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

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

### 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.C: interpret situations in terms of given graphs [or create situations that fit given graphs]; and

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.A: use symbols to represent unknowns and variables; and

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.

4.A.8: The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

4.A.8.A: analyze situations and formulate systems of linear equations in two unknowns to solve problems;

4.A.8.B: solve systems of linear equations using [concrete] models, graphs, tables, and algebraic methods; and

4.A.8.C: interpret and determine the reasonableness of solutions to systems of linear equations.

### 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.B: investigate, describe, and predict the effects of changes in a on the graph of y = ax 2 + c;

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

5.A.10: The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods.

5.A.10.A: solve quadratic equations using [concrete] models, tables, graphs, and algebraic methods; and

5.A.10.B: make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function.

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

6.G.5: The student uses a variety of representations to describe geometric relationships and solve problems.

6.G.5.C: use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations; and

6.G.10: The student applies the concept of congruence to justify properties of figures and solve problems.

6.G.10.A: use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane.

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

7.G.6: The student analyzes the relationship between three-dimensional geometric figures and related two-dimensional representations and uses these representations to solve problems.

7.G.6.B: use nets to represent [and construct] three-dimensional geometric figures; and

7.G.6.C: use orthographic and isometric views of three-dimensional geometric figures to represent [and construct] three-dimensional geometric figures and solve problems.

7.G.7: The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly.

7.G.7.A: use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures;

7.G.7.C: derive and use formulas involving length, slope, and midpoint.

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

8.G.8: The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter, area, and volume in problem situations.

8.G.8.A: find areas of regular polygons, circles, and composite figures;

8.G.8.C: [derive,] extend, and use the Pythagorean Theorem; and

8.G.8.D: find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations.

8.G.11: The student applies the concepts of similarity to justify properties of figures and solve problems.

8.G.11.A: use and extend similarity properties and transformations to explore and justify conjectures about geometric figures;

8.G.11.B: use ratios to solve problems involving similar figures;

8.G.11.C: [develop,] apply, and justify triangle similarity relationships, such as right triangle ratios, [trigonometric ratios,] and Pythagorean triples using a variety of methods; and

8.G.11.D: describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems.

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

9.8.3: The student identifies proportional or non-proportional linear relationships in problem situations and solves problems.

9.8.3.B: estimate and find solutions to application problems involving percents and other proportional relationships, such as similarity and rates.

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.

### 10: The student will demonstrate an understanding of the mathematical processes and tools used in problem solving.

10.8.14: The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school.

10.8.14.A: identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;

10.8.15: The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models.

10.8.15.A: communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.

10.8.16: The student uses logical reasoning to make conjectures and verify conclusions.

10.8.16.A: make conjectures from patterns or sets of examples and nonexamples; and

10.8.16.B: validate his/her conclusions using mathematical properties and relationships.

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.