### 1: The student understands and applies the concepts and procedures of mathematics.

#### 1.1: Understand and apply concepts and procedures from number sense.

1.1.4: Apply understanding of direct and inverse proportion to solve problems.

1.1.4.a: Explain a method for determining whether a real-world problem involves direct proportion or inverse proportion.

1.1.4.b: Explain a method for solving a real-world problem involving direct proportion

1.1.4.c: Explain a method for solving a real-world problem involving inverse proportion.

1.1.4.d: Solve problems using direct or inverse models (e.g., similarity, age of car vs. worth).

1.1.4.e: Explain, illustrate, or describe examples of direct proportion.

1.1.4.f: Explain, illustrate, or describe examples of inverse proportion.

1.1.4.g: Use direct or inverse proportion to determine a number of objects or a measurement in a given situation.

1.1.6: Apply strategies to compute fluently with rational numbers in all forms including whole number exponents.

1.1.6.a: Complete multi-step computations using order of operations in situations involving combinations of rational numbers including whole number exponents and square roots of square numbers.

1.1.8: Apply estimation strategies to determine the reasonableness of results in situations involving multi-step computations with rational numbers including whole number powers and square and cube roots.

1.1.8.d: Describe various strategies used during estimation involving integers, rational numbers.

#### 1.2: Understand and apply concepts and procedures from measurement.

1.2.1: Analyze how changes in one or two dimensions of an object affect perimeter, area, surface area, and volume.

1.2.1.a: Describe and compare the impact that a change in one or more dimensions has on objects (e.g., how doubling one dimension of a cube affects the surface area and volume).

1.2.1.b: Describe how changes in the dimensions of objects affect perimeter, area, and volume in real-world situations (e.g., how does the change in the diameter of an oil drum affect the area and volume?).

1.2.1.c: Solve problems by deriving the changes in two dimensions necessary to obtain a desired surface area and/or volume (e.g., given a box with certain dimensions, make the volume of the box y cubic units by changing two dimensions of the box).

1.2.1.d: Compare a given change in one or two dimensions on the perimeter, area, surface areas, or volumes of two objects.

1.2.1.e: Determine the change in one dimension given a change in perimeter, area, volume, or surface area.

1.2.5: Apply formulas to calculate measurements of right prisms or right circular cylinders.

1.2.5.a: Explain how to use a formula for finding the volume of a prism or cylinder.

1.2.5.b: Use a formula to find the volume of a prism or cylinder.

1.2.5.c: Use a formula to derive a dimension of a right prism or right cylinder given other measures.

1.2.5.d: Use formulas to describe and compare the surface areas and volumes of two or more right prisms and/or right cylinders.

1.2.5.e: Use formulas to obtain measurements needed to describe a right cylinder or right prism.

1.2.6: Understand and apply strategies to obtain reasonable measurements at an appropriate level of precision.

1.2.6.b: Estimate a reasonable measurement at an appropriate level of precision.

1.2.6.e: Apply a process that can be used to find a reasonable estimate for the volume of prisms, pyramids, cylinders, and cones.

1.2.6.f: Estimate volume and surface area for right cylinders and right prisms.

#### 1.3: Understand and apply concepts and procedures from geometric sense.

1.3.1: Understand the relationship among characteristics of one-dimensional, two-dimensional, and threedimensional figures.

1.3.1.a: Identify and label one- and twodimensional characteristics (rays, lines, end points, line segments, vertices, and angles) in three-dimensional figures.

1.3.1.c: Draw and label with names and symbols nets of right prisms and right cylinders.

1.3.1.d: Describe everyday objects in terms of their geometric characteristics.

1.3.1.e: Describe or classify various shapes based on their characteristics.

1.3.1.f: Make and test conjectures about twodimensional and three-dimensional shapes and their individual attributes and relationships using physical, symbolic, and technological models (e.g., diagonal of a rectangle or prism is the longest interior segment; what figures make up cross-sections of a given three-dimensional shape?).

1.3.2: Apply understanding of geometric properties and relationships.

1.3.2.a: Use geometric properties and relationships to describe, compare, and draw two-dimensional and three-dimensional shapes and figures.

1.3.2.b: Construct geometric figures using a variety of tools and technologies (e.g., angle bisectors, perpendicular bisectors, triangles given specific characteristics).

1.3.2.d: Use the properties of two-dimensional and three-dimensional shapes to solve mathematical problems (e.g., find the width of a river based on similar triangles; given a set of parallel lines, a transversal, and an angle, find the other angles).

1.3.2.e: Compare two-dimensional and threedimensional shapes according to characteristics including faces, edges, and vertices, using actual and virtual modeling.

1.3.3: Apply understanding of geometric properties and location of points.

1.3.3.f: Identify, interpret, and use the meaning of slope of a line as a rate of change using physical, symbolic, and technological models.

1.3.4: Apply understanding of multiple transformations to figures.

1.3.4.a: Apply multiple transformations to create congruent and similar figures in any or all of the four quadrants.

1.3.4.b: Use multiple transformations (combinations of translations, reflections, or rotations) to draw an image.

1.3.4.c: Use dilation (expansion or contraction) of a given shape to form a similar shape.

1.3.4.d: Determine the final coordinates of a point after a series of transformations.

1.3.4.e: Examine figures to determine rotational symmetry about the center of the shape.

1.3.4.f: Define a set of transformations that would map one onto the other given two similar shapes.

1.3.4.g: Create a design with or without technology using a combination of two or more transformations with one or two two-dimensional figures.

#### 1.4: Understand and apply concepts and procedures from probability and statistics.

1.4.1: Understand the concept of conditional probability.

1.4.1.a: Compare the probabilities of dependent and independent events.

1.4.1.c: Explain the difference between dependent and independent events.

1.4.1.d: Explain and give examples of compound events.

1.4.2: Apply understanding of dependent and independent events to calculate probabilities.

1.4.2.a: Determine probabilities of dependent and independent events.

1.4.2.b: Generate the outcomes and probability of multiple independent and dependent events using a model or procedure (e.g., tree diagram, area model, counting procedures).

1.4.2.d: Explain the relationship between theoretical probability and empirical frequency of dependent events using simulations with and without technology.

1.4.2.e: Create a simple game based on independent probabilities wherein all players have an equal probability of winning.

1.4.2.f: Create a simple game based on compound probabilities.

1.4.2.g: Determine the sample space for independent or dependent events.

1.4.4: Understand and apply techniques to find the equation for a reasonable linear model.

1.4.4.b: Determine the equation of a line that fits the data displayed on a scatter plot.

1.4.4.f: Create a graph based on the equation for a line.

1.4.5: Analyze a linear model to judge its appropriateness for a data set.

1.4.5.a: Determine whether a straight line is an appropriate way to describe a trend in a set of bivariate data.

1.4.5.b: Determine whether the underlying model for a set of data is linear.

1.4.6: Apply understanding of statistics to make, analyze, or evaluate a statistical argument.

1.4.6.a: Identify trends in a set of data in order to make a prediction based on the information.

1.4.6.c: State possible factors that may influence a trend but not be reflected in the data (e.g., population growth of deer vs. availability of natural resources or hunting permits).

#### 1.5: Understand and apply concepts and procedures from algebraic sense.

1.5.1: Apply processes that use repeated addition (linear) or repeated multiplication (exponential).

1.5.1.a: Recognize, extend, or create a pattern or sequence between sets of numbers and/or linear patterns.

1.5.1.b: Identify, extend, or create a geometric or arithmetic sequence or pattern.

1.5.1.c: Translate among equivalent numerical, graphical, and algebraic forms of a linear function.

1.5.2: Analyze a pattern, table, graph, or model involving repeated addition (linear) or repeated multiplication (exponential) to write an equation or rule.

1.5.2.a: Find the equation of a line in a variety of ways (e.g., from a table, graph, slopeintercept, point-slope, two points).

1.5.2.c: Identify or write an equation or rule to describe a pattern, sequence, and/or a linear function.

1.5.2.d: Write an equation for a line given a set of information (e.g., two points, point-slope, etc.).

1.5.2.e: Write a recursive definition of a geometric pattern (e.g., Start and New = Old * Number).

1.5.2.f: Represent systems of equations and inequalities graphically.

1.5.2.h: Write an expression, equation, or inequality with two variables representing a linear model of a real-world problem.

1.5.4: Apply understanding of equations, tables, or graphs to represent situations involving relationships that can be written as repeated addition (linear) or repeated multiplication (exponential).

1.5.4.a: Represent variable quantities through expressions, equations, inequalities, graphs, and tables to represent linear situations involving whole number powers and square and cube roots.

1.5.4.b: Identify and use variable quantities to read and write expressions and equations to represent situations that can be described using repeated addition (e.g., models that are linear in nature).

1.5.4.c: Identify and use variable quantities to read and write expressions and equations to represent situations that can be described using repeated multiplication (e.g., models that are exponential such as savings accounts and early stages of population growth).

1.5.4.d: Recognize and write equations in recursive form for additive models (e.g., starting value, New = Old + some number).

1.5.4.e: Recognize and write equations in recursive form for multiplicative models (e.g., starting value, New = Old x some number).

1.5.4.f: Select an expression or equation to represent a given real world situation.

1.5.5: Apply procedures to simplify expressions.

1.5.5.a: Simplify expressions and evaluate formulas involving exponents.

1.5.5.b: Justify a simplification of an expression involving exponents.

1.5.6: Apply procedures to solve equations and systems of equations.

1.5.6.a: Rearrange formulas to solve for a particular variable (e.g., given A =.5bh, solve for h).

1.5.6.b: Solve real-world situations involving linear relationships and verify that the solution makes sense in relation to the problem.

1.5.6.c: Find the solution to a system of linear equations using tables, graphs, and symbols.

1.5.6.d: Interpret solutions of systems of equations.

1.5.6.e: Solve multi-step equations.

1.5.6.f: Use systems of equations to analyze and solve real-life problems.

1.5.6.g: Determine when two linear options yield the same outcome (e.g., given two different investment or profit options, determine when both options will yield the same result).

### 3: The student uses mathematical reasoning.

#### 3.1: Analyze information.

3.1.1: Synthesize information from multiple sources in order to answer questions.

3.1.1.a: Use the properties of two-dimensional and three-dimensional figures to solve mathematical problems (e.g., find the width of a river based on similar triangles; given a set of parallel lines, a transversal, and an angle, find the other angles).

#### 3.2: Make predictions, inferences, conjectures, and draw conclusions.

3.2.1: Apply skill of conjecturing and analyze conjectures by formulating a proof or constructing a counter example.

3.2.1.a: Make and test conjectures about twodimensional and three-dimensional figures and their individual attributes and relationships using physical, symbolic, and technological models (e.g., diagonal of a rectangle or prism is the longest interior segment; what figures make up cross-sections of a given three-dimensional shape).

3.2.2: Analyze information to draw conclusions and support them using inductive and deductive reasoning.

3.2.2.a: Compare and describe the volume of cylinders, cones, and prisms when an attribute is changed (e.g., the area of the base, the height of solid).

#### 3.3: Verify results.

3.3.1: Analyze results using inductive and deductive reasoning.

3.3.1.a: Compare and contrast similar twodimensional figures and shapes using properties of two-dimensional figures and shapes.

3.3.1.b: Find a reasonable estimate for the volume of prisms, pyramids, cylinders, and cones.

### 4: The student communicates knowledge and understanding in both everyday and mathematical language.

#### 4.1: Gather information.

4.1.2: Synthesize mathematical information for a given purpose from multiple, selfselected sources.

4.1.2.a: State possible factors that may influence a trend but not be reflected in the data (e.g., population growth of deer vs. availability of natural resources or hunting permits).

#### 4.2: Organize, represent, and share information.

4.2.2: Understand how to express ideas and situations using mathematical language and notation.

4.2.2.c: Describe and compare the impact that a change in one or more dimensions has on objects (e.g., doubling the edge of a cube affects the surface area).

4.2.2.d: Explain the relationship between theoretical probability and empirical frequency of dependent events using simulations with and without technology.

### 5: The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real-life situations.

#### 5.1: Relate concepts and procedures within mathematics.

5.1.1: Apply multiple mathematical concepts and procedures in a given problem or situation.

5.1.1.b: Determine the final coordinates of a point after a series of transformations.

5.1.2: Understand how to use different mathematical models and representations in the same situation.

5.1.2.a: Identify, interpret, and use the meaning of slope of a line as a rate of change using concrete, symbolic, and technological models.

5.1.2.b: Construct one-dimensional, twodimensional, and three-dimensional geometric figures using a variety of tools and technologies (e.g., angle bisectors, perpendicular bisectors, triangles given specific characteristics).

5.1.2.c: Find the equation of a line in a variety of ways (e.g., from a table, graph, slopeintercept, point-slope, two points).

5.1.2.d: Find the solution to a system of linear equations using tables, graphs and symbols.

#### 5.3: Relate mathematical concepts and procedures to real-world situations.

5.3.1: Understand situations in which mathematics can be used to solve problems with local, national, or international implications.

5.3.1.a: Explain a method for determining whether a real world problem involves direct proportion or inverse proportion.

5.3.1.b: Describe how changes in the dimensions of objects affect perimeter, area, and volume in real-world situations (e.g., how does the change in the diameter of an oil drum affect the area and volume).

Correlation last revised: 11/13/2008

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