<?xml version="1.0"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD MathML 2.0//EN"
"../motor/em.dtd">
<?xml-stylesheet type="text/xsl" href="../motor/pmathml.xsl"?>
<html xmlns="http://www.w3.org/1999/xhtml"
      xmlns:pref="http://www.w3.org/2002/Math/preference"
pref:renderer="mathplayer">
<head>
<title>multifactor error analysis - error correction exercises</title>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"></meta>
<meta name="keywords" content="mathematics,math, mathematics software, problem solving, learning, training, math tutoring, multifactor, error analysis, errors, math tasks, methodical, recommendations, error correction"></meta>
<meta name="description" content="EMTeachline mathematics software offers multifactor analysis of errors in performing math tasks and methodical recommendations for error correction. Performed tasks are analysed severally and jointly."></meta>
<link rel="stylesheet" href="../main.css" type="text/css"></link>
</head>
<body  bgcolor="#FFFFFF" text="#336699" link="#003399" vlink="#666666" alink="#FF0000" leftmargin="15" topmargin="15" marginwidth="15" marginheight="15" background="../../button/emlogobg.jpg">
<h1>
Analysis of errors on solution steps 
</h1>
This page shows the results of analysis of error distribution over solution steps for four performed educational tasks. You see the total number of errors per particular step. Observe that the main errors are related with reduction of fractions; the recommended math problem, accordingly, represents a good example for learning fractions.
<hr  align="center" width="100%" size="1" ></hr>
<div align="center"><h1>Analysis: solution steps - All performed tasks</h1></div>
<b>Contents</b>
<table width="100%"><tr><td></td><td>
<a href="#pont0">Table</a>
</td></tr><tr><td></td><td>
<a href="#tont0">Plot</a>
</td></tr><tr><td></td><td>
<a href="#font0">Methodical recommendations:</a>
</td></tr>
</table>
<a name="font0"></a><a href="#cont0"><b>Methodical recommendations:</b></a><br></br>
<br></br>
<b>Perform the task</b>
<br></br>
Rational inequalities<br></br>
Strict linear inequalities<br></br>
Strict linear inequalities. Factorization of quadratic trinomial<br></br>
Solve the inequality<br></br>
<table width="100%">
<tr>
<td>
</td>
<td width="95%">
<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><mfrac><mrow><mrow><mo maxsize="2">(</mo><mrow><mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>18 </mi><msup><mi>r</mi><mi>2</mi></msup></mrow><mrow><mo>+</mo><mi>15 </mi><mi>r</mi></mrow><mrow><mo>+</mo><mi>25 </mi></mrow></mrow></mrow><mo maxsize="2">)</mo></mrow><mo>&#x00B7;</mo><mrow><mo maxsize="2">(</mo><mrow><mrow><mrow><mi>2 </mi><mi>r</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>6 </mi></mrow></mrow></mrow><mo maxsize="2">)</mo></mrow></mrow><mrow><mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>6 </mi><mi>r</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>5 </mi></mrow></mrow></mrow></mfrac></mrow><mo>-</mo><mrow><mfrac><mrow><mrow><mo maxsize="2">(</mo><mrow><mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>14 </mi><msup><mi>r</mi><mi>2</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>32 </mi><mi>r</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>8 </mi></mrow></mrow></mrow><mo maxsize="2">)</mo></mrow><mo>&#x00B7;</mo><mrow><mo maxsize="2">(</mo><mrow><mrow><mrow><mi>3 </mi><mi>r</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>6 </mi></mrow></mrow></mrow><mo maxsize="2">)</mo></mrow></mrow><mrow><mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>7 </mi><mi>r</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>2 </mi></mrow></mrow></mrow></mfrac></mrow><mo>&#x003C;</mo><mrow><mrow><mi>0 </mi></mrow></mrow></mrow></mrow></math>
</td>
</tr>
</table>
<b>Solve the problem with any of the following techniques </b>
<table width="100%">
<tr>
<td>
</td>
<td width="95%">
Scheme "To view 1"
</td>
</tr>
<tr>
<td>
</td>
<td width="95%">
Scheme "To insert 1"
</td>
</tr>
<tr>
<td>
</td>
<td width="95%">
Scheme "To insert 2"
</td>
</tr>
<tr>
<td>
</td>
<td width="95%">
Scheme "To solve independently 1"
</td>
</tr>
</table>
<a name="pont0"></a><a href="#cont0"><b>Table</b></a>
<br></br>
<br></br>
<table width="100%" border="1" cellspacing="1" cellpadding="1" bordercolor="#3399CC">
<tr bgcolor="#336699" class="tableh1">
<td width="3%">
<b>N</b>
</td>
<td><div align="center">
Step
</div></td>
<td width="5%">
Errors:
</td>
<td width="5%">
Hints:
</td>
<td width="5%">
Total:
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>0</b>
</td>
<td >
Applying the main property of fractions, let us reduce fractional expression by the linear nonzero polynomial (expression of the form "ax+b")
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>2</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>2</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>1</b>
</td>
<td >
Let's factor quadratic trinomial(s), using the theorem of factorization of quadratic trinomial
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>2</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>2</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>2</b>
</td>
<td >
Let's solve linear equation(s), applying the addition and multiplication principles of equations equivalence
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>2</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>2</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>3</b>
</td>
<td >
Let's apply the method of intervals to the obtained inequality
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>4</b>
</td>
<td >
Using the multiplication principle of equivalence of inequalities, let us divide both sides of the inequality by numerical coefficient at the argument
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>5</b>
</td>
<td >
Using the addition principle of equivalence of inequalities, let us move the numeric addend from the left-hand side of the inequality to its right-hand side
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>6</b>
</td>
<td >
Let's divide both sides of inequality by the greatest common divisor of coefficients of polynomial forming the inequality
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>7</b>
</td>
<td >
Let's multiply both sides of inequality by "-1"
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>8</b>
</td>
<td >
Let's add up coefficients at the like terms
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>9</b>
</td>
<td >
Let's collect similar terms of polynomial
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>10</b>
</td>
<td >
Let's combine polynomials, using the definition of operation of addition
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>11</b>
</td>
<td >
Let's multiply polynomials by each other, using the distributive law
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>12</b>
</td>
<td >
What is called an equation?
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
</tr>
</table>
<br></br>
<a name="tont0"></a><a href="#cont0"><b>Plot</b></a>
<div align="center"><table>
<tr>
<td>
<img src="5.jpg"  border="0" align="bottom" alt="detail" width="726" height="520"></img>
</td>
</tr>
</table></div>
<hr  align="center" width="100%" size="1" ></hr>
<div align="center"><span class="bottom">
<div>EMTeachline &#x00A9; 2003-2005</div>
<div>Utrecht, The Netherlands </div></span></div>
</body>
</html>
