### 1: Numeric Reasoning: Students will develop Numeric Reasoning and an understanding of Number and Operations by solving problems in which there is a need to represent and model real numbers verbally, physically, and symbolically; to explain the relationship between numbers; to determine the relative magnitude of real numbers; to use operations with understanding; and to select appropriate methods of calculations from among mental math, paper-and-pencil, calculators, or computers.

#### 1.1: Number sense

1.1.2: Use square numbers and square roots to reason about the relationship between the side of a square and area of the square (e.g., side of a square with an area of 9 is the square root of 9 or 3, side of a square with area of 5 is the square root of 5)

1.1.3: Apply knowledge of factors and multiples, evens and odds, primes and composites, to generalizations

1.1.4: Explore the meaning of irrational numbers such as pi, or the square root of 3

#### 1.2: Operations

1.2.1: Perform computations with exponents, powers of 10, and scientific notation

1.2.3: Demonstrate the reasonableness of an exact calculation by using an estimation or mental math strategy

1.2.4: Explain how the distributive property is used to multiply (e.g., partial products, mixed numbers)

1.2.6: Apply proportional reasoning strategies to solve real-world problems

1.2.7: Select and use appropriate methods and tools for computing (e.g., mental computation, estimation, calculators, paper and pencil) depending on the context and nature of the computation

### 2: Algebraic Reasoning: Students will develop Algebraic Reasoning and an understanding of Patterns and Functions by solving problems in which there is a need to recognize and extend a variety of patterns; to progress from the concrete to the abstract using physical models, equations, and graphs; to describe, represent, and analyze relationships among variable quantities; and to analyze, represent, model, and describe real-world functional relationships.

#### 2.1: Patterns and change

2.1.1: Determine the slope of a line given two points on the line (as coordinates, in a graph, in a table)

2.1.2: Use y-intercept and slope to graph the equation of a line

2.1.3: Compare the rates of change in tables and graphs and classify them as linear or nonlinear

2.1.4: Recognize exponential rates of growth and decay in tables and graphs

#### 2.2: Representations

2.2.1: Write an equation given the tabular or graphic form of a linear problem

2.2.2: Analyze the interrelationships among tables, graphs, and equations of lines, paying particular attention to the meaning of intercept and slope in the context of the problem

2.2.3: Demonstrate the equivalence of two algebraic expressions using physical models

2.2.4: Use tables, graphs and symbolic reasoning to identify functions as linear or nonlinear

#### 2.3: Symbols

2.3.1: Apply the order of operations

2.3.2: Explore the factor/product relationship between a quadratic expression and its linear factors.

2.3.3: Use physical models to develop and write exponential and power models

2.3.4: Combine two algebraic expressions to form a new expression

2.3.6: Solve linear equations using inverse operations and properties of equality.

### 3: Geometric Reasoning: Students will develop Geometric Reasoning and an understanding of Geometry and Measurement by solving problems in which there is a need to recognize, construct, transform, analyze properties of, and discover relationships among geometric figures; and to measure to a required degree pf accuracy by selecting appropriate tools and units.

#### 3.1: Classification

3.1.1: Apply angle relationships to solve problems

#### 3.2: Location and transformation

3.2.1: Apply proportional reasoning strategies to find unknown sides of similar triangle

3.2.3: Use the Pythagorean Theorem to find missing sides of right triangles

#### 3.3: Measurement

3.3.1: Demonstrate the relationship between the area of the base and volume of prisms and cylinders

3.3.2: Demonstrate the effects of scaling on volume and surface area of rectangular prisms (i.e., how does doubling the side lengths affect the volume?)

3.3.4: Find the measures of corresponding parts of similar figures

### 4: Quantitative Reasoning: Students will develop Quantitative Reasoning and an understanding of Data Analysis and Probability by solving problems in which there is a need to collect, appropriately represent, and interpret data; to make inferences or predictions and to present convincing arguments; and to model mathematical situations to determine the probability.

#### 4.1: Collect

4.1.1: Pose questions that can be answered by collecting and organizing data from experiments, surveys, and relevant print and electronic resources

4.1.2: Use random sampling methods to collect the necessary information to answer questions

#### 4.2: Represent

4.2.1: Construct displays of data to represent individual sets of data (e.g., histograms, box plots) or to explore the relationship between related sets of data (scatter plots, line graphs); describe the correspondence between data sets and their graphical displays

#### 4.3: Analyze

4.3.1: Defend or dispute conclusions drawn from the interpretation of data by comparing sets of data or exploring possible relationships based upon scatter plots of related data and approximate lines of fit

4.3.2: Analyze a representative sample to make inferences about a population

4.3.3: Find and use appropriate measures of center (mean, media, mode) and spread (range, interquartile range) to interpret data

### 0: Compare the usefulness of the mean and median as measures of center; describe the effect of changes in the data on the mean and median of the data set(s)

#### 4.4: Probability

4.4.1: Compare and make predictions based on theoretical and experimental probabilities, using sample data generated through actual experiments or computer simulations

4.4.2: Construct an appropriate sample space and apply principles of probability for a simple or compound event

4.4.3: Investigate and describe the difference between the experimental probability of a simulated event (experiment) and the theoretical probability of the same event

4.4.4: Explore the concepts of randomness and random sample

Correlation last revised: 5/9/2018

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