Standard 1 : Mathematical Processes (Mathematics)

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View this standard as a learning progression
Conceptual Strand
The Mathematical Process Standards are embedded in the content standards to reap the learning benefits gained from attention to them. These standards exemplify best teaching practices in mathematical instruction and mirror the NCTM Process Standards as well as the Common Core Mathematical Practices.
Guiding Question
What is the role of the mathematical processes standards in formative instruction?
 
Grade K
Grade Learning Expectations
GLE 0006.1.1  Use mathematical language, symbols, and definitions while developing mathematical reasoning.
GLE 0006.1.2  Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
GLE 0006.1.3  Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
GLE 0006.1.4  Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution strategies.
GLE 0006.1.5  Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
GLE 0006.1.6  Read and interpret the language of mathematics and use written/oral communication to express mathematical ideas precisely.
GLE 0006.1.7  Recognize the historical development of mathematics, mathematics in context, and the connections between mathematics and the real world.
GLE 0006.1.8  Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and reliable models of mathematical concepts.
Checks for Understanding
0006.1.1  Model addition and subtraction (e.g., using a number chart, number line and/or concrete objects).
0006.1.2  Begin to develop the concept of estimation using concrete objects.
0006.1.3  Use words to describe time (e.g., day, night, morning, afternoon, yesterday, today, tomorrow).
0006.1.4  Tell time to the hour.
0006.1.5  Recognize a calendar as a way of measuring time.
0006.1.6  Name and identify coins and their values.
0006.1.7  Use words to describe temperature (e.g., hot, warm, cool, cold).
0006.1.8  Recognize a thermometer as a way of measuring temperature.
0006.1.9  Use age-appropriate books, stories, and videos to convey ideas of mathematics.
State Performance Indicators
 
Grade 1
Grade Learning Expectations
GLE 0106.1.1  Use mathematical language, symbols, and definitions while developing mathematical reasoning.
GLE 0106.1.2  Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
GLE 0106.1.3  Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
GLE 0106.1.4  Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution strategies.
GLE 0106.1.5  Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
GLE 0106.1.6  Read and interpret the language of mathematics and use written/oral communication to express mathematical ideas precisely.
GLE 0106.1.7  Recognize the historical development of mathematics, mathematics in context, and the connections between mathematics and the real world.
GLE 0106.1.8  Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and reliable models of mathematical concepts.
Checks for Understanding
0106.1.1  Describe the relationship between days and months.
0106.1.2  Read and write time to the hour, half-hour, and quarter-hour.
0106.1.3  Compare units of time.
0106.1.4  Count the value of a set of coins up to fifty cents.
0106.1.5  Use a thermometer to measure temperature.
0106.1.6  Recognize scales as a way of measuring weight.
0106.1.7  Apply spatial sense to recreate a figure from memory.
0106.1.8  Recognize the “word clues” and mathematical symbols for addition and subtraction.
0106.1.9  Use age-appropriate books, stories, and videos to convey ideas of mathematics.
0106.1.10  Match the spoken, written, concrete, and pictorial representations of whole numbers, one-half, and one-fourth.
State Performance Indicators
 
Grade 2
Grade Learning Expectations
GLE 0206.1.1  Use mathematical language, symbols, and definitions while developing mathematical reasoning.
GLE 0206.1.2  Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
GLE 0206.1.3  Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
GLE 0206.1.4  Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution strategies.
GLE 0206.1.5  Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
GLE 0206.1.6  Read and interpret the language of mathematics and use written/oral communication to express mathematical ideas precisely.
GLE 0206.1.7  Recognize the historical development of mathematics, mathematics in context, and the connections between mathematics and the real world.
GLE 0206.1.8  Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and reliable models of mathematical concepts.
Checks for Understanding
0206.1.1  Read and write time up to five-minute intervals.
0206.1.2  Relate days, dates, weeks, months, and years to a calendar.
0206.1.3  Use strategies to make estimates of time.
0206.1.4  Solve problems involving elapsed time in hour and half-hour intervals.
0206.1.5  Count the value of a set of coins up to one dollar and use the transitive property of equality to recognize equivalent forms of values up to $1.00.
0206.1.6  Read thermometers with Fahrenheit and Celsius scales.
0206.1.7  Measure weight to the nearest pound or kilogram.
0206.1.8  Use concrete models or pictures to show whether a fraction is less than a half, more than a half, or equal to a half.
0206.1.9  Match the spoken, written, concrete, and pictorial representations of halves, thirds, and fourths.
0206.1.10  Develop a story problem that illustrates a given addition or subtraction number sentence.
0206.1.11  Use manipulatives to demonstrate addition and subtraction sentences written symbolically.
0206.1.12  Write numbers and translate word clues to number sentences and vice versa.
0206.1.13  Use manipulatives such as pattern blocks, tangrams, etc. to explore geometric concepts of symmetry and transformations.
0206.1.14  Create and observe numerical patterns on a calculator by repeatedly adding or subtracting the same number from some starting number.
0206.1.15  Use age-appropriate books, stories, and videos to convey ideas of mathematics.
State Performance Indicators
 
Grade 3
Grade Learning Expectations
GLE 0306.1.1  Use mathematical language, symbols, and definitions while developing mathematical reasoning.
GLE 0306.1.2  Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
GLE 0306.1.3  Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
GLE 0306.1.4  Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution strategies.
GLE 0306.1.5  Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
GLE 0306.1.6  Read and interpret the language of mathematics and use written/oral communication to express mathematical ideas precisely.
GLE 0306.1.7  Recognize the historical development of mathematics, mathematics in context, and the connections between mathematics and the real world.
GLE 0306.1.8  Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and reliable models of mathematical concepts.
Checks for Understanding
0306.1.1  Read and write time to the nearest minute.
0306.1.2  Compare and order decimal amounts in the context of money.
0306.1.3  Count the value of combinations of coins and bills up to five dollars.
0306.1.4  Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, and observing patterns.
0306.1.5  Determine when and how to break a problem into simpler parts.
0306.1.6  Use estimation to check answers for reasonableness, and calculators to check for accuracy.
0306.1.7  Make and investigate mathematical conjectures.
0306.1.8  Explain and justify answers on the basis of mathematical properties, structures, and relationships.
0306.1.9  Use manipulatives to demonstrate that the commutative property holds for addition but not for subtraction.
0306.1.10  Use correct, clearly written and oral mathematical language to pose questions and communicate ideas.
0306.1.11  Develop strategies for solving problems involving addition and subtraction of measurements.
0306.1.12  Analyze and evaluate the mathematical thinking and strategies of others.
0306.1.13  Create and use representations to organize, record, and communicate mathematical ideas.
0306.1.14  Use age-appropriate books, stories, and videos to convey ideas of mathematics.
State Performance Indicators
SPI 0306.1.1  Solve problems using a calendar.
SPI 0306.1.2  Solve problems involving elapsed time.
SPI 0306.1.3  Determine the correct change from a transaction less than a dollar.
SPI 0306.1.4  Match the spoken, written, concrete, and pictorial representations of fractions with denominators up to ten.
SPI 0306.1.5  Represent problems mathematically using diagrams, numbers, and symbolic expressions.
SPI 0306.1.6  Identify and use vocabulary to describe attributes of two- and three-dimensional shapes.
SPI 0306.1.7  Select appropriate units and tools to solve problems involving measures.
SPI 0306.1.8  Express answers clearly in verbal, numerical, or graphical (bar and picture) form, using units when appropriate.
 
Grade 4
Grade Learning Expectations
GLE 0406.1.1  Use mathematical language, symbols, and definitions while developing mathematical reasoning.
GLE 0406.1.2  Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
GLE 0406.1.3  Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
GLE 0406.1.4  Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution strategies.
GLE 0406.1.5  Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
GLE 0406.1.6  Read and interpret the language of mathematics and use written/oral communication to express mathematical ideas precisely.
GLE 0406.1.7  Recognize the historical development of mathematics, mathematics in context, and the connections between mathematics and the real world.
GLE 0406.1.8  Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and reliable models of mathematical concepts.
Checks for Understanding
0406.1.1  Understand the relationship between use of answers and the accuracy of the number.
0406.1.2  Identify the range of appropriate estimates, including over-estimate and under-estimate.
0406.1.3  Connect operations with decimals to money and make estimates.
0406.1.4  Use commutative, associative, and distributive properties of numbers including oral descriptions of mathematical reasoning.
0406.1.5  Measure using ruler, meter stick, clock, thermometer, or other scaled instruments.
0406.1.6  Identify geometric or physical attributes that are appropriate to measure in a given situation.
0406.1.7  Translate the details of a contextual problem into diagrams and/or numerical expressions, and express answers using appropriate units.
0406.1.8  Match the spoken, written, concrete (including base ten blocks), and pictorial representations of decimals.
0406.1.9  Develop a story problem that illustrates a given multiplication or division number sentence.
0406.1.10  Use age-appropriate books, stories, and videos to convey ideas of mathematics.
State Performance Indicators
SPI 0406.1.1  Verify a conclusion using the commutative, associative and distributive properties.
SPI 0406.1.2  Compare decimals using concrete and pictorial representations.
SPI 0406.1.3  Determine the correct change from a transaction.
SPI 0406.1.4  Compare objects with respect to a given geometric or physical attribute and select appropriate measurement instrument.
 
Grade 5
Grade Learning Expectations
GLE 0506.1.1  Use mathematical language, symbols, and definitions while developing mathematical reasoning.
GLE 0506.1.2  Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
GLE 0506.1.3  Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
GLE 0506.1.4  Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution strategies.
GLE 0506.1.5  Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
GLE 0506.1.6  Read and interpret the language of mathematics and use written/oral communication to express mathematical ideas precisely.
GLE 0506.1.7  Recognize the historical development of mathematics, mathematics in context, and the connections between mathematics and the real world.
GLE 0506.1.8  Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and reliable models of mathematical concepts.
Checks for Understanding
0506.1.1  Make and test conjectures about geometric properties and develop logical arguments to justify conclusions.
0506.1.2  Make reasonable estimates of fraction and decimal sums or differences using models.
0506.1.3  Explore different methods of estimation including rounding and truncating.
0506.1.4  Explore problems in different contexts to interpret the meaning of remainders as discrete values or not.
0506.1.5  Solve problems in more than one way and explain why one process may be more effective than another.
0506.1.6  Communicate answers in correct verbal and numerical form; including use of mixed numbers or fractions and use of units.
0506.1.7  Organize and consolidate verbal statements involving fractions and mixed numbers into diagrams, symbols, and numerical expressions.
0506.1.8  Use patterns, models, and relationships as contexts for writing inequalities and simple equations.
0506.1.9  Use age-appropriate books, stories, and videos to convey ideas of mathematics.
State Performance Indicators
SPI 0506.1.1  Given a series of geometric statements, draw a conclusion about the figure described.
SPI 0506.1.2  Estimate fraction and decimal sums or differences.
SPI 0506.1.3  Recognize the unit associated with the remainder in a division problem or the meaning of the fractional part of a whole given in either decimal or fraction form.
SPI 0506.1.4  Identify missing information and/or too much information in contextual problems.
 
Grade 6
Grade Learning Expectations
GLE 0606.1.1  Use mathematical language, symbols, and definitions while developing mathematical reasoning.
GLE 0606.1.2  Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
GLE 0606.1.3  Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
GLE 0606.1.4  Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution strategies.
GLE 0606.1.5  Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
GLE 0606.1.6  Read and interpret the language of mathematics and use written/oral communication to express mathematical ideas precisely.
GLE 0606.1.7  Recognize the historical development of mathematics, mathematics in context, and the connections between mathematics and the real world.
GLE 0606.1.8  Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and reliable models of mathematical concepts.
Checks for Understanding
0606.1.1  Recognize different conventions used in calculator and computer spreadsheets (e.g., * for multiplication, ^ for exponent), but use mathematical notation in written work.
0606.1.2  Recognize when an estimate is more appropriate than an exact answer in a variety of problem situations.
0606.1.3  Recognize errors generated by rounding.
0606.1.4  Describe how changes in one quantity or variable result in changes in another.
0606.1.5  Illustrate properties of operations by showing that two expressions are equivalent in a given context (e.g., using an area model for distributive property, and grouping/set models for commutative and associative properties).
0606.1.6  Model situations by devising and carrying out experiments and simulations.
0606.1.7  Formulate questions, design studies, and collect real world data.
0606.1.8  Determine an appropriate sample to test an hypothesis.
0606.1.9  Use age-appropriate books, stories, and videos to convey ideas of mathematics.
0606.1.10  Use various methods (such as dynamic geometry software) to explore properties of triangles and quadrilaterals.
0606.1.11  Model algebraic expressions with manipulatives, technology, and pencil and paper.
State Performance Indicators
SPI 0606.1.1  Make conjectures and predictions based on data.
SPI 0606.1.2  Judge the reasonableness of the results of rational number estimates and/or computations.
SPI 0606.1.3  Use concrete, pictorial, and symbolic representation for integers.
SPI 0606.1.4  Select the representation that models one of the arithmetic properties (commutative, associative, or distributive).
SPI 0606.1.5  Model algebraic expressions using algebra tiles.
 
Grade 7
Grade Learning Expectations
GLE 0706.1.1  Use mathematical language, symbols, and definitions while developing mathematical reasoning.
GLE 0706.1.2  Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
GLE 0706.1.3  Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
GLE 0706.1.4  Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution strategies.
GLE 0706.1.5  Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
GLE 0706.1.6  Read and interpret the language of mathematics and use written/oral communication to express mathematical ideas precisely.
GLE 0706.1.7  Recognize the historical development of mathematics, mathematics in context, and the connections between mathematics and the real world.
GLE 0706.1.8  Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and reliable models of mathematical concepts.
Checks for Understanding
0706.1.1  Recognize common abbreviations (such as gcd/gcf and lcm).
0706.1.2  Recognize round-off error and the inaccuracies it introduces.
0706.1.3  Check answers both by estimation and by appropriate independent calculations, using calculators or computers judiciously.
0706.1.4  Recognize quantities that are inversely proportional (such as the relationship between the lengths of the base and the side of a rectangle with fixed area).
0706.1.5  Understand that a linear function in which f(0) = 0 is called a directly proportional relationship.
0706.1.6  Develop meaning of intercept and rate of change in contextual problems.
0706.1.7  Explain and demonstrate how scale in maps and drawings shows relative size and distance.
0706.1.8  Recognize the applications of scale factor by exploring blueprints, shadow measuring, and scale models.
0706.1.9  Use age-appropriate books, stories, and videos to convey ideas of mathematics.
0706.1.10  Model algebraic equations with manipulatives, technology, and pencil and paper.
0706.1.11  Translate from calculator notation to scientific/standard notation.
0706.1.12  Use dynamic geometry software to explore scale factor and similarity.
State Performance Indicators
SPI 0706.1.1  Use proportional reasoning to solve mixture/concentration problems.
SPI 0706.1.2  Generalize a variety of patterns to a symbolic rule from tables, graphs, or words.
SPI 0706.1.3  Recognize whether information given in a table, graph, or formula suggests a directly proportional, linear, inversely proportional, or other nonlinear relationship.
SPI 0706.1.4  Use scales to read maps.
 
Grade 8
Grade Learning Expectations
GLE 0806.1.1  Use mathematical language, symbols, and definitions while developing mathematical reasoning.
GLE 0806.1.2  Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
GLE 0806.1.3  Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
GLE 0806.1.4  Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution strategies.
GLE 0806.1.5  Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
GLE 0806.1.6  Read and interpret the language of mathematics and use written/oral communication to express mathematical ideas precisely.
GLE 0806.1.7  Recognize the historical development of mathematics, mathematics in context, and the connections between mathematics and the real world.
GLE 0806.1.8  Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and reliable models of mathematical concepts.
Checks for Understanding
0806.1.1  Relate nonlinear functions to geometric contexts of length, area, and volume.
0806.1.2  Draw qualitative graphs (trend graphs) of functions and describe their general shape/trend.
0806.1.3  Research the contributions of Pythagoras to mathematics.
0806.1.4  Relate data concepts to relevant concepts in the earth and space, life, and physical sciences.
0806.1.5  Use age-appropriate books, stories, and videos to convey ideas of mathematics.
0806.1.6  Use models (such as dynamic geometry software, patty paper and geo boards) to explore relationships among angles (complementary, supplementary, interior, exterior, vertical, and corresponding).
0806.1.7  Use a graphing calculator or spreadsheet to create scatterplots of data and approximate lines of best fit.
0806.1.8  Use a variety of methods to solve real-world problems involving multi-step linear equations (e.g., manipulatives, technology, pencil and paper).
State Performance Indicators
SPI 0806.1.1  Solve problems involving rate/time/distance (i.e., d = rt).
SPI 0806.1.2  Interpret a qualitative graph representing a contextual situation.
SPI 0806.1.3  Calculates rates involving cost per unit to determine the best buy.
 
Algebra I
Course Learning Expectations
CLE 3102.1.1  Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning.
CLE 3102.1.2  Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.
CLE 3102.1.3  Develop inductive and deductive reasoning to independently make and evaluate mathematical arguments and construct appropriate proofs; include various types of reasoning, logic, and intuition.
CLE 3102.1.4  Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies.
CLE 3102.1.5  Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies.
CLE 3102.1.6  Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world.
CLE 3102.1.7  Use technologies appropriately to develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate and reliable models.
Checks for Understanding
3102.1.1  Develop meaning for mathematical vocabulary.
3102.1.2  Use the terminology of mathematics correctly.
3102.1.3  Understand and use mathematical symbols, notation, and common mathematical abbreviations correctly.
3102.1.4  Write a rule with variables that expresses a pattern.
3102.1.5  Use formulas, equations, and inequalities to solve real-world problems including time/rate/distance, percent increase/decrease, ratio/proportion, and mixture problems.
3102.1.6  Use a variety of strategies to estimate and compute solutions, including real-world problems.
3102.1.7  Identify missing or irrelevant information in problems.
3102.1.8  Recognize and perform multiple steps in problem solving when necessary.
3102.1.9  Identify and use properties of the real numbers (including commutative, associative, distributive, inverse, identity element, closure, reflexive, symmetric, transitive, operation properties of equality).
3102.1.10  Use algebraic properties to develop a valid mathematical argument.
3102.1.11  Use manipulatives to model algebraic concepts.
3102.1.12  Create and work flexibly among representations of relations (including verbal, equations, tables, mappings, graphs).
3102.1.13  Change from one representation of a relation to another representation, for example, change from a verbal description to a graph.
3102.1.14  Apply graphical transformations that occur when changes are made to coefficients and constants in functions.
3102.1.15  Apply arithmetic concepts in algebraic contexts.
3102.1.16  Understand and express the meaning of the slope and y-intercept of linear functions in real-world contexts.
3102.1.17  Connect the study of algebra to the historical development of algebra.
3102.1.18  Translate syntax of technology to appropriate mathematical notation.
3102.1.19  Recognize and practice appropriate use of technology in representations and in problem solving.
3102.1.20  Estimate solutions to evaluate the reasonableness of results and to check technological computation.
State Performance Indicators
SPI 3102.1.1  Interpret patterns found in sequences, tables, and other forms of quantitative information using variables or function notation.
SPI 3102.1.2  Write an equation symbolically to express a contextual problem.
SPI 3102.1.3  Apply properties to evaluate expressions, simplify expressions, and justify solutions to problems.
SPI 3102.1.4  Translate between representations of functions that depict real-world situations.
SPI 3102.1.5  Recognize and express the effect of changing constants and/or coefficients in problem solving.
SPI 3102.1.6  Determine and interpret slope in multiple contexts including rate of change in real-world problems.
 
Geometry
Course Learning Expectations
CLE 3108.1.1  Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning.
CLE 3108.1.2  Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.
CLE 3108.1.3  Develop inductive and deductive reasoning to independently make and evaluate mathematical arguments and construct appropriate proofs; include various types of reasoning, logic, and intuition.
CLE 3108.1.4  Move flexibly between multiple representations (contextual, physical written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies.
CLE 3108.1.5  Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies.
CLE 3108.1.6  Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world.
CLE 3108.1.7  Use technologies appropriately to develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate and reliable models.
Checks for Understanding
3108.1.1  Check solutions after making reasonable estimates in appropriate units of quantities encountered in contextual situations.
3108.1.2  Determine position using spatial sense with two and three-dimensional coordinate systems.
3108.1.3  Comprehend the concept of length on the number line.
3108.1.4  Recognize that a definition depends on undefined terms and on previous definitions.
3108.1.5  Use technology, hands-on activities, and manipulatives to develop the language and the concepts of geometry, including specialized vocabulary (e.g. graphing calculators, interactive geometry software such as Geometer’s Sketchpad and Cabri, algebra tiles, pattern blocks, tessellation tiles, MIRAs, mirrors, spinners, geoboards, conic section models, volume demonstration kits, Polydrons, measurement tools, compasses, PentaBlocks, pentominoes, cubes, tangrams).
3108.1.6  Use inductive reasoning to write conjectures and/or conditional statements.
3108.1.7  Recognize the capabilities and the limitations of calculators and computers in solving problems.
3108.1.8  Understand how the similarity of right triangles allows the trigonometric functions sine, cosine, and tangent to be defined as ratio of sides.
3108.1.9  Expand analysis of units of measure to include area and volume.
3108.1.10  Use visualization, spatial reasoning, and geometric modeling to solve problems.
3108.1.11  Identify and sketch solids formed by revolving two-dimensional figures around lines.
3108.1.12  Connect the study of geometry to the historical development of geometry.
3108.1.13  Use proofs to further develop and deepen the understanding of the study of geometry (e.g. two-column, paragraph, flow, indirect, coordinate).
3108.1.14  Identify and explain the necessity of postulates, theorems, and corollaries in a mathematical system.
State Performance Indicators
SPI 3108.1.1  Give precise mathematical descriptions or definitions of geometric shapes in the plane and space.
SPI 3108.1.2  Determine areas of planar figures by decomposing them into simpler figures without a grid.
SPI 3108.1.3  Use geometric understanding and spatial visualization of geometric solids to solve problems and/or create drawings.
SPI 3108.1.4  Use definitions, basic postulates, and theorems about points, lines, angles, and planes to write/complete proofs and/or to solve problems.
 
Algebra II
Course Learning Expectations
CLE 3103.1.1  Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning.
CLE 3103.1.2  Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.
CLE 3103.1.3  Develop inductive and deductive reasoning to independently make and evaluate mathematical arguments and construct appropriate proofs; include various types of reasoning, logic, and intuition.
CLE 3103.1.4  Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies.
CLE 3103.1.5  Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies.
CLE 3103.1.6  Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world.
CLE 3103.1.7  Use technologies appropriately to develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate and reliable models.
Checks for Understanding
3103.1.1  Create and analyze scatter-plots of non-linear and transcendental functions.
3103.1.2  Compare and contrast sampling techniques and identify the best technique for a given situation.
3103.1.3  Use calculators to identify regression equations for nonlinear data.
3103.1.4  Identify the weaknesses of calculators and other technologies in representing non-linear data, such as graphs approaching vertical asymptotes, and use alternative techniques to identify these issues and correctly solve problems.
3103.1.5  Determine the accuracy and reliability of a mathematical model.
3103.1.6  Use graphical representations to perform operations on complex numbers.
3103.1.7  Use the unit circle to determine the exact value of trigonometric functions for commonly used angles (0°, 30°, 45°, 60°…).
3103.1.8  Understand and describe the inverse relationship between exponential and logarithmic functions.
3103.1.9  Translate the syntax of technology to appropriate mathematical notation for non-linear and transcendental functions.
3103.2.9  Find and describe geometrically the absolute value of a complex number.
3103.1.10  Interpret the results of mathematical modeling in various contexts to answer questions.
3103.2.10  Draw conclusions based on number concepts, algebraic properties, and/or relationships between expressions and numbers over complex numbers.
State Performance Indicators
SPI 3103.1.1  Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic) of non-linear and transcendental functions to solve problems, to model mathematical ideas, and to communicate solution strategies.
SPI 3103.1.2  Recognize and describe errors in data collection and analysis as well as identifying representations of data as being accurate or misleading.
SPI 3103.1.3  Use technology tools to identify and describe patterns in data using non-linear and transcendental functions that approximate data as well as using those functions to solve contextual problems.
SPI 3103.1.4  Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely to effectively communicate reasoning in the process of solving problems via mathematical modeling with both linear and non-linear functions.