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messages[0] = new Array('/8th/pix/2.0c.jpg','  Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents');
messages[1] = new Array('/8th/pix/2.0.jpg','  Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents');
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messages[3] = new Array('/8th/pix/2.0a.jpg','  Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents');
messages[4] = new Array('/8th/pix/3.0.jpg','  Students solve equations and inequalities involving absolute values');
messages[5] = new Array('/8th/pix/3.0a.jpg','  Students solve equations and inequalities involving absolute values');
messages[6] = new Array('/8th/pix/4.0.jpg','  Students simplify expressions prior to solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12');
messages[7] = new Array('/8th/pix/4.0a.jpg','  Students simplify expressions prior to solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12');
messages[8] = new Array('/8th/pix/5.0b.jpg','  Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step');
messages[9] = new Array('/8th/pix/5.0.jpg','  Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step');
messages[10] = new Array('/8th/pix/5.0c.jpg','  Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step');
messages[11] = new Array('/8th/pix/5.0a.jpg','  Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step');
messages[12] = new Array('/8th/pix/5.0d.jpg','  Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step');
messages[13] = new Array('/8th/pix/6.0.jpg','  Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4');
messages[14] = new Array('/8th/pix/7.0.jpg','  Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations using the point-slope formula');
messages[15] = new Array('/8th/pix/8.0.jpg','  Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point');
messages[16] = new Array('/8th/pix/9.0.jpg','  Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets');
messages[17] = new Array('/8th/pix/10.0.jpg','  Students add, subtract, multiply, and divide monomials polynomials. Students solve multistep problems, including word problems, by using these techniques');
messages[18] = new Array('/8th/pix/10.0a.jpg','  Students add, subtract, multiply, and divide monomials polynomials. Students solve multistep problems, including word problems, by using these techniques');
messages[19] = new Array('/8th/pix/10.0c.jpg','  Students add, subtract, multiply, and divide monomials polynomials. Students solve multistep problems, including word problems, by using these techniques');
messages[20] = new Array('/8th/pix/10.0d.jpg','  Students add, subtract, multiply, and divide monomials polynomials. Students solve multistep problems, including word problems, by using these techniques');
messages[21] = new Array('/8th/pix/11.0.jpg','  Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials');
messages[22] = new Array('/8th/pix/11.0b.jpg','  Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials');
messages[23] = new Array('/8th/pix/14.0.jpg','  Students solve a quadratic equation by factoring or completing the square');
messages[24] = new Array('/8th/pix/14.0a.jpg','  Students solve a quadratic equation by factoring or completing the square');
messages[25] = new Array('/8th/pix/14.0b.jpg','  Students solve a quadratic equation by factoring or completing the square');
messages[26] = new Array('/8th/pix/14.0c.jpg','  Students solve a quadratic equation by factoring or completing the square');
messages[27] = new Array('/8th/pix/15.0.jpg','  Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems');
messages[28] = new Array('/8th/pix/15.0a.jpg','  Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems');
messages[29] = new Array('/8th/pix/15.0b.jpg','  Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems');
messages[30] = new Array('/8th/pix/15.0d.jpg','  Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems');
messages[31] = new Array('/8th/pix/17.0.jpg','  Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression');
messages[32] = new Array('/8th/pix/21.0.jpg','  Students graph quadratic functions and know that their roots are the x-intercepts');
messages[33] = new Array('/8th/pix/23.0.jpg','  Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity');
messages[34] = new Array('/8th/pix/24.2.jpg','  Students apply the hypothesis and conclusion in logical deduction');
messages[35] = new Array('/8th/pix/11.0c.jpg','  Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials');
messages[36] = new Array('/8th/pix/9.0a.jpg','  Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets');
messages[37] = new Array('/8th/pix/9.0b.jpg','  Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets');
messages[38] = new Array('/8th/pix/6.0a.jpg','  Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4');
messages[39] = new Array('/8th/pix/6.0b.jpg','  Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4');
messages[40] = new Array('/8th/pix/7.0a.jpg','  Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations using the point-slope formula');
messages[41] = new Array('/8th/pix/12.0a.gif','  Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms. ');
messages[42] = new Array('/8th/pix/12.0b.gif','  Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms. ');
messages[43] = new Array('/8th/pix/12.0c.gif','  Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms. ');
messages[44] = new Array('/8th/pix/12.0d.gif','  Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms. ');
messages[45] = new Array('/8th/pix/12.0e.gif','  Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms. ');

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