### 1: Number and Operations

#### 1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems

1.1.A: Read, write and compare numbers

1.1.A.1: compare and order rationals and percents, including finding their approximate locations on a number line

1.1.B: Represent and use rational numbers

1.1.B.1: use fractions, decimals and percents to solve problems

1.1.C: Compose and decompose numbers

1.1.C.1: recognize equivalent representations for the same number and generate them by decomposing and composing numbers, including scientific notation

#### 1.2: Understand meanings of operations and how they relate to one another

1.2.C: Apply properties of operations

1.2.C.1: apply properties of operations to rational numbers, including order of operations and inverse operations

1.2.D: Apply operations on real and complex numbers

1.2.D.1: apply the relationship between squares and square roots and cubes and cube roots to solve a problem

#### 1.3: Compute fluently and make reasonable estimates

1.3.C: Compute problems

1.3.C.1: apply all operations on rational numbers

1.3.E: Use proportional reasoning

1.3.E.1: solve problems involving proportions, such as scaling and finding equivalent ratios

### 2: Algebraic Relationships

#### 2.1: Understand patterns, relations, and functions

2.1.B: Create and analyze patterns

2.1.B.1: generalize patterns represented graphically or numerically using words or symbolic rules, including recursive notation

2.1.D: Identify and compare functions

2.1.D.1: compare properties of linear functions between or among tables, graphs and equations

#### 2.2: Represent and analyze mathematical situations and structures using algebraic symbols

2.2.A: Represent mathematical situations

2.2.A.1: use symbolic algebra to represent and solve problems that involve linear relationships, including recursive relationships

2.2.B: Describe and use mathematical manipulation

2.2.B.1: generate equivalent forms for linear expressions

#### 2.3: Use mathematical models to represent and understand quantitative relationships

2.3.A: Use mathematical models

2.3.A.1: model and solve problems, using multiple representations such as graphs, tables, equations or inequalities

#### 2.4: Analyze change in various contexts

2.4.A: Analyze change

2.4.A.1: analyze the nature of changes (including slope and intercepts) in quantities in linear relationships

### 3: Geometric and Spatial Relationships

#### 3.1: Analyze characteristics and properties of two- and three- dimensional geometric shapes and develop mathematical arguments about geometric relationships

3.1.A: Describe and use geometric relationships

3.1.A.1: describe, classify and generalize relationships between and among types of a) 2-dimensional objects and b) 3- dimensional objects using their defining properties including

3.1.A.1.a: Pythagorean Theorem

3.1.B: Apply geometric relationships

3.1.B.1: apply relationships between corresponding sides and corresponding areas of similar polygons to solve problems

#### 3.2: Specify locations and describe spatial relationships using coordinate geometry and other representational systems

3.2.A: Use coordinate systems

3.2.A.1: use coordinate geometry to analyze properties of right triangles and quadrilaterals

#### 3.3: Apply transformations and use symmetry to analyze mathematical situations

3.3.A: Use transformations on objects

3.3.A.1: reposition shapes under formal transformations, such as reflection, rotation and translation

3.3.B: Use transformations on functions

3.3.B.1: describe the relationship between the scale factor and the area of the image using a dilation (stretching/ shrinking)

3.3.C: Use symmetry

3.3.C.1: identify the number of rotational symmetries of regular polygons

### 4: Measurement

#### 4.1: Understand measurable attributes of objects and the units, systems and processes of measurement

4.1.B: Identify equivalent measures

4.1.B.1: identify the equivalent volume measures within a system of measurement (e.g., m cubed to cm cubed)

#### 4.2: Apply appropriate techniques, tools and formulas to determine measurements.

4.2.C: Apply geometric measurements

4.2.C.1: describe how to solve problems involving surface area and/or volume of a rectangular or triangular prism, or cylinder

4.2.D: Analyze precision

4.2.D.1: analyze precision and accuracy in measurement situations and determine number of significant digits

### 5: Data and Probability

#### 5.1: Formulate questions that can be addressed with data and collect, organize and display relevant data to answer them

5.1.C: Represent and interpret data

5.1.C.1: select, create and use appropriate graphical representation of data (including scatter plots)

#### 5.2: Select and use appropriate statistical methods to analyze data

5.2.A: Describe and analyze data

5.2.A.1: find, use and interpret measures of center, outliers and spread, including range and interquartile range

5.2.B: Compare data representations

5.2.B.1: compare different representations of the same data and evaluate how well each representation shows important aspects of the data

#### 5.3: Develop and evaluate inferences and predictions that are based on data

5.3.A: Develop and evaluate inferences

5.3.A.1: make conjectures about possible relationships between 2 characteristics of a sample on the basis of scatter plots of the data and approximate lines of fit

#### 5.4: Understand and apply basic concepts of probability

5.4.A: Apply basic concepts of probability

5.4.A.1: make conjectures (based on theoretical probability) about the results of experiments

Correlation last revised: 10/24/2008

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