#### IM2.1: Students graph linear inequalities in two variables and quadratics. They model data with linear equations.

IM2.1.1: Graph a linear inequality in two variables.

IM2.1.2: Interpret given situations as functions in graphs, formulas, and words.

IM2.1.3: Find a linear equation that models a data set using the median fit method and use the model to make predictions.

IM2.1.4: Graph quadratic functions. Show and explain the effects on the graph of changing a coefficient in a quadratic function. Find and interpret the zeros and maximum or minimum value of quadratic functions.

#### IM2.2: Students identify and describe types of triangles. They define and apply the trigonometric relations. Students apply theorems to triangles and circles.

IM2.2.1: Find the lengths and midpoints of line segments in one-or two-dimensional coordinate systems.

IM2.2.4: Identify and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular.

IM2.2.5: Define, identify, and construct altitudes, medians, angle bisectors, and perpendicular bisectors.

IM2.2.6: Use properties of congruent and similar triangles to solve problems involving lengths and areas.

IM2.2.7: Find measures of sides, perimeters, and areas of triangles, and relate these measures to each other using formulas.

IM2.2.8: Prove, understand, and apply the inequality theorems: triangle inequality, inequality in one triangle, and the hinge theorem.

IM2.2.10: Use special right triangles (30°-60°-90° and 45°-45°-90°) to solve problems.

IM2.2.11: Define and apply the trigonometric functions (sine, cosine, tangent, cotangent, secant, cosecant) defined by angles of right triangles.

IM2.2.12: Know and use the relationship sin²x + cos²x = 1.

IM2.2.15: Define and identify relationships among: radius, diameter, arc, measure of an arc, chord, secant, and tangent.

IM2.2.16: Prove theorems related to circles.

IM2.2.17: Construct tangents to circles and circumscribe and inscribe circles.

IM2.2.20: Define, find, and use measures of circumference, arc length, and areas of circles and sectors. Use these measures to solve problems.

#### IM2.3: Students interpret scatterplots and analyze correlation.

IM2.3.1: Describe the association between two variables by interpreting a scatterplot.

IM2.3.2: Interpret correlation coefficients.

IM2.3.3: Make predictions from the least squares regression line or its equation.

IM2.3.4: Understand that a correlation between two variables does not necessarily imply one directly causes the other.

IM2.3.5: Understand the effects of outliers on correlation coefficients, on the least squares regression line, and on the interpretations of correlation coefficients and regression lines in real-life contexts.

#### IM2.4: Students construct probability distributions, understand fundamental probability concepts, and use counting principles.

IM2.4.1: Construct a probability distribution by simulation and use it to understand and analyze the probabilistic situation.

IM2.4.2: Explore the geometric, or waiting-time, distribution.

IM2.4.3: Understand fundamental concepts of probability (i.e., independent events, multiplication rule, expected value).

IM2.4.5: Use the basic counting principle, combinations, and permutations to compute probabilities.

#### IM2.5: Students use graphs and networks as mathematical models and use matrices to solve problems.

IM2.5.6: Apply matrix operations to solve problems (i.e., row sums, scalar multiplication, addition, subtraction, and matrix multiplication).

IM2.5.7: Use matrices and inverse matrices to answer questions that involve systems of linear equations.

#### IM2.6: Students apply trigonometric ratios to right triangles.

IM2.6.1: Explore properties and applications of the sine, cosine, and tangent ratios for the lengths of sides of right triangles.

#### IM2.7: Students use a variety of strategies to solve problems and develop and evaluate mathematical arguments and proofs.

IM2.7.1: Use the properties of the real number system and the order of operations to justify the steps of simplifying functions and solving equations.

IM2.7.8: 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 as the original. Understand that similar logic applies to solving systems of equations simultaneously.

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.