### 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: Compare and order rational numbers.

1.A.2: Use equivalent representations for rational numbers (e.g., integers, decimals, fractions, percents, ratios, numbers with whole-number exponents).

1.A.5: Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers.

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

1.B.3: Demonstrate the relationship and equivalency among ratios and percents.

1.B.4: Use proportions to solve problems.

1.B.5: Explain and perform:

1.B.5.b: addition, subtraction, multiplication, and division with decimals

1.B.5.c: addition and subtraction with integers

1.B.5.d: addition, subtraction, and multiplication with fractions and mixed numerals

1.B.6: Determine the least common multiple and the greatest common divisor of whole numbers and use them to solve problems with fractions.

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

1.C.3: Determine if a problem situation calls for an exact or approximate answer and perform the appropriate computation.

1.C.4: Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.

1.C.5: Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.

1.C.6: Interpret and use ratios in different contexts.

1.C.7: Compute and perform multiplication and division of fractions and decimals and apply these procedures to solving problems.

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

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

2.A.1: Solve problems involving proportional relationships.

2.A.2: Graph ordered pairs in the coordinate plane.

2.A.3: Explain and use symbols to represent unknown quantities and variable relationships.

2.A.4: Explain and use the relationships among ratios, proportions, and percents.

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

2.B.2: Use letters to represent an unknown in an equation.

2.B.3: Solve one-step linear equations and inequalities in one variable with positive whole-number solutions.

2.B.4: Demonstrate that a variable can represent a single quantity that changes.

2.B.5: Demonstrate how changes in one variable affect other variables.

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

2.C.2: Create, explain, and use mathematical models such as:

2.C.2.b: equations and inequalities to model numerical relationships

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

2.D.1: Represent and explain changes using one-step equations with one variable.

2.D.2: Solve problems that involve change using proportional relationships.

2.D.4: Use tables and symbols to represent and describe proportional and other relationships involving conversions, sequences, and perimeter.

### 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: Identify, describe, and classify the properties of, and the relationships between, plane and solid geometric figures:

3.A.1.a: measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor, drawing software)

3.A.1.b: understand that the sum of angles of any triangle is 180 degrees and the sum of the angles of any quadrilateral is 360 degrees and use this information to solve problems

3.A.1.c: visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids

3.A.2: Classify angles as right, obtuse, or straight.

3.A.3: Describe the properties of geometric figures that include regular polygons, circles, ellipses, cylinders, cones, spheres, and cubes.

3.A.4: Classify polygons as regular or irregular.

3.A.5: Classify triangles as scalene, isosceles, or equilateral and by angles (i.e., right, acute, and obtuse).

3.A.7: Describe the relationship between radius, diameter, and circumference of a circle.

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

3.B.1: Use coordinate geometry to describe location on a plane.

3.B.2: Recognize skewed lines in space.

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

3.C.1: Identify line of symmetry with rotation and scaling.

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

3.D.1: Use appropriate technology, manipulatives, constructions, or drawings to recognize or compare geometric figures.

### 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.3: Select and use units of appropriate size and type to measure angles (e.g., degrees, radians), perimeter, area, and capacity in both U.S. customary and metric systems.

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

4.B.1: Apply various measurement techniques and tools, units of measure, and degrees of accuracy to find accurate rational number representations for length, liquid, weight, perimeter, temperature, and time.

4.B.2: Select and use formulas for perimeters of squares and rectangles.

4.B.4: Select and justify the selection of measurement tools, units of measure, and degrees of accuracy appropriate to the given situation.

### 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.2: Draw and compare different graphical representations of the same data.

5.A.3: Use mean, median, mode, and range to describe data.

5.A.5: Solve problems by collecting, organizing, displaying and interpreting data.

5.A.7: Conduct and explain sampling techniques such as observations, surveys, and random sampling for gathering data.

5.A.8: Determine the median for a rational number data set containing an odd number of data points.

5.A.9: Calculate and explain the median for a whole number data set containing an even number of data points.

5.A.10: Explain advantages and disadvantages of using various display formats for a specific data set.

5.A.11: Formulate and solve problems by collecting, organizing, displaying, and interpreting data.

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

5.B.1: Choose an appropriate graphical format to organize and represent data.

5.B.3: Compute and analyze statistical measurements for data sets:

5.B.3.a: understand how additional data added to data sets may affect the computations of central tendency

5.B.3.b: understand how the inclusion or exclusion of outliers affects measures of central tendency

5.B.3.c: know why a specific measure of central tendency provides the most useful information in a given context

5.B.5: Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and which method makes a sample more representative for a population.

5.B.7: 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.2: Conduct observations, surveys, experiments and/or simulations, record the results in charts, tables, or graphs, and use the results to draw conclusions and make predictions.

5.C.3: Find all possible combinations in a given set (e.g., the number of ways a set of books can be arranged on a shelf).

5.C.4: Compare expected results with actual results in a simple experiment.

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

5.D.1: List all possible outcomes for a compound event composed of two independent events and recognize whether an outcome is certain, impossible, likely, or unlikely.

5.D.2: Determine and compare experimental (empirical) and mathematical (theoretical) probabilities (e.g., flipping two color counters).

5.D.3: Determine theoretical and experimental probabilities and use them to make predictions about events.

5.D.4: Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome.

5.D.5: Use data to estimate the probability of future events (e.g., batting averages).

5.D.6: Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1- P is the probability of the event not occurring.

5.D.7: Describe the difference between independent and dependent events and identify situations involving independent or dependent events.

Correlation last revised: 11/13/2008

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