### 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: Determine the absolute value of rational numbers.

1.A.2: Illustrate the relationships among natural (i.e., counting) numbers, whole numbers, integers, rational and irrational numbers.

1.A.5: Simplify numerical expressions using order of operations.

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

1.B.1: Add, subtract, multiply, and divide rational numbers (e.g., integers, fractions, terminating decimals) and take positive rational numbers to whole-number powers.

1.B.2: Convert terminating decimals into reduced fractions.

1.B.3: Calculate given percentages of quantities and use them to solve problems (e.g., discounts of sales, interest earned, tips, markups, commission, profit, simple interest).

1.B.4: Add and subtract fractions with unlike denominators.

1.B.5: Multiply, divide, and simplify rational numbers by using exponent rules.

1.B.6: Understand the meaning of the absolute value of a number:

1.B.6.a: interpret the absolute value as the distance of the number from zero on a number line

1.B.6.b: determine the absolute value of real numbers

1.B.9: Solve addition, subtraction, multiplication, and division problems that use positive and negative integers and combinations of these operations.

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

1.C.2: Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.

1.C.4: Calculate the percentage of increases and decreases of a quantity.

1.C.5: Add and subtract fractions with unlike denominators.

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

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

2.A.1: Identify and continue patterns presented in a variety of formats.

2.A.2: Represent a variety of relationships using tables, graphs, verbal rules, and possible symbolic notation, and recognize the same general pattern presented in different representations.

2.A.3: Simplify numerical expressions by applying properties of rational numbers, and justify the process used.

2.A.4: Interpret and evaluate expressions involving integer powers and simple roots.

2.A.5: Graph and interpret linear functions.

2.A.6: Solve problems involving rate, average speed, distance, and time.

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

2.B.1: Write verbal expressions and sentences as algebraic expressions and equations:

2.B.1.a: evaluate algebraic expressions

2.B.1.b: solve simple linear equations

2.B.1.c: graph and interpret results

2.B.2: Use variables and appropriate operations to write an expression, an equation, or an inequality that represents a verbal description.

2.B.4: Simplify numerical expressions by applying properties of rational numbers.

2.B.5: Graph linear functions and identify slope as positive or negative.

2.B.6: Use letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes.

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

2.C.1: Create scale models and use them for dimensional drawings.

2.C.2: Understand and use the coordinate plane to graph ordered pairs and linear equations.

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

2.D.1: Use variables and appropriate operations to write an expression, an equation, and/or an inequality that represents a verbal description involving change.

2.D.2: Interpret and evaluate expressions involving integer powers and simple roots as they relate to change.

2.D.3: Graph and interpret linear functions as they are used to solve problems.

2.D.4: Solve two-step equations and inequalities with one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.

### 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: Classify geometric figures as similar or congruent.

3.A.2: Understand the concept of a constant (e.g., pi) and use the formulas for the circumference and area of a circle.

3.A.3: Explain and use the Pythagorean theorem.

3.A.4: Determine the radius, diameter, and circumference of a circle and explain their relationship.

3.A.5: Use properties to classify solids including pyramids, cones, prisms, and cylinders.

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

3.B.1: Construct and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine the image under translations and reflections.

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

3.D.1: Compute the perimeter and area of common geometric shapes and use the results to find measures of less common objects.

3.D.2: Identify and describe the properties of two-dimensional figures:

3.D.2.a: identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms

3.D.2.b: use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle

### 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: Choose appropriate units of measure and ratios to recognize new equivalences (e.g., 1 square yard equals 9 square feet) to solve problems.

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

4.B.2: Select and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles.

4.B.3: Solve problems involving scale factors, ratios, and proportions.

### 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: Describe how data representations influences interpretation.

5.A.2: Select and use appropriate representation for presenting collected data and justify the selection.

5.A.3: Use measures of central tendency and spread to describe a set of data.

5.A.4: Choose between median and mode to describe a set of data and justify the choice for a particular situation.

5.A.5: Determine the quartiles of a data set.

5.A.6: Identify ordered pairs of data from a graph and interpret the data in terms of the situation depicted by the graph.

5.A.7: Use various scales and formats to display the same data set.

5.A.9: Collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set.

5.A.10: Compute the minimum, lower quartile, median, upper quartile, and maximum of a data set.

5.A.12: Use and explain sampling techniques (e.g., observations, surveys, and random sampling) for gathering data.

5.A.13: Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, and selecting, collecting, and displaying appropriate data to address the problem.

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

5.B.1: Choose and justify appropriate measures of central tendencies (e.g., mean, median, mode, range) to describe given or derived data.

5.B.2: Know various ways to display data sets (e.g., stem and leaf plot, box and whisker plot, scatter plots) and use these forms to display a single set of data or to compare two sets of data.

5.B.4: Use appropriate technology to gather and display data sets and identify the relationships that exist among variables within the data set.

5.B.6: Identify data that represent sampling errors and explain why the sample and the display might be biased.

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

5.C.3: Approximate a line of best fit for a data set in a scatter plot form and make predictions using the simple equation of that line.

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

5.D.1: Determine the probability of a compound event composed of two independent events.

5.D.2: Identify examples of events having the probability of one or zero.

5.D.3: Describe the probability of events using fractions, decimals, and percents.

5.D.4: Express probability as a fraction, zero, or one.

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

5.D.6: Make predictions based on theoretical probabilities of compound events.

5.D.7: Determine the probability of a simple event or a compound event composed of a simple, independent events.

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.