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

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

1.1.1: Understand the concept of rational numbers (integers, decimals, fractions).

1.1.1.a: Create a model when given a symbolic representation of a rational number.

1.1.1.b: Write the rational number when given a model (e.g., number line, area model, situation, diagram, picture).

1.1.1.c: Identify and convert between equivalent forms of rational numbers (e.g., fractions to decimals, percents to fractions).

1.1.1.d: Identify prime, square, or composite numbers.

1.1.2: Understand the relative values of rational numbers.

1.1.2.a: Compare and order rational numbers using physical models or implementing strategies (e.g., like denominators, changing to the same form).

1.1.2.b: Locate symbolic representations of rational numbers on a model (e.g., a number line, fraction line, decimal grid, and circle graph).

1.1.3: Apply properties of addition and multiplication including inverse properties to the rational number system.

1.1.3.a: Use the inverse relationships between multiplication and division to simplify computations and solve problems.

1.1.3.b: Use the inverse properties of addition and multiplication to simplify computations with integers, fractions, and decimals.

1.1.4: Understand the concept of direct proportion.

1.1.4.a: Express proportional relationships using objects, pictures, and symbols.

1.1.4.b: Explain the meaning of a proportion.

1.1.4.c: Represent a new relationship from a given ratio (e.g., height of a totem pole, maypole).

1.1.4.d: Represent percentages less than 1% or greater than 100% using objects, pictures, and symbols.

1.1.4.e: Complete or write a proportion for a given situation.

1.1.4.f: Solve problems involving proportions (e.g., determine the number and kinds of baked goods to bring to a bake sale based on proportions of different goods sold at previous bake sales).

1.1.4.g: Use ratios to make predictions about proportions in a future situation.

1.1.5: Understand the meaning of addition and subtraction on integers.

1.1.5.a: Explain the meaning of addition and subtraction of integers using real-world models (e.g., reducing debt, temperature increase or decrease, yards gained and lost, movement of a hot-air balloon).

1.1.5.b: Create a problem situation involving addition or subtraction of integers.

1.1.5.c: Explain or show the meaning of addition or subtraction of integers.

1.1.5.d: Use technology to demonstrate addition and subtraction with integers.

1.1.6: Apply computational procedures with fluency for multiplication and division on non-negative rational numbers.

1.1.6.a: Find the product or quotient using nonnegative decimals and fractions with unlike denominators.

1.1.6.b: Apply percentages to solve a problem in a variety of situations (e.g., taxes, discounts, interest).

1.1.6.c: Use multiplication and division to solve real-world problems involving non-negative rational numbers.

1.1.6.d: Multiply non-negative decimal numbers to the hundredths place.

1.1.7: Understand and apply strategies and tools to complete tasks involving addition and subtraction on integers and the four basic operations on non-negative rational numbers.

1.1.7.b: Convert between fractions, decimals, whole numbers, and percents mentally, on paper, or with a calculator.

1.1.7.c: Use calculators to add and subtract with integers of two or more digits.

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

1.2.1: Analyze how a change in a linear dimension affects other linear measurements (perimeter, circumference) and area measurements.

1.2.1.a: Describe the relationships among linear dimensions (e.g., radius of a circle, length of a side or base, changes in the diameter affects the amount of deer hide needed to cover a drum face) and area of the figure (e.g., change the radius or length of a side, and check the change in area; describe that change).

1.2.1.b: Explain changing one, two, or three dimensions in a rectangular prism and how it affects the surface area and volume; give three examples.

1.2.1.c: Solve problems involving the effects of changes in one dimension on area (e.g., given a garden with certain dimensions, make the area of the garden x square units by changing only one dimension of the garden).

1.2.3: Understand how the unit of measure affects the precision of measurement.

1.2.3.a: Select the appropriate measurement tool to match the precision needed (e.g., if needing measurement to the nearest 1/16 inch, select a ruler that has 1/32 increments).

1.2.3.b: Explain how the unit selected for a situation can affect the precision of the measurement (e.g., when you have a ruler that has only 1/10 increments, you cannot measure something to the nearest hundredth with confidence of precision).

1.2.3.c: Explain how measurement systems allow for different levels of precision (e.g., millimeters give more precise measurement than centimeters).

1.2.5: Apply formulas to find measurements of circles, triangles, and rectangular prisms.

1.2.5.a: Apply formulas to determine missing measurements for circles, rectangular prisms, and triangles.

1.2.5.b: Explain how to use a formula for finding the area and circumference of a circle (e.g, calculate the area needed to cover a drum face).

1.2.5.c: Find and compare the volumes of rectangular prisms that have a given volume (e.g., if two rectangular prisms have the same volume and one has twice the height of the other, determine how the areas of their bases compare).

1.2.5.d: Justify the standard formula for finding the area of a right triangle (e.g., 1/2 of a rectangle).

1.2.5.e: Use given dimensions to determine surface area and volume.

1.2.6: Understand and apply strategies to obtain reasonable estimates of circle measurements, right triangles, and surface area for rectangular prisms.

1.2.6.c: Use common approximations of pi (3.14; 22/7) to calculate the approximate circumference and the area of circles.

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

1.3.1: Understand the concept of similarity.

1.3.1.a: Identify corresponding sides and angles of two similar figures.

1.3.1.b: Determine and justify if two figures are similar using the definition of similarity.

1.3.1.c: Differentiate between similar and congruent figures, either geometric figures or real-world objects, and justify the conclusion.

1.3.1.d: Explain how a scale drawing is an example of similarity.

1.3.2: Apply understanding of the characteristics of rectangular prisms and circles.

1.3.2.b: Draw rectangular prisms and circles with specified properties (e.g., circumference of an 18-centimeter quadrilateral having equal sides but no right angles; a triangle with no equal sides).

1.3.2.c: Use the properties of rectangular prisms and circles to solve problems (e.g., determine which of two rectangular prismshaped boxes will hold the most cans of food at the food drive and explain how the geometric characteristics affect capacity).

1.3.2.d: Compare two rectangular prisms based on their characteristics (e.g., compare the geometric characteristics of two rectangular prisms with different dimensions and the same volume).

1.3.3: Understand the location of points on a coordinate grid in any of the four quadrants.

1.3.3.a: Identify the coordinates of the fourth point to make a rectangle given three points.

1.3.3.b: Plot and label ordered pairs in any of the four quadrants.

1.3.3.c: Name the coordinates of a given point in any of the four quadrants.

1.3.3.d: Identify objects or the location of objects on a coordinate grid using coordinates or labels.

1.3.3.f: Use ordered pairs to describe the location of objects on a grid.

1.3.4: Understand and apply combinations of translations (slides) and reflections (flips) to two-dimensional figures.

1.3.4.a: Identify and explain whether a shape has been translated (slid) or reflected (flipped) with or without a grid.

1.3.4.b: Use transformations to create congruent figures and shapes in multiple orientations.

1.3.4.c: Find the coordinate pairs for a translation or a reflection across an axis given a shape on a coordinate grid.

1.3.4.d: Match a shape with its image following one or two transformations (sliding or flipping).

1.3.4.e: Use combinations of translations and reflections to draw congruent figures.

1.3.4.f: Use ordered pairs to describe the location of an object on a coordinate grid after a translation and reflection.

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

1.4.2: Understand and apply the procedures for determining the probabilities of multiple trials.

1.4.2.a: Calculate the probabilities of independent or mutually exclusive outcomes or events.

1.4.2.b: Calculate the probability of an event given the probability of its complement.

1.4.2.c: Create a game that has an equal probability for all players to win.

1.4.2.e: Determine, interpret, or express probabilities in the form of a fraction, decimal, or percent.

1.4.2.f: Predict the probability of outcomes of experiments and test the predictions.

1.4.4: Understand how variations in data may affect the choice of data analysis techniques used.

1.4.4.a: Determine and use range and measures of central tendency to describe a set of data.

1.4.4.b: Describe the effects of extreme values on means in a population.

1.4.4.c: Explain the difference between median or mean as a measure of central tendency in a given situation (e.g., when an extreme value skews the mean).

1.4.4.d: Describe how additional data added to data sets may affect the result of measures of central tendency.

1.4.4.e: Find the range of a set of data.

1.4.4.f: Explain what the range adds to measures of central tendency.

1.4.5: Understand and apply various data display techniques including box-andwhisker plots.

1.4.5.b: Determine the appropriate representation for given data.

1.4.5.c: Construct bar graphs, circle graphs, line graphs, box-and-whisker and scatter plots using collected data.

1.4.5.d: Use scatter plots to describe trends and interpret relationships.

1.4.5.e: Read and interpret data from box-andwhisker plots and determine when using this type of graph is appropriate.

1.4.5.f: Describe statistical information given a box-and-whisker plot (e.g., median, range, interquartile range).

1.4.5.g: Compare different graphical representations of the same data.

1.4.6: Evaluate how different representations of the same set of data can support different points of view.

1.4.6.a: Critique the use of data and data displays for univariate data.

1.4.6.d: Explain how different representations of the same set of data can support different points of view.

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

1.5.1: Apply understanding of linear relationships to analyze patterns, sequences, and situations.

1.5.1.a: Identify patterns that are linear relations and provide missing terms.

1.5.1.b: Describe the relationship between the terms in a sequence and their positions in the sequence.

1.5.1.c: Identify, extend, or represent patterns and sequences using tables, graphs, or expressions.

1.5.1.d: Use technology to generate graphic representations of linear relationships.

1.5.1.e: Make predictions using linear relationships in situations.

1.5.1.f: Identify a linear relationship that has the same pattern as another linear relationship.

1.5.1.g: Create a representation of a linear relationship given a rule.

1.5.2: Apply understanding of linear patterns in a table, graph, or situation to develop a rule.

1.5.2.a: Describe the rule and/or construct a table to represent a pattern with combinations of two arithmetic operations in the rule.

1.5.2.b: Write an expression or equation with a single variable representing a situation or real-world problem.

1.5.2.c: Write a story about a situation that represents a given linear equation, expression, or graph.

1.5.2.d: Describe the rule or construct a table to represent a pattern with combinations of two arithmetic operations in the rule.

1.5.2.e: Use technology to determine the rule for a linear relationship.

1.5.3: Understand relationships between quantities using squares and square roots.

1.5.3.b: Simplify square roots of square numbers (e.g., the square root of 9 is 3).

1.5.3.c: Demonstrate understanding of square roots with physical models and examples.

1.5.4: Apply understanding of equations, tables, and graphs to represent situations involving linear relationships.

1.5.4.a: Represent linear relationships through expressions, equations, tables, and graphs of situations involving nonnegative rational numbers.

1.5.4.b: Graph data to demonstrate relationships in familiar contexts (e.g., conversions, perimeter, area, volume, and scaling).

1.5.4.c: Develop a situation that corresponds to a given equation or expression.

1.5.4.d: Create a table or graph given a description of, or an equation for, a situation involving a linear relationship.

1.5.4.e: Describe a situation involving a linear or non-linear relationship that matches a given graph (e.g., time-distance, timeheight).

1.5.4.f: Explain the meaning of a variable in a formula, expression, or equation.

1.5.5: Understand and apply procedures to evaluate expressions and formulas considering order of operations.

1.5.5.b: Explain the simplification of expressions and equations using order of operations.

1.5.5.c: Evaluate expressions and formulas considering order of operations.

1.5.5.f: Write expressions or equations for a situation.

1.5.6: Understand and apply a variety of strategies to solve two-step equations with one variable.

1.5.6.b: Solve two-step equations with one variable on only one side of the equal sign (e.g., 2x + 4 = 12).

### 3: The student uses mathematical reasoning.

#### 3.1: Analyze information.

3.1.1: Analyze information from a variety of sources to interpret and compare information.

3.1.1.a: Explain and compare conclusions reached from data (e.g., from newspapers, web sites, opinion polls).

3.1.1.b: Use graphs to describe trends, compare, and interpret relationships from data (e.g., from newspapers, web sites, opinion polls).

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

3.2.1: Apply prediction and inference skills to make or evaluate conjectures.

3.2.1.a: Predict the probability of future events based on empirical data.

3.2.3: Analyze procedures and results in various situations.

3.2.3.a: Describe how additional data added to data sets may affect the computations of measures of central tendency in various situations.

#### 3.3: Verify results.

3.3.1: Analyze procedures and information used to justify results using evidence.

3.3.1.c: Apply estimation strategies prior to computing addition and subtraction of integers and operations on non-negative rational numbers to determine reasonableness of answers.

3.3.2: Analyze thinking and mathematical ideas using models, known facts, patterns, relationships, or counter examples.

3.3.2.a: Explain how different representations of the same set of data can support different points of view.

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

#### 4.1: Gather information.

4.1.2: Understand how to extract information from multiple sources using reading, listening, and observation.

4.1.2.a: Create a table or graph given a description of, or an equation for, a situation involving a linear or non-linear relationship.

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

4.2.1: Apply organizational skills for a given purpose.

4.2.1.a: Identify, determine, interpret, or express probabilities in the form of a fraction, decimal, or percent.

4.2.2: Apply communication skills to clearly and effectively express or present ideas and situations using mathematical language or notation.

4.2.2.a: Identify data that may represent sampling errors and explain why the sample (and the display) might be biased.

4.2.2.b: Explain when estimation might be used rather than computation.

### 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 concepts and procedures from a variety of mathematical areas in a given problem or situation.

5.1.1.b: Given a set of data, compare various representations (e.g., box-and-whisker, bar, circle graph) for a given situation.

5.1.2: Apply different mathematical models and representations to the same situation.

5.1.2.a: Explain how different representations of the same set of data can support different points of view.

#### 5.2: Relate mathematical concepts procedures to other disciplines.

5.2.1: Analyze mathematical patterns and ideas to extend mathematical thinking and modeling to other disciplines.

5.2.1.g: Mix paint in the correct proportions to create a particular color.

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

5.3.1: Understand that mathematics is used in daily life and extensively outside the classroom.

5.3.1.b: Use properties of polygons and circles to solve real-world problems (e.g., find the amount of fencing needed for a pasture).

Correlation last revised: 11/13/2008

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