### 1: Students will understand numerical concepts and mathematical operations.

#### 1.A: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

1.A.1: Sort numbers by their properties (e.g., prime, composite, square, square root).

#### 1.B: Understand the meaning of operations and how they relate to one another.

1.B.1: Use real number properties (e.g., commutative, associative, distributive) to perform various computational procedures.

1.B.2: Perform arithmetic operations and their inverses (e.g., addition/subtraction, multiplication/division, square roots of perfect squares, cube roots of perfect cubes) on real numbers.

1.B.3: Find roots of real numbers using calculators.

#### 1.C: Compute fluently and make reasonable estimates.

1.C.1: Formulate algebraic expressions that include real numbers to describe and solve real-world problems.

1.C.2: Use a variety of computational methods to estimate quantities involving real numbers.

1.C.4: Use real number properties to perform various computational procedures and explain how they were used.

1.C.5: Perform and explain computations with rational numbers, pi, and first-degree algebraic expressions in one variable in a variety of situations.

1.C.6: Select and use appropriate forms of rational numbers to solve real-world problems including those involving proportional relationships.

1.C.9: Estimate answers and use formulas to solve application problems involving surface area and volume.

### 2: Students will understand algebraic concepts and applications.

#### 2.A: Understand patterns, relations, and functions.

2.A.1: Move between numerical, tabular, and graphical representations of linear relationships.

2.A.2: Use variables to generalize patterns and information presented in tables, charts, and graphs:

2.A.2.a: graph linear functions noting that the vertical change per unit of horizontal change (the slope of the graph) is always the same

2.A.2.b: plot the values of quantities whose ratios are always the same, fit a line to the plot, and understand that the slope of the line equals the quantities

#### 2.B: Represent and analyze mathematical situations and structures using algebraic symbols.

2.B.1: Demonstrate the difference between an equation and an expression.

2.B.2: Solve two-step linear equations and inequalities in one variable with rational solutions.

2.B.4: Demonstrate understanding of the relationships between ratios, proportions, and percents and solve for a missing term in a proportion.

2.B.5: Graph solution sets of linear equations in two variables on the coordinate plane.

2.B.6: Formulate and solve problems involving simple linear relationships, find percents of a given number, variable situations, and unknown quantities.

2.B.7: Use symbols, variables, expressions, inequalities, equations, and simple systems of equations to represent problem situations that involve variables or unknown quantities.

#### 2.C: Use mathematical models to represent and understand quantitative relationships.

2.C.1: Generate different representations to model a specific numerical relationship given one representation of data (e.g., a table, a graph, an equation, a verbal description).

#### 2.D: Analyze changes in various contexts.

2.D.1: Use graphs, tables, and algebraic representations to make predictions and solve problems that involve change.

2.D.2: Estimate, find, and justify solutions to problems that involve change using tables, graphs, and algebraic expressions.

2.D.4: Solve multi-step problems that involve changes in rate, average speed, distance, and time.

2.D.5: Analyze problems that involve change by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing, and observing patterns.

2.D.6: Generalize a pattern of change using algebra and show the relationship among the equation, graph, and table of values.

### 3: Students will understand geometric concepts and applications.

#### 3.A: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematics arguments about geometric relationships.

3.A.1: Recognize, classify, and discuss properties of all geometric figures including point, line, and plane.

3.A.2: Identify arc, chord, and semicircle and explain their attributes.

3.A.3: Use the Pythagorean theorem and its converse to find the missing side of a right triangle and the lengths of the other line segments.

#### 3.B: Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

3.B.1: Represent, formulate, and solve distance and geometry problems using the language and symbols of algebra and the coordinate plane and space (e.g., ordered triplets).

#### 3.C: Apply transformations and use symmetry to analyze mathematical situations.

3.C.1: Describe the symmetry of three-dimensional figures.

3.C.2: Describe and perform single and multiple transformations that include rotation, reflection, translation, and dilation (i.e., shrink or magnify) to two-dimensional figures.

#### 3.D: Use visualization, spatial reasoning, and geometric modeling to solve problems.

3.D.1: Understand angle relationships formed by parallel lines cut by a transversal.

3.D.2: Recognize and apply properties of corresponding parts of similar and congruent triangles and quadrilaterals.

3.D.3: Represent and solve problems relating to size, shape, area, and volume using geometric models.

3.D.4: Develop and use formulas for area, perimeter, circumference, and volume.

3.D.5: Construct two-dimensional patterns for three-dimensional models (e.g., cylinders, prisms, cones).

### 4: Students will understand measurement systems and applications.

#### 4.A: Understand measurable attributes of objects and the units, systems, and processes of measurement.

4.A.1: Understand the concept of volume and use the appropriate units in common measuring systems (e.g., cubic centimeter, cubic inch, cubic yard) to compute the volume of rectangular solids.

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

4.B.1: Use ratios and proportions to measure hard-to-measure objects.

4.B.3: Use proportional relationships in similar shapes to find missing measurements.

4.B.4: Apply strategies to determine the surface area and volume of prisms, pyramids, and cylinders.

4.B.6: Estimate volume in cubic units.

4.B.7: Solve simple problems involving rates and derived measurements for such properties as velocity and density.

### 5: Students will understand how to formulate questions, analyze data, and determine probabilities.

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

5.A.1: Represent two numerical variables on a plot, describe how the data points are distributed, and identify relationships that exist between the two variables.

5.A.3: Organize, analyze, and display appropriate quantitative and qualitative data to address specific questions including:

5.A.3.a: frequency distributions

5.A.3.b: plots

5.A.3.c: histograms

5.A.3.d: bar, line, and pie graphs

5.A.3.e: diagram and pictorial displays

5.A.3.f: charts and tables

5.A.4: Select the appropriate measure of central tendency to describe a set of data for a particular problem situation.

5.A.5: Simulate an event selecting and using different models.

#### 5.B: Select and use appropriate statistical methods to analyze data.

5.B.3: Analyze data to make decisions and to develop convincing arguments from data displayed in a variety of formats that include:

5.B.3.d: scatter plots

5.B.4: Interpret and analyze data from graphical representations and draw simple conclusions (e.g., line of best fit).

5.B.6: Use appropriate central tendency and spread as a means for effective decision-making in analyzing data and outliers.

5.B.7: Identify simple graphic misrepresentations and distortions of sets of data (e.g., unequal interval sizes, omission of parts of axis range, scaling).

5.B.8: Use appropriate technology to display data as lists, tables, matrices, graphs, and plots and to analyze the relationships of variables in the data displayed.

#### 5.C: Develop and evaluate inferences and predictions that are based on data.

5.C.1: Describe how changes in scale, intervals, or categories influence arguments for a particular interpretation of the data.

5.C.2: Describe how reader bias, measurement errors, and display distortion can affect the interpretation of data, predictions, and inferences based on data.

5.C.3: Conduct simple experiments and/or simulations, record results in charts, tables, or graphs, and use the results to draw conclusions and make predictions.

5.C.4: Compare expected results with experimental results and information used in predictions and inferences.

#### 5.D: Understand and apply basic concepts of probability.

5.D.2: Design and use an appropriate simulation to estimate the probability of a real-world event (e.g., disk toss, cube toss).

5.D.3: Explain the relationship between probability and odds and calculate the odds of a desired outcome in a simple experiment.

5.D.4: Use theoretical or experimental probability to make predictions about real-world events.

5.D.5: Use probability to generate convincing arguments, draw conclusions, and make decisions in a variety of situations.

5.D.6: Understand that the probability of two unrelated events occurring is the sum of the two individual possibilities and that the probability of one event following another, in independent trials, is the product of the two probabilities.

Correlation last revised: 11/13/2008

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