IM3.1: Students solve inequalities, quadratic equations, and systems of equations. They graph polynomial, rational, algebraic, and piece-wise defined functions. They graph and write the equations of conic sections and compute with and factor polynomials and algebraic fractions. They solve problems involving exponential and logarithmic expressions, as well as define and use arithmetic and geometric sequences and series.

IM3.1.1: Solve combined linear inequalities.

IM3.1.2: Use a graph to find the solution set of a pair of linear inequalities in two variables.

IM3.1.3: Find a common monomial factor in a polynomial.

IM3.1.4: Factor the difference of two squares and other quadratics.

IM3.1.7: Solve quadratic equations by factoring.

IM3.1.9: Complete the square to solve quadratic equations.

IM3.1.10: Derive the quadratic formula by completing the square.

IM3.1.11: Solve equations that contain radical expressions.

IM3.1.12: Recognize and graph various types of functions, including polynomials, rational, and algebraic functions.

IM3.1.14: Understand composition of functions and combine functions by composition.

IM3.1.15: Graph relations and functions with and without graphing technology.

IM3.1.17: Solve an inequality by examining the graph.

IM3.1.18: Graph functions defined piece-wise.

IM3.1.19: Graph absolute value equations and inequalities.

IM3.1.20: Use substitution, elimination, and matrices to solve systems of two or three equations in two or three variables.

IM3.1.21: Use system of equations and inequalities to solve word problems.

IM3.1.22: Define complex numbers and perform basic operations with them.

IM3.1.23: Understand how real and complex numbers are related, including plotting complex numbers as points in the plane.

IM3.1.24: Solve quadratic equations in the complex number system.

IM3.1.25: Solve word problems using quadratic equations.

IM3.1.26: Solve equations that contain radical expressions.

IM3.1.28: Write the equations of conic sections (circle, ellipse, parabola, and hyperbola).

IM3.1.29: Graph conic sections.

IM3.1.31: Divide polynomials by others of lower degree.

IM3.1.32: Factor polynomials completely and solve polynomial equations by factoring.

IM3.1.37: Understand and use negative and fractional exponents.

IM3.1.40: Solve equations involving algebraic fractions.

IM3.1.42: Solve problems of direct, inverse, and joint variation.

IM3.1.45: Solve logarithmic and exponential equations and inequalities.

IM3.1.50: Define arithmetic and geometric sequences and series.

IM3.1.51: Find specified terms of arithmetic and geometric sequences.

IM3.2: Students describe and use parallel and perpendicular lines. They use coordinate geometry and prove that triangles are congruent or similar. They find the equation of a circle in the coordinate plane and describe and use properties of solids.

IM3.2.1: Understand and use the relationships between special pairs of angles formed by parallel lines and transversals.

IM3.2.2: Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines.

IM3.2.3: Use properties of congruent and similar polygons to solve problems.

IM3.2.5: Describe, classify, and understand relationships among quadrilaterals square, rectangles, rhombus, parallelogram, trapezoid, and kite.

IM3.2.9: Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles.

IM3.2.15: Find and use measures of sides, volumes of solids, and surface areas of solids. Relate these measures to each other using formulas.

IM3.3: Students design and interpret surveys, use sampling distributions, and understand standard deviation.

IM3.3.1: Understand and apply basic ideas related to the design and interpretation of surveys, such as background information, random sampling, and bias.

IM3.3.2: Construct simulated sampling distributions of sample proportions and use sampling distributions to identify which proportions are likely to be found in a sample of a given size.

IM3.3.3: Construct and interpret margin of error and confidence intervals for population proportions.

IM3.3.4: Understand the standard deviation as a measure of variability in a distribution.

IM3.5: Students use iteration and recursion to solve problems.

IM3.5.1: Use iteration and recursion as tools to represent, analyze, and solve problems involving sequential change.

IM3.7: Students use a variety of strategies to solve problems and develop and evaluate mathematical arguments and proofs.

IM3.7.1: Understand that the logic of equation solving begins with the assumption that the variable is a number that satisfies the equation, and that the steps taken when solving equations create new equations that have, in most cases, the same solution set as the original. Understand that similar logic applies to solving systems of equations simultaneously.

IM3.7.4: Identify the hypothesis and conclusion in a logical deduction.

IM3.7.5: Use counterexamples to show that statements are false, recognizing that a single counterexample is sufficient to prove a general statement false.

IM3.7.6: Use properties of number systems and the order of operations to justify the steps of simplifying functions and solving equations.

IM3.7.7: Identify and give examples of undefined terms, axioms, and theorems, and inductive and deductive proof.

IM3.7.8: Construct logical arguments, judge their validity, and give counterexamples to disprove statements.

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.