### 1: Calculations and Estimations

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

1.1.2: Apply proportions to solve problems

1.1.3: Locate rational number on a number line

1.1.4: Apply equivalent forms of rational number (including percents) to solve problems

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

1.2.1: Develop and analyze algorithms and compute with rational numbers

1.2.2: Use order of operation rules, including exponents

1.2.3: Develop and use strategies to estimate the results of rational number computations and judge the reasonableness of results

1.2.4: Estimate square roots of whole numbers less than 100 and cube roots of whole numbers less than 1000 between two whole numbers

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

1.3.1: Demonstrate the meaning of square roots as lengths of the sides of squares and cube roots as lengths of edges of cubes

1.3.2: Use the inverse operations of squares and square roots to solve problems and check solutions

1.3.3: Apply the associative, commutative, and distributive properties to simplify computations with rational numbers

### 2: Statistics and Probability

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

2.1.1: Choose appropriate measures of central tendencies to describe given or derived data

2.1.2: Estimate a line of best fit on a scatter plot and informally explain the meaning of the line and use the line to make predictions

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

2.2.2: Apply theoretical probability to determine if an event or game is fair or unfair and pose and evaluate modifications to change the fairness

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

2.3.2: Represent bivariate data in a scatter plot and identify relationships in the plot

### 3: Algebraic Relationships

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

3.1.1: Represent, analyze and determine rules for finding patterns relating to linear functions, non-linear functions and arithmetic sequences with tables, graphs, and symbolic rules

3.1.2: Identify functions as linear or nonlinear from tables, graphs, or equations and contrast their properties

3.1.3: Interpret the meaning of the rate of change and y-intercept of a linear relationship in a problem setting

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

3.2.1: Represent and solve equations of the form ax+b=c or k(ax+ b) = c

3.2.2: Approximate solutions of systems of linear equations from a graph

3.2.3: Recognize and generate equivalent symbolic forms for algebraic expressions with an emphasis on linear relationships

3.2.4: Evaluate algebraic expressions and formulas, including expressions involving exponents and parentheses, by substituting rational numbers

3.2.5: Translate between and interpret linear relationships represented by words, symbols, tables, and graphs

3.2.6: Determine the slope and x- and y-intercepts given the graph of a linear equation

3.2.7: Graph a linear equation given the slope and an initial value (y-intercept)

3.2.8: Recognize and graph the solutions of linear inequalities on a coordinate plane

3.2.9: Graph simple quadratic equations (y=kx² or y=kx²+b) by generating a table of values for a given equation

3.2.10: Identify and describe the effects of changing the slope or y-intercept on the graph of a linear relationship of the form y=kx or y=kx+b

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

3.3.1: Model situations, make predictions and inferences, and solve problems using linear equations and inequalities

3.3.2: Recognize and represent direct variation using tables, graphs, and equations

3.3.3: Determine when data represented in a table or graph represents a linear or non-linear relationship

#### 3.4: Analyze change in various contexts

3.4.1: Understand that the rate of change in a linear function is constant and is equal to the slope of its graphed line

3.4.3: Analyze the nature of change in quantities in linear relationships represented by graphs, tables, or formulas

### 4: Measurement

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

4.2.1: Calculate and analyze changes in area and volume in relation to changes in linear measures of figures

4.2.2: Analyze how changes in surface area and volume of a solid affect the dimensions of the solid

4.2.3: Solve problems involving rates and derived measurements for such attributes as speed, velocity, and density

4.2.4: Determine actual distances from scale drawings, blueprints, and maps and solve problems involving scale factors

### 5: Geometry

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

5.1.1: Determine defining properties that characterize classes of triangles including side and angle measurements and their component parts (e.g., angle bisectors, altitudes, medians)

5.1.2: Use proportional reasoning, drawings, models or technology to demonstrate similarity and congruence of polygons with an emphasis on triangles

5.1.3: Determine the measures of corresponding sides and angles of congruent and similar triangles and their component parts

5.1.4: Use similar triangles to measure distances indirectly (e.g., flagpole and shadow)

5.1.5: Use the Pythagorean theorem to determine if triangles are right triangles and determine the lengths of missing sides in right triangles

5.1.6: Investigate triangles and their components parts and draw conclusion about their properties

5.1.7: Create and critique inductive and deductive arguments to verify the pythagorean theorem

5.1.8: Justify conclusions that two triangles are or are not congruent and are or are not similar

#### 5.2: Use visualization, spatial reasoning, and geometric modeling to solve problems

5.2.1: Draw to scale two-dimensional representations of rectangular prisms and triangles with specified side lengths or angle measures

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

5.3.1: On a coordinate plane, determine the relative placement (e.g., intersecting, parallel, perpendicular) of two lines

5.3.2: Determine the distance between two points on a coordinate graph using right triangles and the Pythagorean theorem

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

5.4.1: Classify transformations based on whether they produce congruent or similar non-congruent figures (e.g., compare pairs of shapes (where the image has been transformed, identify the type of translation and use angles, diagonals and lines of symmetry to determine congruence)

5.4.2: Identify and sketch the figure that is the result of a given rotation, translation, reflection or dilation or a combination of two transformations

5.4.3: Know properties of dilated images

5.4.4: Determine the effects of a transformation on linear and area measurements of the original figure

Correlation last revised: 10/24/2008

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