### 1: Number and Operations

#### 1.1: Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.

1.1.1: Compare and order real numbers including very large and small integers, and decimals and fractions close to zero.

1.1.2: Classify real numbers as rational or irrational.

1.1.4: Model and solve problems involving absolute value.

#### 1.2: Understand and apply numerical operations and their relationship to one another.

1.2.1: Solve problems with factors, multiples, divisibility or remainders, prime numbers, and composite numbers.

1.2.2: Describe the effect of multiplying and dividing a rational number by

1.2.2.b: a number between zero and one,

1.2.2.c: one, and

1.2.2.d: a number greater than one.

1.2.3: Solve problems involving percent increase, percent decrease, and simple interest rates.

1.2.4: Convert standard notation to scientific notation and vice versa (include positive and negative exponents).

1.2.5: Simplify numerical expressions using the order of operations that include grouping symbols, square roots, cube roots, absolute values, and positive exponents.

### 2: Data Analysis, Probability, and Discrete Mathematics

#### 2.1: Understand and apply data collection, organization, and representation to analyze and sort data.

2.1.1: Solve problems by selecting, constructing, interpreting, and calculating with displays of data, including box and whisker plots and scatterplots.

2.1.3: Describe how summary statistics relate to the shape of the distribution.

2.1.4: Determine whether information is represented effectively and appropriately given a graph or a set of data by identifying sources of bias and compare and contrast the effectiveness of different representations of data.

#### 2.2: Understand and apply the basic concepts of probability.

2.2.1: Determine theoretical and experimental conditional probabilities in compound probability experiments.

2.2.2: Interpret probabilities within a given context and compare the outcome of an experiment to predictions made prior to performing the experiment.

2.2.3: Use all possible outcomes (sample space) to determine the probability of dependent and independent events.

#### 2.3: Understand and demonstrate the systematic listing and counting of possible outcomes.

2.3.2: Solve counting problems and represent counting principles algebraically including factorial notation.

### 3: Patterns, Algebra, and Functions

#### 3.1: Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.

3.1.1: Recognize, describe, create, and analyze numerical and geometric sequences using tables, graphs, words, or symbols; make conjectures about these sequences.

#### 3.2: Describe and model functions and their relationships.

3.2.1: Sketch and interpret a graph that models a given context; describe a context that is modeled by a given graph.

3.2.2: Determine if a relationship represented by a graph or table is a function.

3.2.3: Write the rule for a simple function using algebraic notation.

3.2.4: Identify functions as linear or nonlinear and contrast distinguishing properties of functions using equations, graphs, or tables.

3.2.5: Demonstrate that proportional relationships are linear using equations, graphs, or tables.

#### 3.3: Represent and analyze mathematical situations and structures using algebraic representations.

3.3.1: Write or identify algebraic expressions, equations, or inequalities that represent a situation.

3.3.3: Analyze situations, simplify, and solve problems involving linear equations and inequalities using the properties of the real number system.

3.3.4: Translate between different representations of linear equations using symbols, graphs, tables, or written descriptions.

3.3.5: Graph an inequality on a number line.

#### 3.4: Analyze how changing the values of one quantity corresponds to change in the values of another quantity.

3.4.1: Interpret the relationship between a linear equation and its graph, identifying and computing slope and intercepts.

### 4: Geometry and Measurement

#### 4.1: Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.

4.1.1: Identify the attributes of circles: radius, diameter, chords, tangents, secants, inscribed angles, central angles, intercepted arcs, circumference, and area.

4.1.2: Predict results of combining, subdividing, and changing shapes of plane figures and solids.

4.1.3: Use proportional reasoning to determine congruence and similarity of triangles.

4.1.4: Use the Pythagorean Theorem to solve problems.

#### 4.2: Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.

4.2.1: Model the result of rotations in multiples of 45 degrees of a 2-dimensional figure about the origin.

4.2.3: Identify lines of symmetry in plane figures or classify types of symmetries of 2-dimensional figures.

#### 4.3: Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands.

4.3.2: Use the Pythagorean Theorem to find the distance between two points in the coordinate plane.

#### 4.4: Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.

4.4.1: Solve problems involving conversions within the same measurement system.

4.4.2: Solve geometric problems using ratios and proportions.

4.4.3: Calculate the surface area and volume of rectangular prisms, right triangular prisms, and cylinders.

4.4.6: Describe the relationship between the volume of a figure and the area of its base.

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.