A fourteen years old learner is expected to be able to:
- Understand the notation for radicals in terms of rational exponents. For example, cube root of 7 can be represented as as well as
- Simplify the radical expression
- Discuss why the sum of a rational number and a radical number is radical and that the product of a non zero rational number and radical number is radical.
- Understand expressions that represent a quantity in terms of its context.
- Understand parts of an expression, such as terms, factors, and coefficients.
- Understand complicated expressions by viewing one or more of their parts as a single entity. For example, interpret as the product of P and a factor not depending on P.
- Rewrite the expression using the structure of an expression. For example, see as , thus recognizing it as a difference of squares that can be factored as .
- Identify the zeros by factoring the quadratic expression.
- Discover that polynomials form a system similar to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
- Prove polynomial identities and apply them to describe numerical rela For example, the polynomial identity can be used to write equivalent expression.
- Recognize that rational expressions form a system similar to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expres
- Verify that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
- Use substitution method or elimination method to solve systems of linear equations in two variables ex
- Recognize that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
- Discuss why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear functions.
- Graph the solutions to a linear inequality in two variables, and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
- Verify theorems about parallelogr Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
- Apply the definition of similarity in terms of similarity transformations to decide if two given figures are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of
- Apply the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
- Verify theorems about similar Theorems include: basic proportionality theorem and its converse; the Pythagorean Theorem proved using triangle similarity.
- Apply congruence and similarity criteria for triangles to solve problems and to verify relationships in geometric figur
- Know that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute
- Use the Pythagorean Theorem to solve right triangles in applied problems
- Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e., find the equation of a line parallel or perpendicular to a given line that passes through a given point).