Intermediate Level Learning Targets

Learning Target #1: Develop proficiency in analyzing, graphing and solving linear equations and inequalities.

COMPONENTS

Vocabulary: TO BE DONE SOON

Standards:
F12.1,2,3,4
B12.3
C12.4 / Assessable Specifications:
1.1Students will be able to identify different types of relations and functions.
1.2Students will be able to model real-world data using scatter plots and estimate a line of best fit.
1.3Students will be able to graph inequalities on the coordinate plane.
1.4Students will be able to translate verbal expressions and sentences into algebraic expressions and equations and solve them.
1.5Students will be able to solve formulas for a specific variable.
1.6Students will be able to solve equations in one variable including those involving absolute value.
1.7Students will be able to solve simple and compound inequalities, including those involving absolute value, and graph the solution sets.
1.8Students will be able to graph a relation, state its domain and range and determine if it is a function.
1.9Students will be able to write an equation of a line using slope and/or points.
1.10Students will be able to write the equation of a line that is parallel or perpendicular to the graph of a given equation. / Thinking Levels
2
3/4
2
2/3
3
3
3
2
3
3 / Instructional Time

Learning Target #2: Develop proficiency with matrices and linear systems of equations and inequalities.

COMPONENTS

Vocabulary: TO BE DONE SOON

Standards:
COMPONENTS
F12.1,2,3 / Assessable Specifications:
2.1Students will be able to perform operations with matrices.
2.2Students will be able to solve systems of equations and inequalities using various methods including Cramer’s Rule.
2.3Students will be able to solve problems involving maximum and minimum values by using linear programming.
2.4Students will be able to evaluate the determinant of a 2X2 and 3X3 matrix and find the area of a triangle, given the coordinates of its vertices.
2.5Students will be able to write the identity matrix for any square matrix and find the inverse of a 2X2 matrix. / Thinking Levels
2
3
3
3/4
3/4 / Instructional Time

Learning Target #3: Develop proficiency to simplify and/or factor polynomials and radical expressions.

COMPONENTS

Vocabulary: TO BE DONE SOON Synthetic Division

Standards:
F12.2,3
B12.2, 4 / Assessable Specifications:
3.1Students will be able to simplify expressions containing polynomials.
3.2Students will be able to factor polynomials.
3.3Students will be able to add, subtract, multiply and divide polynomials.
3.4Students will be able to multiply and divide monomials and expressions written in scientific notation.
3.5Students will be able to add, subtract, multiply, divide and simplify radical expressions and rationalize the denominator of a fraction containing a radical expression.
3.6Students will be able to simplify square roots containing negative radicands, add, subtract and multiply complex numbers and simplify rational expressions containing complex numbers in the denominator. / Thinking Levels
2
3
2
2
2
3 / Instructional Time

Learning Target #4: Develop proficiency with radical and rational expressions, equations and inequalities.

COMPONENTS

Vocabulary: TO BE DONE SOON

Standards:
COMPONENTS
B.12.4
F.12.1,2,B12.4 / Assessable Specifications:
4.1Students will be able to simplify expressions containing rational exponents and radicals.
4.2Students will be able to solve equations using radicals.
4.3Students will be able to add, subtract, multiply and divide rational and radical expressions.
4.4Students will be able to solve problems involving direct, inverse and joint variation.
4.5Students will be able to simplify rational expressions and complex fractions.
4.6Students will be able find the least common denominator of two or more algebraic expressions.
4.7Students will be able to solve rational equations and inequalities. / Thinking Levels
2
3
2
3
2/3
2
3 / Instructional Time

Learning Target #5: Develop proficiency with quadratic equations and inequalities.

COMPONENTS

Vocabulary: TO BE DONE SOON

Standards:
B.12.3,4
F12.3,2,4 / Assessable Specifications:
5.1Students will be able to write a quadratic equation given two roots in either standard or vertex form.
5.2Students will be able to write the equation of a quadratic function given points on a graph.
5.3Students will be able to solve quadratic inequalities graphically or algebraically.
5.4Students will be able to identify quadratic, linear and a constant term in a function.
5.5Students will be able to graph and solve a quadratic function finding the vertex and its axis of symmetry.
5.6Students will be able to write and/or solve a quadratic equation and related real-world problems.
5.7Students will be able to describe the nature of the roots (real, imaginary, rational, irrational) of the quadratic equation by finding the value of the descriminant.
5.8Students will be able to solve quadratic equations that have complex solutions.
5.9Students will be able to name the vertex, axis of symmetry, direction of the opening and graph of a quadratic equation if the equation is in the form y=a(x-h)+k. / Thinking Levels
3
3
3
1
3
3
4
3
2 / Instructional Time

Learning Target #6: Develop proficiency with coordinate geometry, parabolas and circles.

COMPONENTS

Vocabulary: TO BE DONE SOON

Standards:
C.12.1
D12.3 / Assessable Specifications:
6.1Students will be able use the midpoint and distance formulas to solve problems.
6.2Students will be able to identify the equation of a parabola given its vertex, focus, directrix and/or line of symmetry, and find the vertex, focus, directrix and/or line of symmetry given its equation.
6.3Students will be able to identify the equation of a circle given its center and radius and graph a circle given its equation.
6.4Students will be able to graph and write an equation of a circle if the coordinate of the center and the length of the radius are given.
6.5Students will be able to find the coordinates of the center and the length of the radius of a circle if the equation of the circle is given. / Thinking Levels
2
3
3
3
2 / Instructional Time

Learning Target #7: Develop proficiency with polynomial.

COMPONENTS

Vocabulary: TO BE DONE SOON

Standards:
F12.2,4 / Assessable Specifications:
7.1Students will be able to identify whether a polynomial function is odd or even based on its graph and/or equation.
7.2Students will be able to identify zeros of a polynomial function by graphing or by use of the remainder and factor theorems.
7.3Students will be able to identify and approximate zeros and relative maxima or minima given the graph of a polynomial function.
7.4Students will be able to identify the number of positive, negative and complex zeros for polynomial functions.
7.5Students will be able to use Descartes’ rule of signs, the rational root theorem and the quadratic equation techniques to solve for all zeros of appropriate polynomial functions.
7.6Students will be able use synthetic division to evaluate a polynomial for any value x and to find its factors.
7.7Students will be able to list all possible rational zeros of a polynomial function.
7.8Students will be able to use quadratic techniques to solve polynomial equations and related real world problems. / Thinking Levels
2
2
2
2
3
2
3
4 / Instructional Time

Learning Target #8: Develop proficiency with exponential and logarithmic functions and graphs.

COMPONENTS

Vocabulary: TO BE DONE SOON

Standards:
B12.2,3
F12.4 / Assessable Specifications:
8.1Students will be able to simplify exponential expressions and solve basic exponential equations.
8.2Students will be able to evaluate common and natural logarithms and their inverses.
8.3Students will be able evaluate logarithms using the change of base formula.
8.4Students will be able express a logarithm as a sum or difference of simpler logarithmic expressions.
8.5Students will be able to find the value of any missing variable (base, root or number) in a logarithm equation.
8.6Students will be able to evaluate logarithmic expression, solve equation and real world problems using logarithms.
8.7Students will be able to graph a relation, state its domain and range and determine if it is a function.
8.8Students will be able to write use logarithms to solve real world problems (i.e. exponential growth and decay). / Thinking Levels
3
2
2
3
3
4
2
4 / Instructional Time

Learning Target #9:Develop proficiency with right and oblique triangle trigonometry and the trigonometric identities.

COMPONENTS

Vocabulary: TO BE DONE SOON Oblique

Standards:
C12.5,2 / Assessable Specifications:
9.1Students will be able to apply the trigonometric functions to solve problems involving right triangles.
9.2Students will be able change between radian measures and degrees.
9.3Students will be able to solve problems using the trigonometric identities.
9.4Students will be able to solve triangles using the Law of Sines.
9.5Students will be able to solve triangles using the Law of Cosines.
9.6Students will be able define and use the trigonometric functions based on the unit circle.
9.7Students will be able to write an equation of a line using slope and/or points. / Thinking Levels
4
2
4
3
3
3
2 / Instructional Time

Learning Target #10:Develop proficiency with permutations, combinations and probability.

COMPONENTS

Vocabulary: TO BE DONE SOON

Standards:
B12.1
E12.5 / Assessable Specifications:
10.1Students will be able to solve problems by using the fundamental counting principle.
10.2Students will be able to solve problems involving linear and circular permutations.
10.3Students will be able to solve problems involving combinations.
10.4Students will be able find the probability of an event and the odds of success and failure of an event.
10.5Students will be able to find the probability of two or more independent or dependent events.
10.6Students will be able find the probability of mutually exclusive or inclusive events. / Thinking Levels
2
3
3
3
3
4 / Instructional Time

Learning Target #11: Develop proficiency with arithmetic and geometric sequences and series.

COMPONENTS

Vocabulary: TO BE DONE SOON

Standards:
F12.1 / Assessable Specifications:
11.1Students will be able to find the next term in a sequence by looking for a pattern.
11.2Students will be able to find the nth term of an arithmetic and a geometric sequence and/or the position of a given term in either type of sequence.
11.3Students will be able to find sums of arithmetic and geometric series.
11.4Students will be able to expand powers of binomials by using Pascal’s Triangle and the Binomial Theorem and specific terms of binomial expansions. / Thinking Levels
2
2
2
3 / Instructional Time

Milwaukee Public Schools – Mathematics Intermediate Level Learning Targets page 1

Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.