Q&A #6297

Simultaneous equations

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From: Marielouise (for Teacher2Teacher Service)
Date: May 08, 2001 at 17:39:53
Subject: Re: Simultaneous equations

Hi, Sue, Simulataneous equations are two or more equations with a common solution. That means that a value of (x,y) = (a,b) where x = a and y = b will be true for all of the equations. There are different methods for solving them: 1. by graphing on the same grid 2. by elimination of one or more of the equations by multiplication/addition/ subtraction for equivalent equations. For example, x + y = -3 is the same equation as -2x - 2y = 6 3. by solving one equation for one variable and substituting the expression for the variable in the other equations. Another associate wrote the following: >being a teacher i would like to know the different ways of teaching algebraic expression and equations also i would appreciate activities for learning and teaching simultaneous equations. > thankyou for giving opportunity to learn from you. That is a pretty big order! One thing in teaching algebraic expressions, is to use algebra tiles or algeblocks?? I don't know if you are familiar with the process. For some of the students who tend to be more visual learners, it allows them a way to abstract to the algebraic expressions a little easier. There is a wonderful book published by NCTM (National Council of Teachers of Mathematics) called ALGEBRA FOR EVERYONE. I recall reading in the book about the students struggling from going from 23 to be a number composed of 2*10+3*1...then we automatically throw ab at them, and expect them to understand that the expression means a times b. It was a moment of reflection for me. The best idea I have ever heard about teaching simultaneous equations, begins with what a friend of mine calls "spaghetti systems". Lets take a simple coin problem. Jeni has 20 coins consisting of nickels and dimes which total $1.40. How many of each coin? Most students can pick two numbers that will give a sum of 20. Give each student a sheet of graph paper and two pieces of uncooked spaghetti (Linguini maybe better because it doesn't roll as easily). Say the student says 10 + 10 or 15 + 5. Decide which axis is nickels and which are dimes. Put one piece of spaghetti as the line between those two points. (Review geometry...two points determine a line) Then have them pick two solutions for the $1.40... 14 dimes and 0 nickels or 10 dimes and 8 nickels....use the other piece of spaghetti. Where the two pieces of pasta intersect is the solution. This is a nice non threatening way of introducing systems to students, especially those afraid of word problems. Then you go to other methods, since the spaghetti might be hard to estimate fraction or decimal values, or not long enough for large number solutions.......... You might also want to check out the www.enc.org web site. THe Eisenhower National Clearinghouse has lots of projects, activities and lessons for all topics in math and science. -Claudia, for the Teacher2Teacher service-Marielouise, for the T2T service

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