The student errors in multiplying by double-digit multiplicands and multipliers were not basic fact errors. The student knew that 2*4 = 8 and 3*1 = 3. They did not understand the form of columns representing decimal places in relationship to multiplication. They dutifully followed the rules they had learned in addition. The top-to-bottom procedure related to their experience with columns in adding double-digit numbers. I imagine the student thinking, “Why would anyone suddenly cross over to the ones column to multiply 3 * 4 in “32 * 14 = 38?” I assessed a fourth-grader who obviously had been taught the term “cross over” to multiply this type of problem. She dutifully used the term “cross over” as she placed the products in locations only an artist would appreciate. An array breaks the double-digit numbers into parts that can be kept in the proper decimal columns. The transitional strategy shows the student where numbers originate and their proper decimal place in the product. The relationships of the numbers become clearer to the students with visible scaffolding.

## “Illuminations” Pan Balance

The *Illuminations* Pan Balance game was a bit frustrating for this digital foreigner. Once I got the hang of the drag and drop, I was relieved that I found the answer to the first shape quickly. I had a few more trials and errors on the triangles. Balancing the kites were easier. Surprisingly, I did not have to change the representations into algorithms. The relationships became evident once I had two values to substitute and count. The representation gave me experience with substituting an unknown value. That experience would make seeing an algorithm much less intimidating for a student.

The teacher’s function in the article was facilitator, asking questions that allowed the students to talk about their reasoning without fear of being wrong. She encouraged them to share their ideas with one another and support through their differences. Talking about their thinking, metacognition, made it easier to recognize their errors.

## Hello ELED 5301-090 Fellows!

Are we having fun yet! At last, I don’t have to yell at the TV when I disagree with a politician or think a newscaster is an idiot. I can blog about it!