It builds and draws on conceptual understanding and skills, and helps us make decisions and solve problems. In this draft document we have tried to connect the notion of problem solving to conceptual understanding and skill development by embedding it within the content strands at every grade. Given here are only some of the ways you will see this exemplified. Students compute with and simplify rational expressions and those containing fractional exponents. 1.1 add and subtract rational expressions having the same denominator, multiply, divide, reduce, and evaluate simple algebraic fractions 1.2 add, subtract, multiply, divide, and simplify expressions containing radicals and fractional exponents 2.
Students carry out counting procedures involving sets and arrangements.
2.1 find and solve problems involving the intersection and union of sets 2.2 use combinations and permutations to count the number of arrangements of a set of elements and distinguish between the two Symbols and Algebra 1. Students solve quadratic, rational, radical, absolute value, and factorable polynomial equations in one variable and non-linear systems of equations in two variables. 2.1 give the center and radius of a circle, the center, vertices, foci, and axes of an ellipse or hyperbola, and the vertex, axis of symmetry, focus, and directrix of a parabola given an equation in standard form and use this information to graph the figure. Students understand the use of matrices to organize information and perform simple operations. 3.1 use matrices to represent and organize data and identify and interpret the meaning of a matrix cell for a given context 3.2 perform and interpret the meaning of matrix addition, subtraction, multipication, and scalar multiplication 3.3 use matrices to represent and solve systems of two linear equations in two variables 3.4 use matrices to translate, reflect, rotate, or scale polygonal figures represented on the coordinate plane 4.