Talk:Algebra tile

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After reading this article, I was both intrigued and confused on the use of the tiles. After learning more about these manipulatives, I have created some changes to three fields in the article. Thinking that most people looking up this concept would be pre-service teachers, home-school teachers or other teachers, I thought some sections should be geared more towards lessons that could be learned using the tiles. So I have suggestions starting with updating the Virtual Algebra Tiles, changing the subtracting of integer section and finishing with modifying the multiplication of integers. Additions for Virtual Algebra Tiles. There are numerous online resources, lesson plans, and activities to practice using Algebra Tiles. Many are copyrighted and may only be used for personal reasons and not while being paid to tutor or part of the classroom. Make sure to read and understand the Terms of Use of any website used. To learn acceptable ways to combining Algebra Tiles before presenting the manipulatives to your class, try some of these interactive games. http://www.x-power.com/Flash/Tools/AlgebraTiles.html and http://illuminations.nctm.org/ActivityDetail.aspx?ID=216 Edit for subtracting integers. This paragraph was confusing, even for a math teacher. I would keep the majority of the first two sentences and then change the order and explanation of the middle. The section could be rewritten to present the opposite of a number first then using that to show similarities between -4 – (-2) and -4 + 2. Here’s my suggestion. Algebra tiles can also be used for subtracting integers. A student can take a problem such as    6 – 3 = ? To begin, start with a group of six positive unit tiles and then take three positives away to leave you with three positive unit tiles left over, so then 6 – 3 = 3. Before introducing subtracting negative numbers, show that the opposite of negative 2 is positive 2. To do this, place two zeros on the desk. As mentioned before, a zero is one positive unit tile and one negative unit tile grouped together. Notice the mathematical representation for “the opposite of negative 2”. Numerically, it would look like – (-2). With Algebra Tiles, this would be represented by taking away two negative unit tiles. Still on the desk would be two positive unit tiles. Thus, -(-2) = 2. Now use the Algebra Tiles to solve problems like -4 – (-2) = ? Start with 4 negative unit tiles on the desk. Take away 2 negative unit tiles. What is the result? There will be two negative unit tiles on the desk. Follow this with presenting the problem -4 + 2 = ? Again, there will be 4 negative unit tiles on the desk. Add 2 positive unit tiles to the desk. Remove the resulting zeros. What is the answer? The students will have the same answer as they had for -4 – (-2). Have the class create some of their own. The rest of the section on subtracting integers is clear and can be left as is. Edit for multiplication of integers. To attract more interest in using Algebra Tiles to show multiplication of integers, some changes in the wording of this section is needed. Using the words “groups of” would help clarify the role of multiplication. The first two sentences are clear. However, I would change the rest of the paragraph. For instance, in order to determine 3 X 4, take three groups of four positive unit tiles. Arrange these tiles into a rectangular shape with each group of 4 being a column. Now the class can count the number of unit tiles in the rectangle, which would be 12. In doing so, the class visually sees that the area of the rectangle is made up of squares so the answer is 12 unit squares. I would also include in this section an example of why multiplying a negative number times a negative number equals a positive number. This is not an intuitive statement. However, by using Algebra Tiles, a class would be able to see the result and form a conclusion before the rule was given. To accomplish this, start with zeros on the desk. Six to twelve zeros would work. Present the problem -3 X -2. This means take away three groups of negative two. From the group of zeros, remove "negative 2" three separate times. What is left? The answer to    -3 X -2 would be positive 6. Repeat with other similar problems and have the class create the rule. Adjunct00144 (talk) 19:01, 11 April 2012 (UTC)

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