### 1: The student will describe functional relationships in a variety of ways.

1.A.1: The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways.

1.A.1.A: describe independent and dependent quantities in functional relationships;

1.A.1.B: [gather and record data and] use data sets to determine functional relationships between quantities;

1.A.1.C: describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations;

1.A.1.D: represent relationships among quantities using [concrete] models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities; and

1.A.1.E: interpret and make decisions, predictions, and critical judgments from functional relationships.

### 2: The student will demonstrate an understanding of the properties and attributes of functions.

2.A.2: The student uses the properties and attributes of functions.

2.A.2.A: identify [and sketch] the general forms of linear (y = x) and quadratic (y = x 2) parent functions;

2.A.2.B: identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete;

2.A.2.D: [collect and] organize data, [make and] interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.

2.A.3: The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations.

2.A.3.B: look for patterns and represent generalizations algebraically.

2.A.4: The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations.

2.A.4.A: find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations;

2.A.4.B: use the commutative, associative, and distributive properties to simplify algebraic expressions; and

### 3: The student will demonstrate an understanding of linear functions.

3.A.5: The student understands that linear functions can be represented in different ways and translates among their various representations.

3.A.5.A: determine whether or not given situations can be represented by linear functions; and

3.A.5.C: use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions.

3.A.6: The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations.

3.A.6.A: develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations;

3.A.6.B: interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs;

3.A.6.C: investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b;

3.A.6.D: graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept;

3.A.6.E: determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations;

3.A.6.F: interpret and predict the effects of changing slope and y-intercept in applied situations; and

3.A.6.G: relate direct variation to linear functions and solve problems involving proportional change.

### 4: The student will formulate and use linear equations and inequalities.

4.A.7: The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

4.A.7.A: analyze situations involving linear functions and formulate linear equations or inequalities to solve problems;

4.A.7.B: investigate methods for solving linear equations and inequalities using [concrete] models, graphs, and the properties of equality, select a method, and solve the equations and inequalities; and

4.A.7.C: interpret and determine the reasonableness of solutions to linear equations and inequalities.

### 5: The student will demonstrate an understanding of quadratic and other nonlinear functions.

5.A.9: The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions.

5.A.9.C: investigate, describe, and predict the effects of changes in c on the graph of y = ax 2 + c.

5.A.11: The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations.

5.A.11.A: use [patterns to generate] the laws of exponents and apply them in problem-solving situations.

### 6: The student will demonstrate an understanding of geometric relationships and spatial reasoning.

6.8.6: The student uses transformational geometry to develop spatial sense.

6.8.6.A: generate similar figures using dilations including enlargements and reductions; and

6.8.6.B: graph dilations, reflections, and translations on a coordinate plane.

### 7: The student will demonstrate an understanding of two- and three-dimensional representations of geometric relationships and shapes.

7.8.7: The student uses geometry to model and describe the physical world.

7.8.7.A: draw three-dimensional figures from different perspectives;

7.8.7.B: use geometric concepts and properties to solve problems in fields such as art and architecture; and

7.8.7.C: use pictures or models to demonstrate the Pythagorean Theorem.

### 8: The student will demonstrate an understanding of the concepts and uses of measurement and similarity.

8.8.8: The student uses procedures to determine measures of three-dimensional figures.

8.8.8.A: find lateral and total surface area of prisms, pyramids, and cylinders using [concrete] models and nets (two-dimensional models);

8.8.8.B: connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects; and

8.8.8.C: estimate measurements and use formulas to solve application problems involving lateral and total surface area and volume.

8.8.9: The student uses indirect measurement to solve problems.

8.8.9.A: use the Pythagorean Theorem to solve real-life problems; and

8.8.9.B: use proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements.

8.8.10: The student describes how changes in dimensions affect linear, area, and volume measures.

8.8.10.A: describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally; and

8.8.10.B: describe the resulting effect on volume when dimensions of a solid are changed proportionally.

### 9: The student will demonstrate an understanding of percents, proportional relationships, probability, and statistics in application problems.

9.8.1: The student understands that different forms of numbers are appropriate for different situations.

9.8.1.B: select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships.

9.8.11: The student applies concepts of theoretical and experimental probability to make predictions.

9.8.11.A: find the probabilities of dependent and independent events; and

9.8.11.B: use theoretical probabilities and experimental results to make predictions and decisions.

9.8.12: The student uses statistical procedures to describe data.

9.8.12.A: select the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation; and

9.8.12.C: select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, [stem and leaf plots,] circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, with and without the use of technology.

9.8.13: The student evaluates predictions and conclusions based on statistical data.

9.8.13.B: recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis.

Correlation last revised: 3/6/2012

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