Nevada State Standards for Mathematics:

Currently Perma-Bound only has suggested titles for grades K-8 in the Science and Social Studies areas. We are working on expanding this.

NV.A. Problem Solving: Students will develop their ability to solve problems by engaging in developmentally appropriate opportunities where there is a need to use various approaches to investigate and understand mathematical concepts in order to: formulate their own problems; find solutions to problems from everyday situations; develop and apply strategies to solve a variety of problems; and integrate mathematical reasoning, communication and connections.

A.1. Apply previous experience and knowledge to new problem solving situations.

A.2. Explain and verify results with respect to the original problem.

A.3. Try more than one strategy when the first strategy proves to be unproductive.

A.4. Use technology, including calculators, to develop mathematical concepts.

NV.B. Mathematical Communication: Students will develop their ability to communicate mathematically by solving problems where there is a need to obtain information from the real world through reading, listening, and observing in order to: translate information into mathematical language and symbols; process information mathematically; present results in written, oral, and visual formats; discuss and exchange ideas about mathematics as a part of learning; read a variety of fiction and nonfiction texts to learn about mathematics; and use mathematical notation to communicate and explain problems.

B.1. Use inquiry techniques to solve mathematical problems.

B.2. Use physical materials, models, pictures, or writing to represent and communicate mathematical ideas.

B.3. Identify and translate key words and phrases that imply mathematical operations.

B.4. Use everyday language, both orally and in writing, to communicate strategies and solutions to mathematical problems.

NV.C. Mathematical Reasoning: Students will develop their ability to reason mathematically by solving problems where there is a need to investigate mathematical ideas and construct their own learning in all content areas in order to: reinforce and extend their logical reasoning abilities; reflect on, clarify, and justify their thinking; ask questions to extend their thinking; use patterns and relationships to analyze mathematical situations; and determine relevant, irrelevant, and/or sufficient information to solve mathematical problems.

C.1. Draw logical conclusions about mathematical problems.

C.2. Discuss the steps used to solve a mathematical problem.

C.3. Justify and explain the solutions to problems using physical models.

NV.D. Mathematical Connections: Students will develop the ability to make mathematical connections by solving problems where there is a need to view mathematics as an integrated whole in order to: link new concepts to prior knowledge; identify relationships between content strands; integrate mathematics with other disciplines; and allow the flexibility to approach problems in a variety of ways within and beyond the field of mathematics.

D.1. Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science.

D.2. Identify mathematics used in everyday life.

NV.1.0. Numbers, Number Sense, and Computation: Students will accurately calculate and use estimation techniques, number relationships, operation rules, and algorithms; they will determine the reasonableness of answers and the accuracy of solutions to solve problems, communicate, reason, and make connections within and beyond the field of mathematics.

1.K.3 Comparison and Ordering

1.K.3.a. Recognize, read, and write numbers from 0 - 10.

1.K.3.b. Identify ordinal positions first to third.

1.K.3.c. Match the number of objects in a set to the correct numeral 0 - 10.

1.K.3.d. Recognize relationships of more than, less than, and equal to.

1.K.4 Counting

1.K.4.a. Count to 20 by demonstrating one-to-one correspondence using objects.

1.K.5 Facts

1.K.5.a. Use concrete objects to model simple addition and subtraction.

NV.2.0. Patterns, Functions, and Algebra: Students will use various algebraic methods to analyze, illustrate, extend, and create numerous representations (words, numbers, tables, and graphs) of patterns, functions, and algebraic relations as modeled in practical situations to solve problems, communicate, reason, and make connections within and beyond the field of mathematics.

2.K.1 Patterns

2.K.1.a. Identify attributes used to sort objects.

2.K.3 Number Sentences, Expressions, and Polynomials

2.K.3.a. Identify and create sets of objects with unequal amounts, describing them as greater than or less than.

NV.3.0. Measurement: Students will use appropriate tools and techniques of measurement to determine, estimate, record, and verify direct and indirect measurements to solve problems, communicate, reason, and make connections within and beyond the field of mathematics.

3.K.1 Comparison, Estimation, and Conversion

3.K.1.a. Compare, order, and describe objects by size.

3.K.4 Money

3.K.4.a. Identify and sort pennies, nickels, and dimes.

3.K.6 Time

3.K.6.a. Recite in order the days of the week.

NV.4.0. Spatial Relationships, Geometry, and Logic: Students will identify, represent, verify, and apply spatial relationships and geometric properties to solve problems, communicate, and make connections within and beyond the field of mathematics.

4.K.1 Two-Dimensional Shapes

4.K.1.a. Identify two-dimensional shapes (circles, triangles, rectangles including squares) regardless of orientation.

4.K.2 Congruence, Similarity, and Transformations

4.K.2.a. Demonstrate an understanding of relative position words, including before/after, far/near, and over/under, to place objects.

4.K.3 Coordinate Geometry and Lines of Symmetry

4.K.3.a. Identify two-dimensional figures (windows are shaped like rectangles) as they appear in the environment.

4.K.4 Three-Dimensional Figures

4.K.4.a. Identify three-dimensional figures in the environment.

4.K.9 Logic

4.K.9.a. Sort and classify objects by color and shape.

4.K.9.b. Put events in a logical sequence.

NV.5.0. Data Analysis: Students will collect, organize, display, interpret, and analyze data to determine statistical relationships and probability projections to solve problems, communicate, reason, and make connections within and beyond the field of mathematics.

5.K.1 Data Collection and Organization

5.K.1.a. Collect, organize, and record data using objects and pictures.

5.K.1.b. Represent data in a variety of ways in response to questions posed by teachers.

A.1. Apply previous experience and knowledge to new problem solving situations.

A.2. Explain and verify results with respect to the original problem.

A.3. Try more than one strategy when the first strategy proves to be unproductive.

A.4. Use technology, including calculators, to develop mathematical concepts.

B.1. Use inquiry techniques to solve mathematical problems.

B.2. Use physical materials, models, pictures, or writing to represent and communicate mathematical ideas.

B.3. Identify and translate key words and phrases that imply mathematical operations.

B.4. Use everyday language, both orally and in writing, to communicate strategies and solutions to mathematical problems.

C.1. Draw logical conclusions about mathematical problems.

C.2. Discuss the steps used to solve a mathematical problem.

C.3. Justify and explain the solutions to problems using physical models.

D.1. Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science.

D.2. Identify mathematics used in everyday life.

1.1.1 Place Value

1.1.1.a. Identify, model, read, and write place value positions of 1's and 10's.

1.1.1.b. Identify the value of a given digit in the 1's and 10's place.

1.1.2 Fractions

1.1.2.a. Identify and model a whole.

1.1.2.b. Identify and model 1/2 as two equal parts of a whole or a set of objects.

1.1.3 Comparison and Ordering

1.1.3.a. Read, write, compare, and order numbers from 0 - 100.

1.1.3.b. Identify ordinal positions first to tenth.

1.1.3.c. Read and write number words to 10.

1.1.3.d. Create, compare, and describe sets of objects and numbers from 0 - 100 as greater than, less than, or equal to (>, <, =).

1.1.4 Counting

1.1.4.a. Use number patterns and models to count by 2's, 5's, and 10's to 100.

1.1.5 Facts

1.1.5.a. Identify and model basic addition facts (sums to 10) and the corresponding subtraction facts.

1.1.6 Estimating and Estimation Strategies

1.1.6.a. Estimate the number of objects in a set to 10 and verify by counting.

1.1.8 Solving Problems and Number Theory

1.1.8.a. Demonstrate the joining and separating of sets with 20 or fewer objects.

1.1.8.b. Model the meaning of addition and subtraction in a variety of ways including the comparison of sets using objects, pictorial representations, and symbols.

1.1.8.c. Use mathematical vocabulary and symbols to describe addition, subtraction, and equality.

2.1.1 Patterns

2.1.1.a. Recognize, describe, label, extend, and create simple repeating patterns using symbols, objects, and manipulatives.

2.1.2 Variables and Unknowns

2.1.2.a. Recognize that unknowns in an addition or subtraction equation represent a missing value that will make the statement true.

2.1.3 Number Sentences, Expressions, and Polynomials

2.1.3.a. Create, compare, and describe sets of objects as greater than, less than, or equal to.

3.1.1 Comparison, Estimation, and Conversion

3.1.1.a. Compare, order, describe, and represent objects by length and weight.

3.1.2 Precision in Measurements

3.1.2.a. Compare and measure length and weight using non-standard measurement.

3.1.4 Money

3.1.4.a. Determine the value of any set of pennies, nickels, and dimes.

3.1.6 Time

3.1.6.a. Recite in order the months of the year.

3.1.6.b. Use a calendar to identify days, weeks, months, and a year.

3.1.6.c. Read time to the nearest hour.

4.1.1 Two-Dimensional Shapes

4.1.1.a. Name, sort, and sketch two-dimensional shapes (circles, triangles, rectangles including squares) regardless of orientation.

4.1.2 Congruence, Similarity, and Transformations

4.1.2.a. Demonstrate an understanding of position words, including down/up, left/right, top/bottom, and between/middle, by describing the relative location of objects.

4.1.3 Coordinate Geometry and Lines of Symmetry

4.1.3.a. Identify and copy two-dimensional designs that contain a line of symmetry.

4.1.4 Three-Dimensional Figures

4.1.4.a. Identify and name three-dimensional figures in the environment.

4.1.9 Logic

4.1.9.a. Sort and classify objects by size or thickness.

4.1.9.b. Identify what comes next in a step-by-step story or event sequence.

5.1.1 Data Collection and Organization

5.1.1.a. Collect, organize, and record data in response to questions posed by teacher and/or students.

5.1.1.b. Use tally marks to represent data.

A.1. Apply previous experience and knowledge to new problem solving situations.

A.2. Explain and verify results with respect to the original problem.

A.3. Try more than one strategy when the first strategy proves to be unproductive.

A.4. Use technology, including calculators, to develop mathematical concepts.

B.1. Use inquiry techniques to solve mathematical problems.

B.2. Use physical materials, models, pictures, or writing to represent and communicate mathematical ideas.

B.3. Identify and translate key words and phrases that imply mathematical operations.

B.4. Use everyday language, both orally and in writing, to communicate strategies and solutions to mathematical problems.

C.1. Draw logical conclusions about mathematical problems.

C.2. Discuss the steps used to solve a mathematical problem.

C.3. Justify and explain the solutions to problems using physical models.

D.1. Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science.

D.2. Identify mathematics used in everyday life.

1.2.1 Place Value

1.2.1.a. Identify, use, and model place value positions of 1's, 10's and 100's.

1.2.1.b. Identify the value of a given digit in the 1's, 10's and 100's place.

1.2.2 Fractions

1.2.2.a. Identify equal parts of a whole.

1.2.2.b. Identify and model the unit fractions 1/2 and 1/4 as equal parts of a whole or sets of objects.

1.2.3 Comparison and Ordering

1.2.3.a. Read, write, compare, and order numbers from 0 - 999.

1.2.3.b. Identify ordinal positions first to twentieth.

1.2.3.c. Read and write number words to 20.

1.2.3.d. Create, compare, and describe sets of objects and numbers from 0 - 999 as greater than, less than, or equal to (>, <, =).

1.2.4 Counting

1.2.4.a. Use number patterns to skip count.

1.2.5 Facts

1.2.5.a. Identify and model basic addition facts (sums to 18) and the corresponding subtraction facts.

1.2.5.b. Immediately recall basic addition facts (sums to 18) and the corresponding subtraction facts.

1.2.6 Estimating and Estimation Strategies

1.2.6.a. Estimate the number of objects in a set to 20 and verify by counting.

1.2.7 Computation

1.2.7.a. Add and subtract one- and two-digit numbers without regrouping.

1.2.8 Solving Problems and Number Theory

1.2.8.a. Generate and solve one-step addition and subtraction problems based on practical situations.

1.2.8.b. Model addition and subtraction in a variety of ways using pictorial representations and symbols to illustrate subtraction of sets, comparison of sets, and missing addends.

1.2.8.c. Reinforce the use of mathematical vocabulary and symbols to describe addition, subtraction, and equality.

2.2.1 Patterns

2.2.1.a. Recognize, describe, extend, and create repeating and increasing patterns using symbols, objects, and manipulatives.

2.2.1.b. Use patterns and their extensions to solve problems.

2.2.2 Variables and Unknowns

2.2.2.a. Model, explain, and identify missing operations and missing numbers in open number sentences involving number facts in addition and subtraction.

2.2.3 Number Sentences, Expressions, and Polynomials

2.2.3.a. Complete number sentences with the appropriate words and symbols (+, -, =). Represent mathematical situations using numbers, symbols, and words.

3.2.1 Comparison, Estimation, and Conversion

3.2.1.a. Compare, order, and describe objects by various measurable attributes for length, weight, and temperature.

3.2.2 Precision in Measurements

3.2.2.a. Compare objects to standard whole units to find objects that are greater than, less than, and/or equal to a given unit.

3.2.4 Money

3.2.4.a. Determine the value of any given set of coins.

3.2.4.b. Use decimals to show money amounts.

3.2.4.c. Recognize equivalent combinations of coins.

3.2.6 Time

3.2.6.a. Read time to the nearest half hour and quarter hour.

3.2.6.b. Use elapsed time in one hour increments, beginning on the hour, to determine start, end, and elapsed time.

3.2.6.c. Recognize that there are 12 months in 1 year, 7 days in 1 week, and 24 hours in 1 day.

4.2.1 Two-Dimensional Shapes

4.2.1.a. Describe, sketch, and compare two-dimensional shapes regardless of orientation.

4.2.2 Congruence, Similarity, and Transformations

4.2.2.a. Identify congruent and similar shapes (circles, triangles, and rectangles including squares).

4.2.3 Coordinate Geometry and Lines of Symmetry

4.2.3.a. Identify figures with symmetry as they appear in the environment.

4.2.4 Three-Dimensional Figures

4.2.4.a. Identify, name, sort, and describe two- and three-dimensional geometric figures and objects including circle/sphere and square/cube.

4.2.9 Logic

4.2.9.a. Sort and classify objects by two or more attributes.

5.2.1 Data Collection and Organization

5.2.1.a. Collect, record, and classify data in response to questions posed by teacher and/or students.

5.2.1.b. Use tables, pictographs, and bar graphs to represent data.

5.2.5 Experimental and Theoretical Probability

5.2.5.a. Use informal concepts of probability (certain and impossible) to make predictions about future events.

A.1. Generalize and apply previous experiences and strategies to new problem solving situations.

A.2. Determine an efficient strategy, verify, interpret, and evaluate the results with respect to the original problem.

A.3. Try more than one strategy when the first strategy proves to be unproductive.

A.4. Interpret and solve a variety of mathematical problems by paraphrasing.

A.5. Identify necessary and extraneous information.

A.6. Check the reasonableness of a solution.

A.7. Use technology, including calculators, to develop mathematical concepts.

B.1. Use inquiry techniques to solve mathematical problems.

B.2. Use a variety of methods to represent and communicate mathematical ideas through oral, verbal, and written formats.

B.3. Identify and translate key words and phrases that imply mathematical operations.

B.4. Use everyday language, both orally and in writing, to communicate strategies and solutions to mathematical problems.

C.1. Draw logical conclusions about mathematical problems.

C.2. Follow a logical argument and judge its validity.

C.3. Review and refine the assumptions and steps used to derive conclusions in mathematical arguments.

C.4. Justify and explain the solutions to problems using manipulatives and physical models.

D.1. Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics.

D.2. Use physical models to explain the relationship between concepts and procedures.

D.3. Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science.

D.4. Identify, explain, and use mathematics in everyday life.

1.3.1 Place Value

1.3.1.a. Identify, use, and model place value positions of 1's, 10's, 100's, and 1,000's.

1.3.1.b. Identify the value of a given digit in the 1's, 10's, 100's, and 1,000's place.

1.3.2 Fractions

1.3.2.a. Identify and model the unit fractions 1/2, 1/3, 1/4, 1/6, and 1/8 as equal parts of a whole or sets of objects.

1.3.2.b. Read and write unit fractions with numbers and words.

1.3.3 Comparison and Ordering

1.3.3.a. Read, write, compare, and order numbers from 0 - 9,999.

1.3.3.b. Read and write numbers words to 100.

1.3.4 Counting

1.3.4.a. Model and explain multiplication and division as skip counting patterns.

1.3.4.b. Model and explain multiplication and division as repeated addition or subtraction.

1.3.5 Facts

1.3.5.a. Immediately recall and use addition and subtraction facts.

1.3.5.b. Immediately recall multiplication facts (products to 81).

1.3.6 Estimating and Estimation Strategies

1.3.6.a. Estimate the number of objects in a set using various techniques.

1.3.7 Computation

1.3.7.a. Add and subtract two- and three-digit numbers with and without regrouping.

1.3.7.b. Add and subtract decimals using money as a model.

1.3.8 Solving Problems and Number Theory

1.3.8.a. Generate and solve two-step addition and subtraction problems and one-step multiplication problems based on practical situations.

1.3.8.b. Model addition, subtraction, multiplication, and division in a variety of ways.

1.3.8.c. Use mathematical vocabulary and symbols to describe multiplication and division.

2.3.1 Patterns

2.3.1.a. Recognize, describe, and create patterns using objects and numbers found in tables, number charts, and charts.

2.3.1.b. Record results of patterns created using manipulatives, pictures, and numeric representations and describe how they are extended.

2.3.2 Variables and Unknowns

2.3.2.a. Model, explain, and solve open number sentences involving addition, subtraction, and multiplication facts.

2.3.2.b. Use variables and open sentences to express relationships.

2.3.3 Number Sentences, Expressions, and Polynomials

2.3.3.a. Complete number sentences with the appropriate words and symbols (+, -, >, <, =).

3.3.1 Comparison, Estimation, and Conversion

3.3.1.a. Compare, order, and describe objects by various measurable attributes for area and volume/capacity.

3.3.2 Precision in Measurements

3.3.2.a. Select and use appropriate units of measure.

3.3.2.b. Measure to a required degree of accuracy (to the nearest 1/2 unit).

3.3.4 Money

3.3.4.a. Determine possible combinations of coins and bills to equal given amounts.

3.3.4.b. Read, write, and use money notation.

3.3.4.c. Recognize equivalent relationships between and among bills and coins.

3.3.6 Time

3.3.6.a. Tell time to the nearest minute, using analog and digital clocks.

3.3.6.b. Use elapsed time in half-hour increments, beginning on the hour or half-hour, to determine start, end, and elapsed time.

3.3.6.c. Recognize that there are 60 minutes in 1 hour.

4.3.1 Two-Dimensional Shapes

4.3.1.a. Describe, sketch, compare, and contrast plane geometric figures.

4.3.2 Congruence, Similarity, and Transformations

4.3.2.a. Demonstrate and describe the transformational motions of geometric figures (translation/slide, reflection/flip, and rotation/turn).

4.3.3 Coordinate Geometry and Lines of Symmetry

4.3.3.a. Create two-dimensional designs that contain a line of symmetry.

4.3.4 Three-Dimensional Figures

4.3.4.a. Compare, contrast, sketch, model, and build two- and three-dimensional geometric figures and objects.

4.3.6 Lines, Angles, and Their Properties

4.3.6.a. Identify, draw, and describe horizontal, vertical, and oblique lines.

4.3.9 Logic

4.3.9.a. Use the quantifiers all, some, and none to describe the characteristics of a set.

5.3.1 Data Collection and Organization

5.3.1.a. Pose questions that can be used to guide data collection, organization, and representation.

5.3.1.b. Use graphical representations, including number lines, frequency tables, and pictographs to represent data.

5.3.5 Experimental and Theoretical Probability

5.3.5.a. Use informal concepts of probability (certain, likely, unlikely, impossible) to make predictions about future events.

A.1. Generalize and apply previous experiences and strategies to new problem solving situations.

A.2. Determine an efficient strategy, verify, interpret, and evaluate the results with respect to the original problem.

A.3. Try more than one strategy when the first strategy proves to be unproductive.

A.4. Interpret and solve a variety of mathematical problems by paraphrasing.

A.5. Identify necessary and extraneous information.

A.6. Check the reasonableness of a solution.

A.7. Use technology, including calculators, to develop mathematical concepts.

B.1. Use inquiry techniques to solve mathematical problems.

B.2. Use a variety of methods to represent and communicate mathematical ideas through oral, verbal, and written formats.

B.3. Identify and translate key words and phrases that imply mathematical operations.

B.4. Use everyday language, both orally and in writing, to communicate strategies and solutions to mathematical problems.

C.1. Draw logical conclusions about mathematical problems.

C.2. Follow a logical argument and judge its validity.

C.3. Review and refine the assumptions and steps used to derive conclusions in mathematical arguments.

C.4. Justify and explain the solutions to problems using manipulatives and physical models.

D.1. Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics.

D.2. Use physical models to explain the relationship between concepts and procedures.

D.3. Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science.

D.4. Identify, explain, and use mathematics in everyday life.

1.4.1 Place Value

1.4.1.a. Identify and use place value positions of whole numbers to one million.

1.4.2 Fractions

1.4.2.a. Identify fractions and compare fractions with like denominators using models, drawings, and numbers.

1.4.3 Comparison and Ordering

1.4.3.a. Read, write, compare, and order whole numbers.

1.4.3.b. Read and write number words.

1.4.4 Counting

1.4.4.a. Count by multiples of a given number.

1.4.4.b. Explain relationships between skip counting, repeated addition, and multiples.

1.4.5 Facts

1.4.5.a. Immediately recall and use multiplication and corresponding division facts (products to 144).

1.4.6 Estimating and Estimation Strategies

1.4.6.a. Estimate to determine the reasonableness of an answer in mathematical and practical situations.

1.4.7 Computation

1.4.7.a. Add and subtract multi-digit numbers.

1.4.7.b. Multiply and divide multi-digit numbers by a one-digit whole number with regrouping, including monetary amounts as decimals.

1.4.8 Solving Problems and Number Theory

1.4.8.a. Generate and solve addition, subtraction, multiplication, and division problems using whole numbers in practical situations.

2.4.1 Patterns

2.4.1.a. Identify, describe, and represent patterns and relationships in the number system, including arithmetic and geometric sequences.

2.4.2 Variables and Unknowns

2.4.2.a. Model, explain, and solve open number sentences involving addition, subtraction, multiplication, and division.

2.4.2.b. Select the solution to an equation from a given set of numbers.

2.4.3 Number Sentences, Expressions, and Polynomials

2.4.3.a. Complete number sentences with the appropriate words and symbols (+, -, x, /, >, <, =).

3.4.1 Comparison, Estimation, and Conversion

3.4.1.a. Estimate and convert units of measure for length, area, and weight within the same measurement system (customary and metric).

3.4.1.b. Estimate temperature in practical situations.

3.4.2 Precision in Measurements

3.4.2.a. Measure length, area, temperature, and weight to a required degree of accuracy in customary and metric systems.

3.4.3 Formulas

3.4.3.a. Define and determine the perimeter of polygons and the area of rectangles, including squares.

3.4.4 Money

3.4.4.a. Determine totals for monetary amounts in practical situations.

3.4.4.b. Use money notation to add and subtract given monetary amounts.

3.4.6 Time

3.4.6.a. Use A.M. and P.M. appropriately in describing time.

3.4.6.b. Use elapsed time in quarter-hour increments, beginning on the quarter-hour, to determine start, end, and elapsed time.

3.4.6.c. Recognize the number of weeks in a year, days in a year, and days in a month.

4.4.1 Two-Dimensional Shapes

4.4.1.a. Identify, draw, and classify angles, including straight, right, obtuse, and acute.

4.4.2 Congruence, Similarity, and Transformations

4.4.2.a. Identify shapes that are congruent, similar, and/or symmetrical using a variety of methods including transformational motions.

4.4.3 Coordinate Geometry and Lines of Symmetry

4.4.3.a. Identify coordinates for a given point in the first quadrant.

4.4.3.b. Locate points of given coordinates on a grid in the first quadrant.

4.4.4 Three-Dimensional Figures

4.4.4.a. Identify, describe, and classify two- and three-dimensional figures by relevant properties including the number of vertices, edges, and faces using models.

4.4.6 Lines, Angles, and Their Properties

4.4.6.a. Identify, draw, label, and describe points, line segments, rays, and angles.

4.4.9 Logic

4.4.9.a. Use the connectors and, or, and not to describe the members of a set.

5.4.1 Data Collection and Organization

5.4.1.a. Pose questions that can be used to guide the collection of categorical and numerical data.

5.4.1.b. Organize and represent data using a variety of graphical representations including frequency tables and line plots.

5.4.2 Central Tendency and Data Distribution

5.4.2.a. Model and compute range.

5.4.2.b. Model the measures of central tendency for mode and median.

5.4.3 Interpretation of Data

5.4.3.a. Interpret data and make predictions using frequency tables and line plots.

5.4.5 Experimental and Theoretical Probability

5.4.5.a. Conduct simple probability experiments using concrete materials.

5.4.5.b. Represent the results of simple probability experiments as fractions to make predictions about future events.

A.1. Generalize and apply previous experiences and strategies to new problem solving situations.

A.2. Determine an efficient strategy, verify, interpret, and evaluate the results with respect to the original problem.

A.3. Try more than one strategy when the first strategy proves to be unproductive.

A.4. Interpret and solve a variety of mathematical problems by paraphrasing.

A.5. Identify necessary and extraneous information.

A.6. Check the reasonableness of a solution.

A.7. Use technology, including calculators, to develop mathematical concepts.

B.1. Use inquiry techniques to solve mathematical problems.

B.2. Use a variety of methods to represent and communicate mathematical ideas through oral, verbal, and written formats.

B.3. Identify and translate key words and phrases that imply mathematical operations.

B.4. Use everyday language, both orally and in writing, to communicate strategies and solutions to mathematical problems.

C.1. Draw logical conclusions about mathematical problems.

C.2. Follow a logical argument and judge its validity.

C.3. Review and refine the assumptions and steps used to derive conclusions in mathematical arguments.

C.4. Justify and explain the solutions to problems using manipulatives and physical models.

D.1. Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics.

D.2. Use physical models to explain the relationship between concepts and procedures.

D.3. Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science.

D.4. Identify, explain, and use mathematics in everyday life.

1.5.1 Place Value

1.5.1.a. Identify and use place value positions of whole numbers and decimals to hundredths.

1.5.2 Fractions

1.5.2.a. Add and subtract fractions with like denominators using models, drawings, and numbers.

1.5.2.b. Compare fractions with unlike denominators using models and drawings, and by finding common denominators.

1.5.2.c. Identify, model, and compare improper fractions and mixed numbers.

1.5.3 Comparison and Ordering

1.5.3.a. Read, write, compare, and order integers in mathematical and practical situations.

1.5.5 Facts

1.5.5.a. Use multiples of 10 to expand knowledge of basic multiplication and division facts.

1.5.6 Estimating and Estimation Strategies

1.5.6.a. Estimate to determine the reasonableness of an answer in mathematical and practical situations involving decimals.

1.5.7 Computation

1.5.7.a. Add and subtract decimals.

1.5.7.b. Multiply and divide decimals by whole numbers in problems representing practical situations.

1.5.7.c. Use order of operations to evaluate expressions with whole numbers.

1.5.8 Solving Problems and Number Theory

1.5.8.a. Generate and solve addition, subtraction, multiplication, and division problems using whole numbers and decimals in practical situations.

2.5.1 Patterns

2.5.1.a. Identify, describe, and represent patterns and relationships in the number system, including triangular numbers and perfect squares.

2.5.2 Variables and Unknowns

2.5.2.a. Find possible solutions to an inequality involving a variable using whole numbers as a replacement set.

2.5.2.b. Solve equations with whole numbers using a variety of methods, including inverse operations, mental math, and guess and check.

2.5.3 Number Sentences, Expressions, and Polynomials

2.5.3.a. Complete number sentences with the appropriate words and symbols including greater than or equal to, less than or equal to and not equal to.

3.5.1 Comparison, Estimation, and Conversion

3.5.1.a. Estimate and convert units of measure for weight and volume/capacity within the same measurement system (customary and metric).

3.5.2 Precision in Measurements

3.5.2.a. Measure volume and weight to a required degree of accuracy in the customary and metric systems.

3.5.3 Formulas

3.5.3.a. Describe the difference between perimeter and area, including the difference in units of measure.

3.5.4 Money

3.5.4.a. Determine totals, differences, and change due for monetary amounts in practical situations.

3.5.6 Time

3.5.6.a. Determine equivalent periods of time, including relationships between and among seconds, minutes, hours, days, months, and years.

4.5.1 Two-Dimensional Shapes

4.5.1.a. Identify, classify, compare, and draw triangles and quadrilaterals based on their properties.

4.5.1.b. Identify and draw circles and parts of circles, describing the relationships between the various parts.

4.5.2 Congruence, Similarity, and Transformations

4.5.2.a. Represent concepts of congruency, similarity, and/or symmetry using a variety of methods including dilation (enlargement/reduction) and transformational motions.

4.5.3 Coordinate Geometry and Lines of Symmetry

4.5.3.a. Graph coordinates representing geometric shapes in the first quadrant.

4.5.4 Three-Dimensional Figures

4.5.4.a. Predict and describe the effects of combining, dividing, and changing shapes into other shapes.

4.5.6 Lines, Angles, and Their Properties

4.5.6.a. Identify, draw, label, and describe planes, parallel lines, intersecting lines, and perpendicular lines.

4.5.7 Triangles

4.5.7.a. Describe characteristics of right, acute, obtuse, scalene, equilateral, and isosceles triangles.

4.5.9 Logic

4.5.9.a. Represent relationships using Venn diagrams.

5.5.1 Data Collection and Organization

5.5.1.a. Pose questions that can be used to guide the collection of categorical and numerical data.

5.5.1.b. Organize and represent data using a variety of graphical representations including stem and leaf plots and histograms.

5.5.2 Central Tendency and Data Distribution

5.5.2.a. Compute range.

5.5.2.b. Model and compute the measures of central tendency for mean, median, and mode.

5.5.3 Interpretation of Data

5.5.3.a. Interpret data and make predictions using stem-and-leaf plots and histograms.

5.5.4 Permutations and Combinations

5.5.4.a. Represent and solve problems involving combinations using a variety of methods.

5.5.5 Experimental and Theoretical Probability

5.5.5.a. Conduct simple probability experiments using concrete materials.

5.5.5.b. Represent the results of simple probability experiments as decimals to make predictions about future events.

5.5.6 Statistical Inferences

5.5.6.a. Select an appropriate type of graph to accurately represent the data and justify the selection.

A.1. Generalize solutions and apply previous knowledge to new problem solving situations.

A.2. Determine an efficient strategy, verify, interpret, and evaluate the results with respect to the original problem.

A.3. Apply problem solving strategies until a solution is found or it is clear that no solution exists.

A.4. Interpret and solve a variety of mathematical problems by paraphrasing.

A.5. Identify necessary and extraneous information.

A.6. Check the reasonableness of a solution.

A.7. Apply technology as a tool in problem solving situations.

B.1. Use formulas, algorithms, inquiry, and other techniques to solve mathematical problems.

B.2. Evaluate written and oral presentations in mathematics.

B.3. Identify and translate key words and phrases that imply mathematical operations.

B.4. Model and explain mathematical relationships using oral, written, graphic, and algebraic methods.

B.5. Use everyday language, both orally and in writing, to communicate strategies and solutions to mathematical problems.

C.1. Recognize and apply deductive and inductive reasoning.

C.2. Review and refine the assumptions and steps used to derive conclusions in mathematical arguments.

C.3. Justify answers and the steps taken to solve problems with and without manipulatives and physical models.

D.1. Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics.

D.2. Use manipulatives and physical models to explain the relationships between concepts and procedures.

D.3. Use the connections among mathematical topics to develop multiple approaches to problems.

D.4. Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science.

D.5. Identify, explain, and apply mathematics in everyday life.

1.6.1 Place Value

1.6.1.a. Identify and use place value positions to thousandths.

1.6.2 Fractions

1.6.2.a. Add and subtract fractions with unlike denominators.

1.6.2.b. Multiply and divide with fractions using models, drawings, and numbers.

1.6.2.c. Use models to translate among fractions, decimals, and percents.

1.6.3 Comparison and Ordering

1.6.3.a. Read, write, compare, and order groups of fractions, groups of decimals, and groups of percents.

1.6.5 Facts

1.6.5.a. Identify equivalent expressions between and among fractions, decimals, and percents.

1.6.6 Estimating and Estimation Strategies

1.6.6.a. Estimate using fractions, decimals, and percents.

1.6.6.b. Use estimation strategies in mathematical and practical situations.

1.6.7 Computation

1.6.7.a. Calculate using fractions, decimals, and percents in mathematical and practical situations.

1.6.7.b. Use order of operations to evaluate expressions with integers.

1.6.8 Solving Problems and Number Theory

1.6.8.a. Use the concepts of number theory, including prime and composite numbers, factors, multiples, and the rules of divisibility to solve problems.

2.6.1 Patterns

2.6.1.a. Use and create tables and charts to extend a pattern in order to describe a rule for input/output tables and to find missing terms in a sequence.

2.6.2 Variables and Unknowns

2.6.2.a. Evaluate formulas and algebraic expressions using whole number values.

2.6.2.b. Solve and graphically represent equations and simple inequalities in one variable.

2.6.3 Number Sentences, Expressions, and Polynomials

2.6.3.a. Write simple expressions and equations using variables to represent mathematical situations.

2.6.4 Relations and Functions

2.6.4.a. When given a rule relating two variables, create a table and represent the ordered pairs on a coordinate plane.

3.6.1 Comparison, Estimation, and Conversion

3.6.1.a. Estimate and compare corresponding units of measure for temperature, length, and weight/mass between customary and metric systems.

3.6.2 Precision in Measurements

3.6.2.a. Given two measurements of the same object, select the one that is more precise.

3.6.2.b. Explain how the size of the unit of measure used effects precision.

3.6.3 Formulas

3.6.3.a. Select, model, and apply formulas to find the perimeter, circumference, and area of plane figures.

3.6.4 Money

3.6.4.a. Compare and use unit cost in practical situations.

3.6.5 Ratios and Proportions

3.6.5.a. Write and apply ratios in mathematical and practical problems involving measurement and monetary conversions.

3.6.6 Time

3.6.6.a. Use equivalent periods of time to solve practical problems.

4.6.1 Two-Dimensional Shapes

4.6.1.a. Measure angles using a protractor.

4.6.1.b. Identify, classify, compare and draw regular and irregular quadrilaterals.

4.6.1.c. Identify, draw, and use central angles to represent fractions of a circle.

4.6.2 Congruence, Similarity, and Transformations

4.6.2.a. Determine actual measurements represented on scale drawings.

4.6.2.b. Convert actual measurements to scale.

4.6.3 Coordinate Geometry and Lines of Symmetry

4.6.3.a. Using a coordinate plane, identify and locate points.

4.6.3.b. Graph coordinates representing geometric shapes in all four quadrants on a coordinate plane.

4.6.4 Three-Dimensional Figures

4.6.4.a. Make a model of a three-dimensional prism from a two-dimensional drawing.

4.6.4.b. Make a two-dimensional drawing of a three-dimensional prism.

4.6.5 Algebraic Connections

4.6.5.a. Model slope (pitch, angle of inclination) using concrete objects and practical examples.

4.6.6 Lines, Angles, and Their Properties

4.6.6.a. Draw, identify, and find measures of complementary and supplementary angles using arithmetic and geometric methods.

4.6.7 Triangles

4.6.7.a. Determine the measure of missing angles of triangles based on the Triangle Sum Theorem.

4.6.8 Constructions

4.6.8.a. Construct circles, angles, and triangles based on given measurements using a variety of methods and tools including compass, straight edge, paper folding, and technology.

4.6.9 Logic

4.6.9.a. Identify counterexamples to disprove a conditional statement.

5.6.1 Data Collection and Organization

5.6.1.a. Pose questions that guide the collection of data.

5.6.1.b. Organize and represent data using a variety of graphical representations including circle graphs and scatter plots.

5.6.2 Central Tendency and Data Distribution

5.6.2.a. Select and apply the measures of central tendency to describe data.

5.6.3 Interpretation of Data

5.6.3.a. Analyze the effect a change of graph type has on the interpretation of a set of data.

5.6.3.b. Interpret data and make predictions using circle graphs and scatter plots.

5.6.4 Permutations and Combinations

5.6.4.a. Find the number of outcomes for a specific event by constructing sample spaces and tree diagrams.

5.6.5 Experimental and Theoretical Probability

5.6.5.a. Find experimental probability using concrete materials.

5.6.5.b. Represent the results of simple probability experiments as fractions, decimals, percents, and ratios to make predictions about future events.

5.6.6 Statistical Inferences

5.6.6.a. Analyze various representations of a set of data to draw conclusions and make predictions.

5.6.6.b. Describe the limitations of various graphical representations.

A.1. Generalize solutions and apply previous knowledge to new problem solving situations.

A.2. Determine an efficient strategy, verify, interpret, and evaluate the results with respect to the original problem.

A.3. Apply problem solving strategies until a solution is found or it is clear that no solution exists.

A.4. Interpret and solve a variety of mathematical problems by paraphrasing.

A.5. Identify necessary and extraneous information.

A.6. Check the reasonableness of a solution.

A.7. Apply technology as a tool in problem solving situations.

B.1. Use formulas, algorithms, inquiry, and other techniques to solve mathematical problems.

B.2. Evaluate written and oral presentations in mathematics.

B.3. Identify and translate key words and phrases that imply mathematical operations.

B.4. Model and explain mathematical relationships using oral, written, graphic, and algebraic methods.

B.5. Use everyday language, both orally and in writing, to communicate strategies and solutions to mathematical problems.

C.1. Recognize and apply deductive and inductive reasoning.

C.2. Review and refine the assumptions and steps used to derive conclusions in mathematical arguments.

C.3. Justify answers and the steps taken to solve problems with and without manipulatives and physical models.

D.1. Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics.

D.2. Use manipulatives and physical models to explain the relationships between concepts and procedures.

D.3. Use the connections among mathematical topics to develop multiple approaches to problems.

D.4. Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science.

D.5. Identify, explain, and apply mathematics in everyday life.

1.7.1 Place Value

1.7.1.a. Identify and use place value in mathematical and practical situations.

1.7.1.b. Write, identify, and use powers of 10 from 10^-3 through 10^6.

1.7.2 Fractions

1.7.2.a. Translate among fractions, decimals, and percents, including fractional percents.

1.7.3 Comparison and Ordering

1.7.3.a. Compare and order a combination of rational numbers, including fractions, decimals, percents, and integers in mathematical and practical situations.

1.7.5 Facts

1.7.5.a. Identify absolute values of integers.

1.7.6 Estimating and Estimation Strategies

1.7.6.a. Generate a reasonable estimate for a computation using a variety of methods.

1.7.6.b. Select and round to the appropriate significant digit.

1.7.7 Computation

1.7.7.a. Calculate with integers and other rational numbers to solve mathematical and practical situations.

1.7.7.b. Use order of operations to evaluate expressions and solve one-step equations (containing rational numbers).

1.7.8 Solving Problems and Number Theory

1.7.8.a. Identify and apply the distributive, commutative, and associative properties of rational numbers to solve problems.

2.7.1 Patterns

2.7.1.a. Use and create tables, charts, and graphs to extend a pattern in order to describe a linear rule, including integer values.

2.7.2 Variables and Unknowns

2.7.2.a. Evaluate formulas and algebraic expressions for given integer values.

2.7.2.b. Solve and graphically represent equations and inequalities in one variable with integer solutions.

2.7.3 Number Sentences, Expressions, and Polynomials

2.7.3.a. Simplify algebraic expressions by combining like terms.

2.7.4 Relations and Functions

2.7.4.a. Generate and graph a set of ordered pairs to represent a linear equation.

2.7.5 Linear Equations and Inequalities

2.7.5.a. Identify linear equations and inequalities.

2.7.5.b. Model and solve equations using concrete and visual representations.

3.7.1 Comparison, Estimation, and Conversion

3.7.1.a. Estimate and compare corresponding units of measure for area and volume/capacity between customary and metric systems.

3.7.2 Precision in Measurements

3.7.2.a. Given a measurement, identify the greatest possible error.

3.7.3 Formulas

3.7.3.a. Select, model, and apply formulas to find the volume and surface area of solid figures.

3.7.4 Money

3.7.4.a. Calculate simple interest in monetary problems.

3.7.5 Ratios and Proportions

3.7.5.a. Write and apply proportions to solve mathematical and practical problems involving measurement and monetary conversions.

3.7.6 Time

3.7.6.a. Use elapsed time to solve practical problems.

4.7.1 Two-Dimensional Shapes

4.7.1.a. Identify, classify, compare, and draw regular and irregular polygons.

4.7.1.b. Find and verify the sum of the measures of interior angles of triangles and quadrilaterals.

4.7.2 Congruence, Similarity, and Transformations

4.7.2.a. Make scale drawings using ratios and proportions.

4.7.3 Coordinate Geometry and Lines of Symmetry

4.7.3.a. Demonstrate translation, reflection, and rotation using coordinate geometry and models.

4.7.3.b. Describe the location of the original figure and its transformation on a coordinate plane.

4.7.4 Three-Dimensional Figures

4.7.4.a. Make a model of a three-dimensional figure from a two-dimensional drawing.

4.7.4.b. Make a two-dimensional drawing of a three-dimensional figure.

4.7.5 Algebraic Connections

4.7.5.a. Determine slope of a line, midpoint of a segment, and the horizontal and vertical distance between two points using coordinate geometry.

4.7.6 Lines, Angles, and Their Properties

4.7.6.a. Describe the geometric relationships of parallel lines, perpendicular lines, triangles, quadrilaterals and bisectors.

4.7.7 Triangles

4.7.7.a. Model the Pythagorean Theorem and solve for the hypotenuse.

4.7.8 Constructions

4.7.8.a. Construct and identify congruent angles, parallel lines, and perpendicular lines.

4.7.9 Logic

4.7.9.a. Make and test conjectures to explain observed mathematical relationships and to develop logical arguments to justify conclusions.

5.7.1 Data Collection and Organization

5.7.1.a. Formulate questions that guide the collection of data.

5.7.1.b. Organize, display, and read data using the appropriate graphical representations (with and without technology).

5.7.2 Central Tendency and Data Distribution

5.7.2.a. Interpret graphical representations of data to describe patterns, trends, and data distribution.

5.7.3 Interpretation of Data

5.7.3.a. Analyze the effect a change of scale will have on statistical charts and graphs.

5.7.4 Permutations and Combinations

5.7.4.a. Find the number of permutations possible for an event in mathematical and practical situations.

5.7.5 Experimental and Theoretical Probability

5.7.5.a. Find the theoretical probability of an event using different counting methods including sample spaces and compare that probability with experimental results.

5.7.5.b. Represent the probability of an event as a number between 0 and 1.

5.7.6 Statistical Inferences

5.7.6.a. Interpolate and extrapolate from data to make predictions for a given set of data.

A.1. Generalize solutions and apply previous knowledge to new problem solving situations.

A.2. Determine an efficient strategy, verify, interpret, and evaluate the results with respect to the original problem.

A.3. Apply problem solving strategies until a solution is found or it is clear that no solution exists.

A.4. Interpret and solve a variety of mathematical problems by paraphrasing.

A.5. Identify necessary and extraneous information.

A.6. Check the reasonableness of a solution.

A.7. Apply technology as a tool in problem solving situations.

B.1. Use formulas, algorithms, inquiry, and other techniques to solve mathematical problems.

B.2. Evaluate written and oral presentations in mathematics.

B.3. Identify and translate key words and phrases that imply mathematical operations.

B.4. Model and explain mathematical relationships using oral, written, graphic, and algebraic methods.

B.5. Use everyday language, both orally and in writing, to communicate strategies and solutions to mathematical problems.

C.1. Recognize and apply deductive and inductive reasoning.

C.2. Review and refine the assumptions and steps used to derive conclusions in mathematical arguments.

C.3. Justify answers and the steps taken to solve problems with and without manipulatives and physical models.

D.1. Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics.

D.2. Use manipulatives and physical models to explain the relationships between concepts and procedures.

D.3. Use the connections among mathematical topics to develop multiple approaches to problems.

D.4. Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science.

D.5. Identify, explain, and apply mathematics in everyday life.

1.8.1 Place Value

1.8.1.a. Represent numbers using scientific notation in mathematical and practical situations.

1.8.2 Fractions

1.8.2.a. Translate among fractions, decimals, and percents, including percents greater than 100 and percents less than 1.

1.8.2.b. Explain and use the relationship among equivalent representations of rational numbers in mathematical and practical situations.

1.8.3 Comparison and Ordering

1.8.3.a. Compare and order real numbers, including powers of whole numbers in mathematical and practical situations.

1.8.5 Facts

1.8.5.a. Identify perfect squares to 225 and their corresponding square roots.

1.8.6 Estimating and Estimation Strategies

1.8.6.a. Use estimation strategies to determine the reasonableness of an answer in mathematical and practical situations.

1.8.7 Computation

1.8.7.a. Calculate with real numbers to solve mathematical and practical situations.

1.8.7.b. Use order of operations to solve equations in the real number system.

1.8.8 Solving Problems and Number Theory

1.8.8.a. Identify and apply the identity property, inverse property, and the absolute value of real numbers to solve problems.

2.8.1 Patterns

2.8.1.a. Find the missing term in a numerical sequence or a pictorial representation of a sequence.

2.8.2 Variables and Unknowns

2.8.2.a. Evaluate formulas and algebraic expressions using rational numbers (with and without technology).

2.8.2.b. Solve and graphically represent equations and inequalities in one variable, including absolute value.

2.8.3 Number Sentences, Expressions, and Polynomials

2.8.3.a. Add and subtract binomials.

2.8.4 Relations and Functions

2.8.4.a. Identify, model, describe, and evaluate functions (with and without technology).

2.8.4.b. Translate among verbal descriptions, graphic, tabular, and algebraic representations of mathematical situations (with and without technology).

2.8.5 Linear Equations and Inequalities

2.8.5.a. Solve linear equations and represent the solution graphically.

2.8.5.b. Solve inequalities and represent the solution on a number line.

2.8.6 Algebraic Representations and Applications

2.8.6.a. Describe how changes in the value of one variable affect the values of the remaining variables in a relation.

3.8.1 Comparison, Estimation, and Conversion

3.8.1.a. Estimate and convert units of measure for mass and capacity within the same measurement system (customary and metric).

3.8.2 Precision in Measurements

3.8.2.a. Demonstrate an understanding of precision, error, and tolerance when using appropriate measurement tools.

3.8.3 Formulas

3.8.3.a. Identify how changes in a dimension of a figure effect changes in its perimeter, area and volume.

3.8.4 Money

3.8.4.a. Calculate percents in monetary problems.

3.8.5 Ratios and Proportions

3.8.5.a. Apply ratios and proportions to calculate rates and solve mathematical and practical problems using indirect measure.

4.8.1 Two-Dimensional Shapes

4.8.1.a. Find and use the sum of the measures of interior angles of polygons.

4.8.2 Congruence, Similarity, and Transformations

4.8.2.a. Apply the properties of equality and proportionality to congruent or similar shapes.

4.8.3 Coordinate Geometry and Lines of Symmetry

4.8.3.a. Demonstrate dilation using coordinate geometry and models.

4.8.3.b. Describe the relationship between an original figure and its transformation or dilation.

4.8.5 Algebraic Connections

4.8.5.a. Calculate slope, midpoint, and distance using equations and formulas (with and without technology).

4.8.5.b. Determine the x- and y- intercepts of a line.

4.8.6 Lines, Angles, and Their Properties

4.8.6.a. Form generalizations and validate conclusions about geometric figures and their properties.

4.8.7 Triangles

4.8.7.a. Verify and explain the Pythagorean Theorem using a variety of methods.

4.8.7.b. Determine the measure of the missing side of a right triangle.

4.8.8 Constructions

4.8.8.a. Construct geometric figures using a variety of tools.

4.8.9 Logic

4.8.9.a. Represent logical relationships using conditional statements.

5.8.1 Data Collection and Organization

5.8.1.a. Formulate questions and design a study that guides the collection of data.

5.8.1.b. Organize, display, and read data including box and whisker plots (with and without technology).

5.8.2 Central Tendency and Data Distribution

5.8.2.a. Select and apply appropriate measures of data distribution, using interquartile range and central tendency.

5.8.3 Interpretation of Data

5.8.3.a. Evaluate statistical arguments that are based on data analysis for accuracy and validity.

5.8.4 Permutations and Combinations

5.8.4.a. Find the number of combinations possible in mathematical and practical situations.

5.8.4.b. Distinguish between permutations and combinations.

5.8.5 Experimental and Theoretical Probability

5.8.5.a. Differentiate between the probability of an event and the odds of an event.

5.8.6 Statistical Inferences

5.8.6.a. Formulate reasonable inferences and predictions through interpolation and extrapolation of data to solve practical problems.

A.1. Generalize solutions and apply previous knowledge to new problem solving situations.

A.2. Determine an efficient strategy, verify, interpret, and evaluate the results with respect to the original problem.

A.3. Apply problem solving strategies until a solution is found or it is clear that no solution exists.

A.4. Interpret and solve a variety of mathematical problems by paraphrasing.

A.5. Identify necessary and extraneous information.

A.6. Check the reasonableness of a solution.

A.7. Apply technology as a tool in problem solving situations.

A.8. Apply combinations of proven strategies and previous knowledge to solve non-routine problems.

B.1. Use a variety of techniques to solve mathematical problems.

B.2. Evaluate written and oral presentations in mathematics..

B.3. Model and explain mathematical relationships using oral, written, graphic, and algebraic methods.

B.4. Communicate and evaluate mathematical thinking based on the use of definitions, properties, rules, and symbols in problem solving.

B.5. Use everyday language, both orally and in writing, communicate strategies and solutions to problems using appropriate mathematical language.

C.1. Recognize and apply deductive and inductive reasoning.

C.2. Review and refine the assumptions and steps used to derive conclusions in mathematical arguments.

C.3. Make and test conjectures about algebraic and geometric properties based on mathematical principles.

C.4. Justify the validity of an argument.

C.5. Construct a valid argument.

D.1. Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics.

D.2. Explain the relationship between concepts and procedures.

D.3. Use the connections among mathematical topics to develop multiple approaches to problems.

D.4. Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science.

D.5. Identify, explain, and apply mathematics in everyday life.

1.12.6 Estimating and Estimation Strategies

1.12.6.a. Determine an approximate value of radical and exponential expressions using a variety of methods.

1.12.7 Computation

1.12.7.a. Solve mathematical problems involving exponents and roots.

1.12.7.b. Perform addition, subtraction, and scalar multiplication on matrices.

1.12.8 Solving Problems and Number Theory

1.12.8.a. Identify and apply real number properties to solve problems.

2.12.1 Patterns

2.12.1.a. Use algebraic expressions to identify and describe the nth term of a sequence.

2.12.2 Variables and Unknowns

2.12.2.a. Isolate any variable in given equations, inequalities, proportions, and formulas to use in mathematical and practical situations.

2.12.3 Number Sentences, Expressions, and Polynomials

2.12.3.a. Add, subtract, multiply, and factor 1st and 2nd degree polynomials connecting the arithmetic and algebraic processes.

2.12.3.b. Simplify algebraic expressions, including exponents and radicals.

2.12.4 Relations and Functions

2.12.4.a. Determine the domain and range of functions, including linear, quadratic, and absolute value, algebraically and graphically.

2.12.4.b. Solve absolute value equations and inequalities both algebraically and graphically.

2.12.5 Linear Equations and Inequalities

2.12.5.a. Solve systems of two linear equations algebraically and graphically and verify solutions (with and without technology).

2.12.6 Algebraic Representations and Applications

2.12.6.a. Solve mathematical and practical problems involving linear and quadratic equations with a variety of methods, including discrete methods (with and without technology).

3.12.1 Comparison, Estimation, and Conversion

3.12.1.a. Estimate and convert between customary and metric systems.

3.12.2 Precision in Measurements

3.12.2.a. Justify, communicate, and differentiate between precision, error, and tolerance in practical problems.

3.12.3 Formulas

3.12.3.a. Select and use appropriate measurement tools, techniques, and formulas to solve problems in mathematical and practical situations.

3.12.4 Money

3.12.4.a. Interpret and apply consumer data presented in charts, tables, and graphs to make informed financial decisions related to practical applications.

3.12.5 Ratios and Proportions

3.12.5.a. Determine the measure of unknown dimensions, angles, areas, and volumes using relationships and formulas to solve problems.

4.12.1 Two-Dimensional Shapes

4.12.1.a. Identify and use the parts of a circle to solve mathematical and practical problems.

4.12.1.b. Identify and apply properties of interior and exterior angles of polygons to solve mathematical and practical problems.

4.12.2 Congruence, Similarity, and Transformations

4.12.2.a. Apply properties of similarity through right triangle trigonometry to find missing angles and sides.

4.12.5 Algebraic Connections

4.12.5.a. Determine the slope of lines using coordinate geometry and algebraic techniques.

4.12.5.b. Identify parallel, perpendicular, and intersecting lines by slope.

4.12.5.c. Graph linear equations and find possible solutions to those equations using coordinate geometry.

4.12.5.d. Find possible solution sets of systems of equations whose slopes indicate parallel, perpendicular, or intersecting lines.

4.12.6 Lines, Angles, and Their Properties

4.12.6.a. Solve problems using complementary and supplementary angles, congruent angles, vertical angles, angles formed when parallel lines are cut by a transversal and angles in polygons.

4.12.7 Triangles

4.12.7.a. Apply the Pythagorean Theorem and its converse in mathematical and practical situations.

4.12.8 Constructions

4.12.8.a. Solve problems by drawing and/or constructing geometric figures to demonstrate geometric relationships.

4.12.9 Logic

4.12.9.a. Formulate, evaluate, and justify arguments using inductive and deductive reasoning in mathematical and practical situations.

5.12.1 Data Collection and Organization

5.12.1.a. Organize statistical data through the use of tables, graphs, and matrices (with and without technology).

5.12.2 Central Tendency and Data Distribution

5.12.2.a. Select and apply appropriate statistical measures in mathematical and practical situations.

5.12.3 Interpretation of Data

5.12.3.a. Distinguish between a sample and a census.

5.12.3.b. Identify sources of bias and their effect on data representations and statistical conclusions.

5.12.3.c. Use the shape of a normal distribution to compare and analyze data from a sample.

5.12.4 Permutations and Combinations

5.12.4.a. Apply permutations and combinations to mathematical and practical situations, including the Fundamental Counting Principle.

5.12.5 Experimental and Theoretical Probability

5.12.5.a. Determine the probability of an event with and without replacement using sample spaces.

5.12.5.b. Design, conduct, analyze, and effectively communicate the results of multi-stage probability experiments.

5.12.6 Statistical Inferences

5.12.6.a. Design, construct, analyze, and select an appropriate type of graphical representations to communicate the results of a statistical experiment.

5.12.6.b. Formulate and justify inferences based on a valid data sample.

A.1. Generalize solutions and apply previous knowledge to new problem solving situations.

A.2. Determine an efficient strategy, verify, interpret, and evaluate the results with respect to the original problem.

A.3. Apply problem solving strategies until a solution is found or it is clear that no solution exists.

A.4. Interpret and solve a variety of mathematical problems by paraphrasing.

A.5. Identify necessary and extraneous information.

A.6. Check the reasonableness of a solution.

A.7. Apply technology as a tool in problem solving situations.

A.8. Apply combinations of proven strategies and previous knowledge to solve non-routine problems.

B.1. Use a variety of techniques to solve mathematical problems.

B.2. Evaluate written and oral presentations in mathematics..

B.3. Model and explain mathematical relationships using oral, written, graphic, and algebraic methods.

B.4. Communicate and evaluate mathematical thinking based on the use of definitions, properties, rules, and symbols in problem solving.

B.5. Use everyday language, both orally and in writing, communicate strategies and solutions to problems using appropriate mathematical language.

C.1. Recognize and apply deductive and inductive reasoning.

C.2. Review and refine the assumptions and steps used to derive conclusions in mathematical arguments.

C.3. Make and test conjectures about algebraic and geometric properties based on mathematical principles.

C.4. Justify the validity of an argument.

C.5. Construct a valid argument.

D.1. Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics.

D.2. Explain the relationship between concepts and procedures.

D.3. Use the connections among mathematical topics to develop multiple approaches to problems.

D.4. Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science.

D.5. Identify, explain, and apply mathematics in everyday life.

1.12.6 Estimating and Estimation Strategies

1.12.6.a. Determine an approximate value of radical and exponential expressions using a variety of methods.

1.12.7 Computation

1.12.7.a. Solve mathematical problems involving exponents and roots.

1.12.7.b. Perform addition, subtraction, and scalar multiplication on matrices.

1.12.8 Solving Problems and Number Theory

1.12.8.a. Identify and apply real number properties to solve problems.

2.12.1 Patterns

2.12.1.a. Use algebraic expressions to identify and describe the nth term of a sequence.

2.12.2 Variables and Unknowns

2.12.2.a. Isolate any variable in given equations, inequalities, proportions, and formulas to use in mathematical and practical situations.

2.12.3 Number Sentences, Expressions, and Polynomials

2.12.3.a. Add, subtract, multiply, and factor 1st and 2nd degree polynomials connecting the arithmetic and algebraic processes.

2.12.3.b. Simplify algebraic expressions, including exponents and radicals.

2.12.4 Relations and Functions

2.12.4.a. Determine the domain and range of functions, including linear, quadratic, and absolute value, algebraically and graphically.

2.12.4.b. Solve absolute value equations and inequalities both algebraically and graphically.

2.12.5 Linear Equations and Inequalities

2.12.5.a. Solve systems of two linear equations algebraically and graphically and verify solutions (with and without technology).

2.12.6 Algebraic Representations and Applications

2.12.6.a. Solve mathematical and practical problems involving linear and quadratic equations with a variety of methods, including discrete methods (with and without technology).

3.12.1 Comparison, Estimation, and Conversion

3.12.1.a. Estimate and convert between customary and metric systems.

3.12.2 Precision in Measurements

3.12.2.a. Justify, communicate, and differentiate between precision, error, and tolerance in practical problems.

3.12.3 Formulas

3.12.3.a. Select and use appropriate measurement tools, techniques, and formulas to solve problems in mathematical and practical situations.

3.12.4 Money

3.12.4.a. Interpret and apply consumer data presented in charts, tables, and graphs to make informed financial decisions related to practical applications.

3.12.5 Ratios and Proportions

3.12.5.a. Determine the measure of unknown dimensions, angles, areas, and volumes using relationships and formulas to solve problems.

4.12.1 Two-Dimensional Shapes

4.12.1.a. Identify and use the parts of a circle to solve mathematical and practical problems.

4.12.1.b. Identify and apply properties of interior and exterior angles of polygons to solve mathematical and practical problems.

4.12.2 Congruence, Similarity, and Transformations

4.12.2.a. Apply properties of similarity through right triangle trigonometry to find missing angles and sides.

4.12.5 Algebraic Connections

4.12.5.a. Determine the slope of lines using coordinate geometry and algebraic techniques.

4.12.5.b. Identify parallel, perpendicular, and intersecting lines by slope.

4.12.5.c. Graph linear equations and find possible solutions to those equations using coordinate geometry.

4.12.5.d. Find possible solution sets of systems of equations whose slopes indicate parallel, perpendicular, or intersecting lines.

4.12.6 Lines, Angles, and Their Properties

4.12.6.a. Solve problems using complementary and supplementary angles, congruent angles, vertical angles, angles formed when parallel lines are cut by a transversal and angles in polygons.

4.12.7 Triangles

4.12.7.a. Apply the Pythagorean Theorem and its converse in mathematical and practical situations.

4.12.8 Constructions

4.12.8.a. Solve problems by drawing and/or constructing geometric figures to demonstrate geometric relationships.

4.12.9 Logic

4.12.9.a. Formulate, evaluate, and justify arguments using inductive and deductive reasoning in mathematical and practical situations.

5.12.1 Data Collection and Organization

5.12.1.a. Organize statistical data through the use of tables, graphs, and matrices (with and without technology).

5.12.2 Central Tendency and Data Distribution

5.12.2.a. Select and apply appropriate statistical measures in mathematical and practical situations.

5.12.3 Interpretation of Data

5.12.3.a. Distinguish between a sample and a census.

5.12.3.b. Identify sources of bias and their effect on data representations and statistical conclusions.

5.12.3.c. Use the shape of a normal distribution to compare and analyze data from a sample.

5.12.4 Permutations and Combinations

5.12.4.a. Apply permutations and combinations to mathematical and practical situations, including the Fundamental Counting Principle.

5.12.5 Experimental and Theoretical Probability

5.12.5.a. Determine the probability of an event with and without replacement using sample spaces.

5.12.5.b. Design, conduct, analyze, and effectively communicate the results of multi-stage probability experiments.

5.12.6 Statistical Inferences

5.12.6.a. Design, construct, analyze, and select an appropriate type of graphical representations to communicate the results of a statistical experiment.

5.12.6.b. Formulate and justify inferences based on a valid data sample.

A.1. Generalize solutions and apply previous knowledge to new problem solving situations.

A.2. Determine an efficient strategy, verify, interpret, and evaluate the results with respect to the original problem.

A.3. Apply problem solving strategies until a solution is found or it is clear that no solution exists.

A.4. Interpret and solve a variety of mathematical problems by paraphrasing.

A.5. Identify necessary and extraneous information.

A.6. Check the reasonableness of a solution.

A.7. Apply technology as a tool in problem solving situations.

A.8. Apply combinations of proven strategies and previous knowledge to solve non-routine problems.

B.1. Use a variety of techniques to solve mathematical problems.

B.2. Evaluate written and oral presentations in mathematics..

B.3. Model and explain mathematical relationships using oral, written, graphic, and algebraic methods.

B.4. Communicate and evaluate mathematical thinking based on the use of definitions, properties, rules, and symbols in problem solving.

B.5. Use everyday language, both orally and in writing, communicate strategies and solutions to problems using appropriate mathematical language.

C.1. Recognize and apply deductive and inductive reasoning.

C.2. Review and refine the assumptions and steps used to derive conclusions in mathematical arguments.

C.3. Make and test conjectures about algebraic and geometric properties based on mathematical principles.

C.4. Justify the validity of an argument.

C.5. Construct a valid argument.

D.1. Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics.

D.2. Explain the relationship between concepts and procedures.

D.3. Use the connections among mathematical topics to develop multiple approaches to problems.

D.4. Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science.

D.5. Identify, explain, and apply mathematics in everyday life.

1.12.6 Estimating and Estimation Strategies

1.12.6.a. Determine an approximate value of radical and exponential expressions using a variety of methods.

1.12.7 Computation

1.12.7.a. Solve mathematical problems involving exponents and roots.

1.12.7.b. Perform addition, subtraction, and scalar multiplication on matrices.

1.12.8 Solving Problems and Number Theory

1.12.8.a. Identify and apply real number properties to solve problems.

2.12.1 Patterns

2.12.1.a. Use algebraic expressions to identify and describe the nth term of a sequence.

2.12.2 Variables and Unknowns

2.12.2.a. Isolate any variable in given equations, inequalities, proportions, and formulas to use in mathematical and practical situations.

2.12.3 Number Sentences, Expressions, and Polynomials

2.12.3.a. Add, subtract, multiply, and factor 1st and 2nd degree polynomials connecting the arithmetic and algebraic processes.

2.12.3.b. Simplify algebraic expressions, including exponents and radicals.

2.12.4 Relations and Functions

2.12.4.a. Determine the domain and range of functions, including linear, quadratic, and absolute value, algebraically and graphically.

2.12.4.b. Solve absolute value equations and inequalities both algebraically and graphically.

2.12.5 Linear Equations and Inequalities

2.12.5.a. Solve systems of two linear equations algebraically and graphically and verify solutions (with and without technology).

2.12.6 Algebraic Representations and Applications

2.12.6.a. Solve mathematical and practical problems involving linear and quadratic equations with a variety of methods, including discrete methods (with and without technology).

3.12.1 Comparison, Estimation, and Conversion

3.12.1.a. Estimate and convert between customary and metric systems.

3.12.2 Precision in Measurements

3.12.2.a. Justify, communicate, and differentiate between precision, error, and tolerance in practical problems.

3.12.3 Formulas

3.12.3.a. Select and use appropriate measurement tools, techniques, and formulas to solve problems in mathematical and practical situations.

3.12.4 Money

3.12.4.a. Interpret and apply consumer data presented in charts, tables, and graphs to make informed financial decisions related to practical applications.

3.12.5 Ratios and Proportions

3.12.5.a. Determine the measure of unknown dimensions, angles, areas, and volumes using relationships and formulas to solve problems.

4.12.1 Two-Dimensional Shapes

4.12.1.a. Identify and use the parts of a circle to solve mathematical and practical problems.

4.12.1.b. Identify and apply properties of interior and exterior angles of polygons to solve mathematical and practical problems.

4.12.2 Congruence, Similarity, and Transformations

4.12.2.a. Apply properties of similarity through right triangle trigonometry to find missing angles and sides.

4.12.5 Algebraic Connections

4.12.5.a. Determine the slope of lines using coordinate geometry and algebraic techniques.

4.12.5.b. Identify parallel, perpendicular, and intersecting lines by slope.

4.12.5.c. Graph linear equations and find possible solutions to those equations using coordinate geometry.

4.12.5.d. Find possible solution sets of systems of equations whose slopes indicate parallel, perpendicular, or intersecting lines.

4.12.6 Lines, Angles, and Their Properties

4.12.6.a. Solve problems using complementary and supplementary angles, congruent angles, vertical angles, angles formed when parallel lines are cut by a transversal and angles in polygons.

4.12.7 Triangles

4.12.7.a. Apply the Pythagorean Theorem and its converse in mathematical and practical situations.

4.12.8 Constructions

4.12.8.a. Solve problems by drawing and/or constructing geometric figures to demonstrate geometric relationships.

4.12.9 Logic

4.12.9.a. Formulate, evaluate, and justify arguments using inductive and deductive reasoning in mathematical and practical situations.

5.12.1 Data Collection and Organization

5.12.1.a. Organize statistical data through the use of tables, graphs, and matrices (with and without technology).

5.12.2 Central Tendency and Data Distribution

5.12.2.a. Select and apply appropriate statistical measures in mathematical and practical situations.

5.12.3 Interpretation of Data

5.12.3.a. Distinguish between a sample and a census.

5.12.3.b. Identify sources of bias and their effect on data representations and statistical conclusions.

5.12.3.c. Use the shape of a normal distribution to compare and analyze data from a sample.

5.12.4 Permutations and Combinations

5.12.4.a. Apply permutations and combinations to mathematical and practical situations, including the Fundamental Counting Principle.

5.12.5 Experimental and Theoretical Probability

5.12.5.a. Determine the probability of an event with and without replacement using sample spaces.

5.12.5.b. Design, conduct, analyze, and effectively communicate the results of multi-stage probability experiments.

5.12.6 Statistical Inferences

5.12.6.a. Design, construct, analyze, and select an appropriate type of graphical representations to communicate the results of a statistical experiment.

5.12.6.b. Formulate and justify inferences based on a valid data sample.

A.1. Generalize solutions and apply previous knowledge to new problem solving situations.

A.2. Determine an efficient strategy, verify, interpret, and evaluate the results with respect to the original problem.

A.3. Apply problem solving strategies until a solution is found or it is clear that no solution exists.

A.4. Interpret and solve a variety of mathematical problems by paraphrasing.

A.5. Identify necessary and extraneous information.

A.6. Check the reasonableness of a solution.

A.7. Apply technology as a tool in problem solving situations.

A.8. Apply combinations of proven strategies and previous knowledge to solve non-routine problems.

B.1. Use a variety of techniques to solve mathematical problems.

B.2. Evaluate written and oral presentations in mathematics..

B.3. Model and explain mathematical relationships using oral, written, graphic, and algebraic methods.

B.4. Communicate and evaluate mathematical thinking based on the use of definitions, properties, rules, and symbols in problem solving.

B.5. Use everyday language, both orally and in writing, communicate strategies and solutions to problems using appropriate mathematical language.

C.1. Recognize and apply deductive and inductive reasoning.

C.2. Review and refine the assumptions and steps used to derive conclusions in mathematical arguments.

C.3. Make and test conjectures about algebraic and geometric properties based on mathematical principles.

C.4. Justify the validity of an argument.

C.5. Construct a valid argument.

D.1. Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics.

D.2. Explain the relationship between concepts and procedures.

D.3. Use the connections among mathematical topics to develop multiple approaches to problems.

D.4. Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science.

D.5. Identify, explain, and apply mathematics in everyday life.

1.12.6 Estimating and Estimation Strategies

1.12.6.a. Determine an approximate value of radical and exponential expressions using a variety of methods.

1.12.7 Computation

1.12.7.a. Solve mathematical problems involving exponents and roots.

1.12.7.b. Perform addition, subtraction, and scalar multiplication on matrices.

1.12.8 Solving Problems and Number Theory

1.12.8.a. Identify and apply real number properties to solve problems.

2.12.1 Patterns

2.12.1.a. Use algebraic expressions to identify and describe the nth term of a sequence.

2.12.2 Variables and Unknowns

2.12.2.a. Isolate any variable in given equations, inequalities, proportions, and formulas to use in mathematical and practical situations.

2.12.3 Number Sentences, Expressions, and Polynomials

2.12.3.a. Add, subtract, multiply, and factor 1st and 2nd degree polynomials connecting the arithmetic and algebraic processes.

2.12.3.b. Simplify algebraic expressions, including exponents and radicals.

2.12.4 Relations and Functions

2.12.4.a. Determine the domain and range of functions, including linear, quadratic, and absolute value, algebraically and graphically.

2.12.4.b. Solve absolute value equations and inequalities both algebraically and graphically.

2.12.5 Linear Equations and Inequalities

2.12.5.a. Solve systems of two linear equations algebraically and graphically and verify solutions (with and without technology).

2.12.6 Algebraic Representations and Applications

2.12.6.a. Solve mathematical and practical problems involving linear and quadratic equations with a variety of methods, including discrete methods (with and without technology).

3.12.1 Comparison, Estimation, and Conversion

3.12.1.a. Estimate and convert between customary and metric systems.

3.12.2 Precision in Measurements

3.12.2.a. Justify, communicate, and differentiate between precision, error, and tolerance in practical problems.

3.12.3 Formulas

3.12.3.a. Select and use appropriate measurement tools, techniques, and formulas to solve problems in mathematical and practical situations.

3.12.4 Money

3.12.4.a. Interpret and apply consumer data presented in charts, tables, and graphs to make informed financial decisions related to practical applications.

3.12.5 Ratios and Proportions

3.12.5.a. Determine the measure of unknown dimensions, angles, areas, and volumes using relationships and formulas to solve problems.

4.12.1 Two-Dimensional Shapes

4.12.1.a. Identify and use the parts of a circle to solve mathematical and practical problems.

4.12.1.b. Identify and apply properties of interior and exterior angles of polygons to solve mathematical and practical problems.

4.12.2 Congruence, Similarity, and Transformations

4.12.2.a. Apply properties of similarity through right triangle trigonometry to find missing angles and sides.

4.12.5 Algebraic Connections

4.12.5.a. Determine the slope of lines using coordinate geometry and algebraic techniques.

4.12.5.b. Identify parallel, perpendicular, and intersecting lines by slope.

4.12.5.c. Graph linear equations and find possible solutions to those equations using coordinate geometry.

4.12.5.d. Find possible solution sets of systems of equations whose slopes indicate parallel, perpendicular, or intersecting lines.

4.12.6 Lines, Angles, and Their Properties

4.12.6.a. Solve problems using complementary and supplementary angles, congruent angles, vertical angles, angles formed when parallel lines are cut by a transversal and angles in polygons.

4.12.7 Triangles

4.12.7.a. Apply the Pythagorean Theorem and its converse in mathematical and practical situations.

4.12.8 Constructions

4.12.8.a. Solve problems by drawing and/or constructing geometric figures to demonstrate geometric relationships.

4.12.9 Logic

4.12.9.a. Formulate, evaluate, and justify arguments using inductive and deductive reasoning in mathematical and practical situations.

5.12.1 Data Collection and Organization

5.12.1.a. Organize statistical data through the use of tables, graphs, and matrices (with and without technology).

5.12.2 Central Tendency and Data Distribution

5.12.2.a. Select and apply appropriate statistical measures in mathematical and practical situations.

5.12.3 Interpretation of Data

5.12.3.a. Distinguish between a sample and a census.

5.12.3.b. Identify sources of bias and their effect on data representations and statistical conclusions.

5.12.3.c. Use the shape of a normal distribution to compare and analyze data from a sample.

5.12.4 Permutations and Combinations

5.12.4.a. Apply permutations and combinations to mathematical and practical situations, including the Fundamental Counting Principle.

5.12.5 Experimental and Theoretical Probability

5.12.5.a. Determine the probability of an event with and without replacement using sample spaces.

5.12.5.b. Design, conduct, analyze, and effectively communicate the results of multi-stage probability experiments.

5.12.6 Statistical Inferences

5.12.6.a. Design, construct, analyze, and select an appropriate type of graphical representations to communicate the results of a statistical experiment.

5.12.6.b. Formulate and justify inferences based on a valid data sample.

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