|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| {{Multiple issues|orphan=October 2008|howto=October 2008|notability=October 2008}}
| | If you are looking for a specific plugin, then you can just search for the name of the plugin. Affilo - Theme is the guaranteed mixing of wordpress theme that Mark Ling use for his internet marketing career. Step-4 Testing: It is the foremost important of your Plugin development process. If you need a special plugin for your website , there are thousands of plugins that can be used to meet those needs. The top 4 reasons to use Business Word - Press Themes for a business website are:. <br><br> |
|
| |
|
| '''Algebra tiles''' are known as [[mathematical manipulatives]] that allow students to better understand ways of algebraic thinking and the concepts of [[algebra]]. These tiles have proven to provide concrete models for [[elementary school]], [[middle school]], [[high school]], and college-level introductory [[algebra]] [[students]]. They have also been used to prepare [[prison]] inmates for their [[General Educational Development]] (GED) tests.<ref name="Kitts, N page 462">Kitts, N: "Using Homemade Algebra Tiles to Develop Algebra and Pre algebra Concepts", page 462. MATHEMATICS TEACHER, 2000.</ref> '''Algebra tiles''' allow both an algebraic and geometric approach to algebraic concepts. They give [[students]] another way to solve algebraic problems other than just abstract manipulation.<ref name="Kitts, N page 463">Kitts, N: "Using Homemade Algebra Tiles to Develop Algebra and Prealgebra Concepts", page 463. MATHEMATICS TEACHER, 2000.</ref> The [[National Council of Teachers of Mathematics]] ([[NCTM]]) recommends a decreased emphasis on the memorization of the rules of [[algebra]] and the symbol manipulation of [[algebra]] in their ''Curriculum and Evaluation Standards for Mathematics''. According to the [[NCTM]] 1989 standards "[r]elating models to one another builds a better understanding of each".<ref>Stein, M: Implementing Standards-Based Mathematics Instruction", page 105. Teachers College Press, 2000.</ref>
| | Choosing what kind of links you'll be using is a ctitical aspect of any linkwheel strategy, especially since there are several different types of links that are assessed by search engines. Best of all, you can still have all the functionality that you desire when you use the Word - Press platform. With the free Word - Press blog, you have the liberty to come up with your own personalized domain name. From my very own experiences, I will let you know why you should choose WPZOOM Live journal templates. Moreover, many Word - Press themes need to be purchased and designing your own WP site can be boring. <br><br>Minor and medium sized corporations also have a lot to obtain by shelling out in a very good website. If you liked this write-up and you would like to receive a lot more information concerning [http://www.nt-protect.host.sk/?wordpress_backup_plugin_616881 backup plugin] kindly pay a visit to the site. As of now, Pin2Press is getting ready to hit the market. You've got invested a great cope of time developing and producing up the topic substance. These frequent updates have created menace in the task of optimization. If you've hosted your Word - Press website on a shared hosting server then it'll be easier for you to confirm the restricted access to your site files. <br><br>Digg Digg Social Sharing - This plugin that is accountable for the floating social icon located at the left aspect corner of just about every submit. I didn't straight consider near it solon than one distance, I got the Popup Ascendancy plugin and it's up and lengthways, likely you make seen it today when you visited our blog, and I yet customize it to fit our Thesis Wound which gives it a rattling uncomparable visage and search than any different popup you know seen before on any added journal, I hump arrogated asset of one of it's quatern themes to make our own. Thus it is difficult to outrank any one of these because of their different usages. IVF ,fertility,infertility expert,surrogacy specialist in India at Rotundaivf. It does take time to come up having a website that gives you the much needed results hence the web developer must be ready to help you along the route. <br><br>A sitemap is useful for enabling web spiders and also on rare occasions clients, too, to more easily and navigate your website. When you sign up with Wordpress, you gain access to several different templates and plug-in that allow you to customize your blog so that it fits in with your business website design seamlessly. However, there are a few other Wordpress plugins also for its development which requires adding files in your Wordpress setup. Change the entire appearance of you blog using themes with one click. As for performing online business, websites and blogs are the only medium that are available to interact with customers and Word - Press perform this work with the help of cross-blog communication tools, comments and full user registration plug-ins. |
| | |
| ==Physical attributes==
| |
| The algebra tiles are made up of small squares, large squares, and rectangles. The [[1 (number)|number one]] is represented by the small square, which is also known as the unit tile. The rectangle represents the [[Variable (mathematics)|variable]] x and the large square represents x<sup>2</sup>. The [[length]] of the side of the large square is equal to the [[length]] of the rectangle, also known as the x tile. When visualizing these tiles it is important to remember that the [[area]] of a square is s<sup>2</sup>, which is the length of the sides squared. So if the [[length]] of the sides of the large square is x then it is understandable that the large square represents x<sup>2</sup>. The width of the x tile is the same [[length]] as the side length of the unit tile. The reason that the algebra tiles are made this way will become clear through understanding their use in [[Factorization|factoring]] and multiplying [[polynomials]].<ref name="Kitts, N page 462" />
| |
| | |
| Commercially made algebra tiles are usually made from plastic and have one side of one color and the other side of another color. the difference in the color is supposed to denote one side that is positive and one side that is negative. Traditionally, one side is red to represent the negative and one side is green to represent the positive.<ref name="Kitts, N page 462" /> Having the two colors on both sides allows for more numbers to be represented with the same tiles. It also makes it easier to change positives to negatives when performing a procedure such as multiplying a positive and a negative number. There are some tiles where the positive x and x<sup>2</sup> tile will be the same color, but the positive unit tile is a different color. This representation is still all right to use, it is just important to have a least two colors to denote positive and negative. Translucent plastic algebra tiles can be bought for the [[overhead projector]].<ref>[http://www.eaieducation.com/525010.html Overhead Projector Algebra Tiles]</ref>
| |
| | |
| Algebra tiles can be made. Templates for the algebra tiles can be found online,[http://www.teachervision.fen.com/algebra/printable/6192.html Algebra tile template], which can be printed and then cut out.<ref>{{cite web|url=http://www.teachervision.fen.com/algebra/printable/6192.html |title=Algebra Tiles Printable (6th - 8th Grade) - TeacherVision.com |publisher=Teachervision.fen.com |date= |accessdate=2013-07-22}}</ref> Once the shapes are cut out of the printer paper they can be used to cut out algebra tiles from [[card stock]] or Foamies, which are [[foam]]-like materials, about 1/8-inch thick.<ref>[http://www.regentsprep.org/regents/math/ALGEBRA/teachres/ttiles.htm Homemade Algebra Tiles]</ref> Algebra tiles can also be made for the [[overhead projector]] by cutting the shapes out of colored plastic report covers.<ref name="Kitts, N page 463" />
| |
| | |
| [[Virtual manipulatives for mathematics|Virtual Algebra Tiles]] are available from The National Library of Virtual Manipulatives,<ref>[http://nlvm.usu.edu/en/nav/vlibrary.html]</ref> the [[Ubersketch]] and in the sample files that ship with [[The Geometer's Sketchpad]].''
| |
| | |
| ==Uses==
| |
| | |
| ===Adding integers===
| |
| | |
| ===Subtracting integers===
| |
| Algebra tiles can also be used for subtracting [[integers]]. A person can take a problem such as <math>6-3=?</math> and begin with a group of six unit tiles and then take three away to leave you with three left over, so then <math>6-3=3</math>. Algebra tiles can also be used to solve problems like <math>-4-(-2)=?</math>.get if you had the problem <math>-4+2</math>. Being able to relate these two problems and why they get the same answer is important because it shows that <math>-(-2)=2</math>. Another way in which algebra tiles can be used for [[integer]] [[subtraction]] can be seen through looking at problems where you subtract a positive [[integer]] from a smaller positive [[integer]], like <math>5-8</math>. Here you would begin with five positive unit tiles and then you would add zero pairs to the five positive unit tiles until there were eight positive unit tiles in front of you. Adding the zero pairs will not change the value of the original five positive unit tiles you originally had. You would then remove the eight positive unit tiles and count the number of negative unit tiles left. This number of negative unit tiles would then be your answer, which would be -3.<ref name="phschool.com">{{cite web|url=http://www.phschool.com/professional_development/teaching_tools/pdf/using_algebra_tiles.pdf |title=Prentice Hall School |publisher=Phschool.com |date= |accessdate=2013-07-22}}</ref>
| |
| | |
| ===Multiplication of integers===
| |
| [[Multiplication]] of [[integers]] with algebra tiles is performed through forming a rectangle with the tiles. The [[length]] and [[width]] of your rectangle would be your two [[divisor|factors]] and then the total number of tiles in the rectangle would be the answer to your [[multiplication]] problem. For instance in order to determine 3×4 you would take three positive unit tiles to represent three rows in the rectangle and then there would be four positive unit tiles to represent the columns in the rectangle. This would lead to having a rectangle with four columns of three positive unit tiles, which represents 3×4. Now you can count the number of unit tiles in the rectangle, which will equal 12.
| |
| | |
| ===Modeling and simplifying algebraic expressions===
| |
| Modeling algebraic expressions with algebra tiles is very similar to modeling [[addition]] and [[subtraction]] of integers using algebra tiles. In an expression such as <math>5x-3</math> you would group five positive x tiles together and then three negative unit tiles together to represent this algebraic expression. Along with modeling these expressions, algebra tiles can also be used to simplify algebraic expressions. For instance, if you have <math>4x+5-2x-3</math> you can combine the positive and negative x tiles and unit tiles to form zero pairs to leave you with the expression <math>2x+2</math>. Since the tiles are laid out right in front of you it is easy to combine the like terms, or the terms that represent the same type of tile.<ref name="phschool.com" />
| |
| | |
| The [[distributive property]] is modeled through the algebra tiles by demonstrating that a(b+c)=(a×b)+(a×c). You would want to model what is being represented on both sides of the equation separately and determine that they are both equal to each other. If we want to show that <math>3(x+1)=3x+3</math> then we would make three sets of one unit tile and one x tile and then combine them together to see if would have <math>3x+3</math>, which we would.<ref>[http://www.regentsprep.org/rEGENTS/math/realnum/Tdistrib.htm ]{{dead link|date=July 2013}}</ref>
| |
| | |
| ===Solving linear equations===
| |
| Manipulating algebra tiles can help students solve [[linear equations]]. In order to solve a problem like <math>x-6=2</math> you would first place one x tile and six negative unit tiles in one group and then two positive unit tiles in another. You would then want to isolate the x tile by adding six positive unit tiles to each group, since whatever you do to one side has to be done to the other or they would not be equal anymore. This would create six zero pairs in the group with the x tile and then there would be eight positive unit tiles in the other group. this would mean that <math>x=8</math>.<ref name="phschool.com" /> You can also use the [[subtraction]] property of equality to solve your [[linear equation]] with algebra tiles. If you have the equation <math>x+7=10</math>, then you can add seven negative unit tiles to both sides and create zero pairs, which is the same as subtracting seven. Once the seven unit tiles are subtracted from both sides you find that your answer is <math>x=3</math>.<ref name="Kitts, N page 464">Kitts, N: "Using Homemade Algebra Tiles to Develop Algebra and Prealgebra Concepts", page 464. MATHEMATICS TEACHER, 2000.</ref> There are programs online that allow students to create their own [[linear equations]] and manipulate the algebra tiles to solve the problem. [http://my.hrw.com/math06_07/nsmedia/tools/Algebra_Tiles/Algebra_Tiles.html Solving Linear Equations Program] This video from [[TeacherTube]] also demonstrates how algebra tiles can be used to solve linear equations. [http://www.teachertube.com/view_video.php?viewkey=7b93931b2e628c6e6244&page=&viewtype=&category= Teacher Tube Solving Equations]
| |
| | |
| ===Solving linear systems===
| |
| Linear systems of equations may be solved algebraically by isolating one of the variables and then performing a substitution. Isolating a variable can be modeled with algebra tiles in a manner similar to solving linear equations (above), and substitution can be modeled with algebra tiles by replacing tiles with other tiles.
| |
| | |
| ===Multiplying polynomials===
| |
| When using algebra tiles to multiply a [[monomial]] by a [[monomial]] you first set up a rectangle where the [[length]] of the rectangle is the one [[monomial]] and then the [[width]] of the rectangle is the other [[monomial]], similar to when you multiply [[integers]] using algebra tiles. Once the sides of the rectangle are represented by the algebra tiles you would then try to figure out which algebra tiles would fill in the rectangle. For instance, if you had x×x the only algebra tile that would complete the rectangle would be x<sup>2</sup>, which is the answer.
| |
| | |
| [[Multiplication]] of [[binomials]] is similar to [[multiplication]] of [[monomials]] when using the algebra tiles . Multiplication of [[binomials]] can also be thought of as creating a rectangle where the [[Integer factorization|factors]] are the [[length]] and [[width]].<ref>Stein, M: Implementing Standards-Based Mathematics Instruction", page 98. Teachers College Press, 2000.</ref> As with the [[monomials]], you set up the sides of the rectangle to be the [[Integer factorization|factors]] and then you fill in the rectangle with the algebra tiles.<ref>Stein, M: Implementing Standards-Based Mathematics Instruction", page 106. Teachers College Press, 2000.</ref> This method of using algebra tiles to multiply [[polynomials]] is known as the area model<ref>Larson R: "Algebra 1", page 516. McDougal Littell, 1998.</ref> and it can also be applied to multiplying [[monomials]] and [[binomials]] with each other. An example of multiplying [[binomials]] is (2x+1)×(x+2) and the first step you would take is set up two positive x tiles and one positive unit tile to represent the [[length]] of a rectangle and then you would take one positive x tile and two positive unit tiles to represent the [[width]]. These two lines of tiles would create a space that looks like a rectangle which can be filled in with certain tiles. In the case of this example the rectangle would be composed of two positive x<sup>2</sup> tiles, five positive x tiles, and two positive unit tiles. So the solution is 2x<sup>2</sup>+5x+2.
| |
| | |
| ===Factoring===
| |
| In order to factor using algebra tiles you start out with a set of tiles that you combine into a rectangle, this may require the use of adding zero pairs in order to make the rectangular shape. An example would be where you are given one positive x<sup>2</sup> tile, three positive x tiles, and two positive unit tiles. You form the rectangle by having the x<sup>2</sup> tile in the upper right corner, then you have two x tiles on the right side of the x<sup>2</sup> tile, one x tile underneath the x<sup>2</sup> tile, and two unit tiles are in the bottom right corner. By placing the algebra tiles to the sides of this rectangle we can determine that we need one positive x tile and one positive unit tile for the [[length]] and then one positive x tile and two positive unit tiles for the [[width]]. This means that the two [[Integer factorization|factors]] are <math>x+1</math> and <math>x+2</math>.<ref name="Kitts, N page 464" /> In a sense this is the reverse of the procedure for multiplying [[polynomials]].
| |
| | |
| ===Completing the square===
| |
| The process of [[completing the square]] can be accomplished using algebra tiles by placing your x<sup>2</sup> tiles and x tiles into a square. You will not be able to completely create the square because there will be a smaller square missing from your larger square that you made from the tiles you were given, which will be filled in by the unit tiles. In order to [[complete the square]] you would determine how many unit tiles would be needed to fill in the missing square. In order to [[complete the square]] of x<sup>2</sup>+6x you start off with one positive x<sup>2</sup> tile and six positive x tiles. You place the x<sup>2</sup> tile in the upper left corner and then you place three positive x tiles to the right of the x<sup>2</sup> tile and three positive unit x tiles under the x<sup>2</sup> tile. In order to fill in the square we need nine positive unit tiles. we have now created x<sup>2</sup>+6x+9, which can be factored into <math>(x+3)(x+3)</math>.<ref>{{cite web|author=Donna Roberts |url=http://www.regentsprep.org/Regents/math/algtrig/ATE12/completesq.htm |title=Using Algebra Tiles to Complete the Square |publisher=Regentsprep.org |date= |accessdate=2013-07-22}}</ref>
| |
| | |
| ==References==
| |
| {{reflist|2}}
| |
| | |
| ==Sources==
| |
| * Kitt, Nancy A. and Annette Ricks Leitze. "Using Homemade Algebra Tiles to Develop Algebra and Prealgebra Concepts." ''MATHEMATICS TEACHER'' 2000. 462-520.
| |
| * Stein, Mary Kay et al., ''IMPLEMENTING STANDARDS-BASED MATHEMATICS INSTRUCTION''. New York: Teachers College Press, 2000.
| |
| * Larson, Ronald E., ''ALGEBRA 1''. Illinois: McDougal Littell,1998.
| |
| | |
| == External links ==
| |
| * [http://www.assessmentservices-edu.com/Algebra-tiles.aspx Algebra tile manipulatives]
| |
| | |
| [[Category:Mathematics education]]
| |
If you are looking for a specific plugin, then you can just search for the name of the plugin. Affilo - Theme is the guaranteed mixing of wordpress theme that Mark Ling use for his internet marketing career. Step-4 Testing: It is the foremost important of your Plugin development process. If you need a special plugin for your website , there are thousands of plugins that can be used to meet those needs. The top 4 reasons to use Business Word - Press Themes for a business website are:.
Choosing what kind of links you'll be using is a ctitical aspect of any linkwheel strategy, especially since there are several different types of links that are assessed by search engines. Best of all, you can still have all the functionality that you desire when you use the Word - Press platform. With the free Word - Press blog, you have the liberty to come up with your own personalized domain name. From my very own experiences, I will let you know why you should choose WPZOOM Live journal templates. Moreover, many Word - Press themes need to be purchased and designing your own WP site can be boring.
Minor and medium sized corporations also have a lot to obtain by shelling out in a very good website. If you liked this write-up and you would like to receive a lot more information concerning backup plugin kindly pay a visit to the site. As of now, Pin2Press is getting ready to hit the market. You've got invested a great cope of time developing and producing up the topic substance. These frequent updates have created menace in the task of optimization. If you've hosted your Word - Press website on a shared hosting server then it'll be easier for you to confirm the restricted access to your site files.
Digg Digg Social Sharing - This plugin that is accountable for the floating social icon located at the left aspect corner of just about every submit. I didn't straight consider near it solon than one distance, I got the Popup Ascendancy plugin and it's up and lengthways, likely you make seen it today when you visited our blog, and I yet customize it to fit our Thesis Wound which gives it a rattling uncomparable visage and search than any different popup you know seen before on any added journal, I hump arrogated asset of one of it's quatern themes to make our own. Thus it is difficult to outrank any one of these because of their different usages. IVF ,fertility,infertility expert,surrogacy specialist in India at Rotundaivf. It does take time to come up having a website that gives you the much needed results hence the web developer must be ready to help you along the route.
A sitemap is useful for enabling web spiders and also on rare occasions clients, too, to more easily and navigate your website. When you sign up with Wordpress, you gain access to several different templates and plug-in that allow you to customize your blog so that it fits in with your business website design seamlessly. However, there are a few other Wordpress plugins also for its development which requires adding files in your Wordpress setup. Change the entire appearance of you blog using themes with one click. As for performing online business, websites and blogs are the only medium that are available to interact with customers and Word - Press perform this work with the help of cross-blog communication tools, comments and full user registration plug-ins.