Illinois 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.
IL.6. Number Sense: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.
6.A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.
6.A.1a. Identify whole numbers and compare them using the symbols <, >, or = and the words less than, greater than, or equal to, applying counting, grouping and place value concepts.
6.A.1b. Identify and model fractions using concrete materials and pictorial representations.
6.B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.
6.B.1. Solve one- and two-step problems with whole numbers using addition, subtraction, multiplication and division.
6.C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.
6.C.1a. Select and perform computational procedures to solve problems with whole numbers.
6.C.1b. Show evidence that whole number computational results are correct and/or that estimates are reasonable.
6.D. Solve problems using comparison of quantities, ratios, proportions and percents.
6.D.1. Compare the numbers of objects in groups.
IL.7. Estimation and Measurement: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.
7.A. Measure and compare quantities using appropriate units, instruments and methods.
7.A.1a. Measure length, volume and weight/mass using rulers, scales and other appropriate measuring instruments in the customary and metric systems.
7.A.1b. Measure units of time using appropriate instruments (e.g., calendars, clocks, watches - both analog and digital).
7.A.1c. Identify and describe the relative values and relationships among coins and solve addition and subtraction problems using currency.
7.A.1d. Read temperatures to the nearest degree from Celsius and Fahrenheit thermometers.
7.B. Estimate measurements and determine acceptable levels of accuracy.
7.B.1a. Given a problem, describe possible methods for estimating a given measure.
7.B.1b. Compare estimated measures to actual measures taken with appropriate measuring instruments.
7.C. Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.
7.C.1. Determine perimeter and area using concrete materials (e.g., geoboards, square tiles, grids, measurement instruments).
IL.8. Algebra and Analytical Methods: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.
8.A. Describe numerical relationships using variables and patterns.
8.A.1a. Identify, describe and extend simple geometric and numeric patterns.
8.A.1b. Solve simple number sentences (e.g., 2 + _ = 5).
8.B. Interpret and describe numerical relationships using tables, graphs and symbols.
8.B.1. Solve problems involving pattern identification and completion of patterns.
8.C. Solve problems using systems of numbers and their properties.
8.C.1. Describe the basic arithmetic operations (addition, subtraction, multiplication, division) orally, in writing and using concrete materials and drawings.
8.D. Use algebraic concepts and procedures to represent and solve problems.
8.D.1. Find the unknown numbers in whole-number addition, subtraction, multiplication and division situations.
IL.9. Geometry: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.
9.A. Demonstrate and apply geometric concepts involving points, lines, planes and space.
9.A.1a. Identify related two- and three-dimensional shapes including circle-sphere, square-cube, triangle-pyramid, rectangle-rectangular prism and their basic properties.
9.A.1b. Draw two-dimensional shapes.
9.B. Identify, describe, classify and compare relationships using points, lines, planes and solids.
9.B.1a. Identify and describe characteristics, similarities and differences of geometric shapes.
9.B.1b. Sort, classify and compare familiar shapes.
9.B.1c. Identify lines of symmetry in simple figures and construct symmetrical figures using various concrete materials.
9.C. Construct convincing arguments and proofs to solve problems.
9.C.1. Draw logical conclusions and communicate reasoning about simple geometric figures and patterns using concrete materials, diagrams and contemporary technology.
IL.10. Data Analysis and Probability: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.
10.A. Organize, describe and make predictions from existing data.
10.A.1a. Organize and display data using pictures, tallies, tables, charts or bar graphs.
10.A.1b. Answer questions and make predictions based on given data.
10.B. Formulate questions, design data collection methods, gather and analyze data and communicate findings.
10.B.1a. Formulate questions of interest and design surveys or experiments to gather data.
10.B.1b. Collect, organize and describe data using pictures, tallies, tables, charts or bar graphs.
10.B.1c. Analyze data, draw conclusions and communicate the results.
10.C. Determine, describe and apply the probabilities of events.
10.C.1a. Describe the concept of probability in relationship to likelihood and chance.
10.C.1b. Systematically list all possible outcomes of a simple one-stage experiment (e.g., the flip of one coin, the toss of one die, the spin of a spinner).
IL.6. Number Sense: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.
6.A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.
6.A.1a. Identify whole numbers and compare them using the symbols <, >, or = and the words less than, greater than, or equal to, applying counting, grouping and place value concepts.
6.A.1b. Identify and model fractions using concrete materials and pictorial representations.
6.B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.
6.B.1. Solve one- and two-step problems with whole numbers using addition, subtraction, multiplication and division.
6.C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.
6.C.1a. Select and perform computational procedures to solve problems with whole numbers.
6.C.1b. Show evidence that whole number computational results are correct and/or that estimates are reasonable.
6.D. Solve problems using comparison of quantities, ratios, proportions and percents.
6.D.1. Compare the numbers of objects in groups.
IL.7. Estimation and Measurement: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.
7.A. Measure and compare quantities using appropriate units, instruments and methods.
7.A.1a. Measure length, volume and weight/mass using rulers, scales and other appropriate measuring instruments in the customary and metric systems.
7.A.1b. Measure units of time using appropriate instruments (e.g., calendars, clocks, watches - both analog and digital).
7.A.1c. Identify and describe the relative values and relationships among coins and solve addition and subtraction problems using currency.
7.A.1d. Read temperatures to the nearest degree from Celsius and Fahrenheit thermometers.
7.B. Estimate measurements and determine acceptable levels of accuracy.
7.B.1a. Given a problem, describe possible methods for estimating a given measure.
7.B.1b. Compare estimated measures to actual measures taken with appropriate measuring instruments.
7.C. Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.
7.C.1. Determine perimeter and area using concrete materials (e.g., geoboards, square tiles, grids, measurement instruments).
IL.8. Algebra and Analytical Methods: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.
8.A. Describe numerical relationships using variables and patterns.
8.A.1a. Identify, describe and extend simple geometric and numeric patterns.
8.A.1b. Solve simple number sentences (e.g., 2 + _ = 5).
8.B. Interpret and describe numerical relationships using tables, graphs and symbols.
8.B.1. Solve problems involving pattern identification and completion of patterns.
8.C. Solve problems using systems of numbers and their properties.
8.C.1. Describe the basic arithmetic operations (addition, subtraction, multiplication, division) orally, in writing and using concrete materials and drawings.
8.D. Use algebraic concepts and procedures to represent and solve problems.
8.D.1. Find the unknown numbers in whole-number addition, subtraction, multiplication and division situations.
IL.9. Geometry: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.
9.A. Demonstrate and apply geometric concepts involving points, lines, planes and space.
9.A.1a. Identify related two- and three-dimensional shapes including circle-sphere, square-cube, triangle-pyramid, rectangle-rectangular prism and their basic properties.
9.A.1b. Draw two-dimensional shapes.
9.B. Identify, describe, classify and compare relationships using points, lines, planes and solids.
9.B.1a. Identify and describe characteristics, similarities and differences of geometric shapes.
9.B.1b. Sort, classify and compare familiar shapes.
9.B.1c. Identify lines of symmetry in simple figures and construct symmetrical figures using various concrete materials.
9.C. Construct convincing arguments and proofs to solve problems.
9.C.1. Draw logical conclusions and communicate reasoning about simple geometric figures and patterns using concrete materials, diagrams and contemporary technology.
IL.10. Data Analysis and Probability: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.
10.A. Organize, describe and make predictions from existing data.
10.A.1a. Organize and display data using pictures, tallies, tables, charts or bar graphs.
10.A.1b. Answer questions and make predictions based on given data.
10.B. Formulate questions, design data collection methods, gather and analyze data and communicate findings.
10.B.1a. Formulate questions of interest and design surveys or experiments to gather data.
10.B.1b. Collect, organize and describe data using pictures, tallies, tables, charts or bar graphs.
10.B.1c. Analyze data, draw conclusions and communicate the results.
10.C. Determine, describe and apply the probabilities of events.
10.C.1a. Describe the concept of probability in relationship to likelihood and chance.
10.C.1b. Systematically list all possible outcomes of a simple one-stage experiment (e.g., the flip of one coin, the toss of one die, the spin of a spinner).
IL.6. Number Sense: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.
6.A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.
6.A.1a. Identify whole numbers and compare them using the symbols <, >, or = and the words less than, greater than, or equal to, applying counting, grouping and place value concepts.
6.A.1b. Identify and model fractions using concrete materials and pictorial representations.
6.B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.
6.B.1. Solve one- and two-step problems with whole numbers using addition, subtraction, multiplication and division.
6.C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.
6.C.1a. Select and perform computational procedures to solve problems with whole numbers.
6.C.1b. Show evidence that whole number computational results are correct and/or that estimates are reasonable.
6.D. Solve problems using comparison of quantities, ratios, proportions and percents.
6.D.1. Compare the numbers of objects in groups.
IL.7. Estimation and Measurement: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.
7.A. Measure and compare quantities using appropriate units, instruments and methods.
7.A.1a. Measure length, volume and weight/mass using rulers, scales and other appropriate measuring instruments in the customary and metric systems.
7.A.1b. Measure units of time using appropriate instruments (e.g., calendars, clocks, watches - both analog and digital).
7.A.1c. Identify and describe the relative values and relationships among coins and solve addition and subtraction problems using currency.
7.A.1d. Read temperatures to the nearest degree from Celsius and Fahrenheit thermometers.
7.B. Estimate measurements and determine acceptable levels of accuracy.
7.B.1a. Given a problem, describe possible methods for estimating a given measure.
7.B.1b. Compare estimated measures to actual measures taken with appropriate measuring instruments.
7.C. Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.
7.C.1. Determine perimeter and area using concrete materials (e.g., geoboards, square tiles, grids, measurement instruments).
IL.8. Algebra and Analytical Methods: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.
8.A. Describe numerical relationships using variables and patterns.
8.A.1a. Identify, describe and extend simple geometric and numeric patterns.
8.A.1b. Solve simple number sentences (e.g., 2 + _ = 5).
8.B. Interpret and describe numerical relationships using tables, graphs and symbols.
8.B.1. Solve problems involving pattern identification and completion of patterns.
8.C. Solve problems using systems of numbers and their properties.
8.C.1. Describe the basic arithmetic operations (addition, subtraction, multiplication, division) orally, in writing and using concrete materials and drawings.
8.D. Use algebraic concepts and procedures to represent and solve problems.
8.D.1. Find the unknown numbers in whole-number addition, subtraction, multiplication and division situations.
IL.9. Geometry: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.
9.A. Demonstrate and apply geometric concepts involving points, lines, planes and space.
9.A.1a. Identify related two- and three-dimensional shapes including circle-sphere, square-cube, triangle-pyramid, rectangle-rectangular prism and their basic properties.
9.A.1b. Draw two-dimensional shapes.
9.B. Identify, describe, classify and compare relationships using points, lines, planes and solids.
9.B.1a. Identify and describe characteristics, similarities and differences of geometric shapes.
9.B.1b. Sort, classify and compare familiar shapes.
9.B.1c. Identify lines of symmetry in simple figures and construct symmetrical figures using various concrete materials.
9.C. Construct convincing arguments and proofs to solve problems.
9.C.1. Draw logical conclusions and communicate reasoning about simple geometric figures and patterns using concrete materials, diagrams and contemporary technology.
IL.10. Data Analysis and Probability: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.
10.A. Organize, describe and make predictions from existing data.
10.A.1a. Organize and display data using pictures, tallies, tables, charts or bar graphs.
10.A.1b. Answer questions and make predictions based on given data.
10.B. Formulate questions, design data collection methods, gather and analyze data and communicate findings.
10.B.1a. Formulate questions of interest and design surveys or experiments to gather data.
10.B.1b. Collect, organize and describe data using pictures, tallies, tables, charts or bar graphs.
10.B.1c. Analyze data, draw conclusions and communicate the results.
10.C. Determine, describe and apply the probabilities of events.
10.C.1a. Describe the concept of probability in relationship to likelihood and chance.
10.C.1b. Systematically list all possible outcomes of a simple one-stage experiment (e.g., the flip of one coin, the toss of one die, the spin of a spinner).
IL.6. Number Sense: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.
6.A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.
6.A.2. Compare and order whole numbers, fractions and decimals using concrete materials, drawings and mathematical symbols.
6.B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.
6.B.2. Solve one- and two-step problems involving whole numbers, fractions and decimals using addition, subtraction, multiplication and division.
6.C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.
6.C.2a. Select and perform computational procedures to solve problems with whole numbers, fractions and decimals.
6.C.2b. Show evidence that computational results using whole numbers, fractions and decimals are correct and/or that estimates are reasonable.
6.D. Solve problems using comparison of quantities, ratios, proportions and percents.
6.D.2. Describe the relationship between two sets of data using ratios and appropriate notations (e.g., a/b, a to b, a:b).
IL.7. Estimation and Measurement: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.
7.A. Measure and compare quantities using appropriate units, instruments and methods.
7.A.2a. Calculate, compare and convert length, perimeter, area, weight/mass and volume within the customary and metric systems.
7.A.2b. Solve addition, subtraction, multiplication and division problems using currency.
7.B. Estimate measurements and determine acceptable levels of accuracy.
7.B.2a. Determine and communicate possible methods for estimating a given measure, selecting proper units in both customary and metric systems.
7.B.2b. Estimate conversions between measures within the customary and metric systems.
7.C. Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.
7.C.2a. Describe relationships in a simple scale drawing.
7.C.2b. Construct or draw figures with given perimeters and areas.
IL.8. Algebra and Analytical Methods: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.
8.A. Describe numerical relationships using variables and patterns.
8.A.2a. Identify, describe, extend and create geometric and numeric patterns.
8.A.2b. Construct and solve number sentences using a variable to represent an unknown quantity.
8.B. Interpret and describe numerical relationships using tables, graphs and symbols.
8.B.2. Analyze a geometric pattern and express the results numerically.
8.C. Solve problems using systems of numbers and their properties.
8.C.2. Explain operations and number properties including commutative, associative, distributive, transitive, zero, equality and order of operations.
8.D. Use algebraic concepts and procedures to represent and solve problems.
8.D.2. Solve linear equations involving whole numbers.
IL.9. Geometry: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.
9.A. Demonstrate and apply geometric concepts involving points, lines, planes and space.
9.A.2a. Build physical models of two- and three-dimensional shapes.
9.A.2b. Identify and describe how geometric figures are used in practical settings (e.g., construction, art, advertising).
9.A.2c. Describe and draw representations of geometric relationships, patterns, symmetries, and designs in two- and three-dimensions with and without technology.
9.B. Identify, describe, classify and compare relationships using points, lines, planes and solids.
9.B.2. Compare geometric figures and determine their properties including parallel, perpendicular, similar, congruent and line symmetry.
9.C. Construct convincing arguments and proofs to solve problems.
9.C.2. Formulate logical arguments about geometric figures and patterns and communicate reasoning.
IL.10. Data Analysis and Probability: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.
10.A. Organize, describe and make predictions from existing data.
10.A.2a. Organize and display data using pictures, tallies, tables, charts, bar graphs, line graphs, line plots and stem-and-leaf graphs.
10.A.2b. Using a data set, determine mean, median, mode and range, with and without the use of technology.
10.A.2c. Make predictions and decisions based on data and communicate their reasoning.
10.B. Formulate questions, design data collection methods, gather and analyze data and communicate findings.
10.B.2a. Formulate questions of interest and select methods to systematically collect data.
10.B.2b. Collect, organize and display data using tables, charts, bar graphs, line graphs, circle graphs, line plots and stem-and-leaf graphs.
10.B.2c. Analyze the data using mean, median, mode and range, as appropriate, with or without the use of technology.
10.B.2d. Interpret results or make relevant decisions based on the data gathered.
10.C. Determine, describe and apply the probabilities of events.
10.C.2a. Calculate the probability of a simple event.
10.C.2b. Compare the likelihood of events in terms of certain, more likely, less likely or impossible.
10.C.2c. Determine the probability of an event involving 'and', or 'or not'.
IL.6. Number Sense: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.
6.A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.
6.A.2. Compare and order whole numbers, fractions and decimals using concrete materials, drawings and mathematical symbols.
6.B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.
6.B.2. Solve one- and two-step problems involving whole numbers, fractions and decimals using addition, subtraction, multiplication and division.
6.C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.
6.C.2a. Select and perform computational procedures to solve problems with whole numbers, fractions and decimals.
6.C.2b. Show evidence that computational results using whole numbers, fractions and decimals are correct and/or that estimates are reasonable.
6.D. Solve problems using comparison of quantities, ratios, proportions and percents.
6.D.2. Describe the relationship between two sets of data using ratios and appropriate notations (e.g., a/b, a to b, a:b).
IL.7. Estimation and Measurement: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.
7.A. Measure and compare quantities using appropriate units, instruments and methods.
7.A.2a. Calculate, compare and convert length, perimeter, area, weight/mass and volume within the customary and metric systems.
7.A.2b. Solve addition, subtraction, multiplication and division problems using currency.
7.B. Estimate measurements and determine acceptable levels of accuracy.
7.B.2a. Determine and communicate possible methods for estimating a given measure, selecting proper units in both customary and metric systems.
7.B.2b. Estimate conversions between measures within the customary and metric systems.
7.C. Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.
7.C.2a. Describe relationships in a simple scale drawing.
7.C.2b. Construct or draw figures with given perimeters and areas.
IL.8. Algebra and Analytical Methods: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.
8.A. Describe numerical relationships using variables and patterns.
8.A.2a. Identify, describe, extend and create geometric and numeric patterns.
8.A.2b. Construct and solve number sentences using a variable to represent an unknown quantity.
8.B. Interpret and describe numerical relationships using tables, graphs and symbols.
8.B.2. Analyze a geometric pattern and express the results numerically.
8.C. Solve problems using systems of numbers and their properties.
8.C.2. Explain operations and number properties including commutative, associative, distributive, transitive, zero, equality and order of operations.
8.D. Use algebraic concepts and procedures to represent and solve problems.
8.D.2. Solve linear equations involving whole numbers.
IL.9. Geometry: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.
9.A. Demonstrate and apply geometric concepts involving points, lines, planes and space.
9.A.2a. Build physical models of two- and three-dimensional shapes.
9.A.2b. Identify and describe how geometric figures are used in practical settings (e.g., construction, art, advertising).
9.A.2c. Describe and draw representations of geometric relationships, patterns, symmetries, and designs in two- and three-dimensions with and without technology.
9.B. Identify, describe, classify and compare relationships using points, lines, planes and solids.
9.B.2. Compare geometric figures and determine their properties including parallel, perpendicular, similar, congruent and line symmetry.
9.C. Construct convincing arguments and proofs to solve problems.
9.C.2. Formulate logical arguments about geometric figures and patterns and communicate reasoning.
IL.10. Data Analysis and Probability: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.
10.A. Organize, describe and make predictions from existing data.
10.A.2a. Organize and display data using pictures, tallies, tables, charts, bar graphs, line graphs, line plots and stem-and-leaf graphs.
10.A.2b. Using a data set, determine mean, median, mode and range, with and without the use of technology.
10.A.2c. Make predictions and decisions based on data and communicate their reasoning.
10.B. Formulate questions, design data collection methods, gather and analyze data and communicate findings.
10.B.2a. Formulate questions of interest and select methods to systematically collect data.
10.B.2b. Collect, organize and display data using tables, charts, bar graphs, line graphs, circle graphs, line plots and stem-and-leaf graphs.
10.B.2c. Analyze the data using mean, median, mode and range, as appropriate, with or without the use of technology.
10.B.2d. Interpret results or make relevant decisions based on the data gathered.
10.C. Determine, describe and apply the probabilities of events.
10.C.2a. Calculate the probability of a simple event.
10.C.2b. Compare the likelihood of events in terms of certain, more likely, less likely or impossible.
10.C.2c. Determine the probability of an event involving 'and', or 'or not'.
IL.6. Number Sense: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.
6.A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.
6.A.2. Compare and order whole numbers, fractions and decimals using concrete materials, drawings and mathematical symbols.
6.B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.
6.B.2. Solve one- and two-step problems involving whole numbers, fractions and decimals using addition, subtraction, multiplication and division.
6.C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.
6.C.2a. Select and perform computational procedures to solve problems with whole numbers, fractions and decimals.
6.C.2b. Show evidence that computational results using whole numbers, fractions and decimals are correct and/or that estimates are reasonable.
6.D. Solve problems using comparison of quantities, ratios, proportions and percents.
6.D.2. Describe the relationship between two sets of data using ratios and appropriate notations (e.g., a/b, a to b, a:b).
IL.7. Estimation and Measurement: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.
7.A. Measure and compare quantities using appropriate units, instruments and methods.
7.A.2a. Calculate, compare and convert length, perimeter, area, weight/mass and volume within the customary and metric systems.
7.A.2b. Solve addition, subtraction, multiplication and division problems using currency.
7.B. Estimate measurements and determine acceptable levels of accuracy.
7.B.2a. Determine and communicate possible methods for estimating a given measure, selecting proper units in both customary and metric systems.
7.B.2b. Estimate conversions between measures within the customary and metric systems.
7.C. Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.
7.C.2a. Describe relationships in a simple scale drawing.
7.C.2b. Construct or draw figures with given perimeters and areas.
IL.8. Algebra and Analytical Methods: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.
8.A. Describe numerical relationships using variables and patterns.
8.A.2a. Identify, describe, extend and create geometric and numeric patterns.
8.A.2b. Construct and solve number sentences using a variable to represent an unknown quantity.
8.B. Interpret and describe numerical relationships using tables, graphs and symbols.
8.B.2. Analyze a geometric pattern and express the results numerically.
8.C. Solve problems using systems of numbers and their properties.
8.C.2. Explain operations and number properties including commutative, associative, distributive, transitive, zero, equality and order of operations.
8.D. Use algebraic concepts and procedures to represent and solve problems.
8.D.2. Solve linear equations involving whole numbers.
IL.9. Geometry: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.
9.A. Demonstrate and apply geometric concepts involving points, lines, planes and space.
9.A.2a. Build physical models of two- and three-dimensional shapes.
9.A.2b. Identify and describe how geometric figures are used in practical settings (e.g., construction, art, advertising).
9.A.2c. Describe and draw representations of geometric relationships, patterns, symmetries, and designs in two- and three-dimensions with and without technology.
9.B. Identify, describe, classify and compare relationships using points, lines, planes and solids.
9.B.2. Compare geometric figures and determine their properties including parallel, perpendicular, similar, congruent and line symmetry.
9.C. Construct convincing arguments and proofs to solve problems.
9.C.2. Formulate logical arguments about geometric figures and patterns and communicate reasoning.
IL.10. Data Analysis and Probability: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.
10.A. Organize, describe and make predictions from existing data.
10.A.2a. Organize and display data using pictures, tallies, tables, charts, bar graphs, line graphs, line plots and stem-and-leaf graphs.
10.A.2b. Using a data set, determine mean, median, mode and range, with and without the use of technology.
10.A.2c. Make predictions and decisions based on data and communicate their reasoning.
10.B. Formulate questions, design data collection methods, gather and analyze data and communicate findings.
10.B.2a. Formulate questions of interest and select methods to systematically collect data.
10.B.2b. Collect, organize and display data using tables, charts, bar graphs, line graphs, circle graphs, line plots and stem-and-leaf graphs.
10.B.2c. Analyze the data using mean, median, mode and range, as appropriate, with or without the use of technology.
10.B.2d. Interpret results or make relevant decisions based on the data gathered.
10.C. Determine, describe and apply the probabilities of events.
10.C.2a. Calculate the probability of a simple event.
10.C.2b. Compare the likelihood of events in terms of certain, more likely, less likely or impossible.
10.C.2c. Determine the probability of an event involving 'and', or 'or not'.
IL.6. Number Sense: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.
6.A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.
6.A.3. Represent fractions, decimals, percentages, exponents and scientific notation in equivalent forms.
6.B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.
6.B.3a. Solve practical computation problems involving whole numbers, integers and rational numbers.
6.B.3b. Apply primes, factors, divisors, multiples, common factors and common multiples in solving problems.
6.B.3c. Identify and apply properties of real numbers including pi, squares, and square roots.
6.C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.
6.C.3a. Select computational procedures and solve problems with whole numbers, fractions, decimals, percents and proportions.
6.C.3b. Show evidence that computational results using whole numbers, fractions, decimals, percents and proportions are correct and/or that estimates are reasonable.
6.D. Solve problems using comparison of quantities, ratios, proportions and percents.
6.D.3. Apply ratios and proportions to solve practical problems.
IL.7. Estimation and Measurement: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.
7.A. Measure and compare quantities using appropriate units, instruments and methods.
7.A.3a. Measure length, capacity, weight/mass and angles using sophisticated instruments (e.g., compass, protractor, trundle wheel).
7.A.3b. Apply the concepts and attributes of length, capacity, weight/mass, perimeter, area, volume, time, temperature and angle measures in practical situations.
7.B. Estimate measurements and determine acceptable levels of accuracy.
7.B.3. Select and apply instruments including rulers and protractors and units of measure to the degree of accuracy required.
7.C. Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.
7.C.3a. Construct a simple scale drawing for a given situation.
7.C.3b. Use concrete and graphic models and appropriate formulas to find perimeters, areas, surface areas and volumes of two- and three-dimensional regions.
IL.8. Algebra and Analytical Methods: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.
8.A. Describe numerical relationships using variables and patterns.
8.A.3a. Apply the basic properties of commutative, associative, distributive, transitive, inverse, identity, zero, equality and order of operations to solve problems.
8.A.3b. Solve problems using linear expressions, equations and inequalities.
8.B. Interpret and describe numerical relationships using tables, graphs and symbols.
8.B.3. Use graphing technology and algebraic methods to analyze and predict linear relationships and make generalizations from linear patterns.
8.C. Solve problems using systems of numbers and their properties.
8.C.3. Apply the properties of numbers and operations including inverses in algebraic settings derived from economics, business and the sciences.
8.D. Use algebraic concepts and procedures to represent and solve problems.
8.D.3a. Solve problems using numeric, graphic or symbolic representations of variables, expressions, equations and inequalities.
8.D.3b. Propose and solve problems using proportions, formulas and linear functions.
8.D.3c. Apply properties of powers, perfect squares and square roots.
IL.9. Geometry: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.
9.A. Demonstrate and apply geometric concepts involving points, lines, planes and space.
9.A.3a. Draw or construct two- and three- dimensional geometric figures including prisms, pyramids, cylinders and cones.
9.A.3b. Draw transformation images of figures, with and without the use of technology.
9.A.3c. Use concepts of symmetry, congruency, similarity, scale, perspective, and angles to describe and analyze two- and three-dimensional shapes found in practical applications (e.g., geodesic domes, A-frame houses, basketball courts, inclined planes, art forms, blueprints).
9.B. Identify, describe, classify and compare relationships using points, lines, planes and solids.
9.B.3. Identify, describe, classify and compare two- and three- dimensional geometric figures and models according to their properties.
9.C. Construct convincing arguments and proofs to solve problems.
9.C.3a. Construct, develop and communicate logical arguments (informal proofs) about geometric figures and patterns.
9.C.3b. Develop and solve problems using geometric relationships and models, with and without the use of technology.
9.D. Use trigonometric ratios and circular functions to solve problems.
9.D.3. Compute distances, lengths and measures of angles using proportions, the Pythagorean theorem and its converse.
IL.10. Data Analysis and Probability: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.
10.A. Organize, describe and make predictions from existing data.
10.A.3a. Construct, read and interpret tables, graphs (including circle graphs) and charts to organize and represent data.
10.A.3b. Compare the mean, median, mode and range, with and without the use of technology.
10.A.3c. Test the reasonableness of an argument based on data and communicate their findings.
10.B. Formulate questions, design data collection methods, gather and analyze data and communicate findings.
10.B.3. Formulate questions (e.g., relationships between car age and mileage, average incomes and years of schooling), devise and conduct experiments or simulations, gather data, draw conclusions and communicate results to an audience using traditional methods and contemporary technologies.
10.C. Determine, describe and apply the probabilities of events.
10.C.3a. Determine the probability and odds of events using fundamental counting principles.
10.C.3b. Analyze problem situations (e.g., board games, grading scales) and make predictions about results.
IL.6. Number Sense: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.
6.A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.
6.A.3. Represent fractions, decimals, percentages, exponents and scientific notation in equivalent forms.
6.B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.
6.B.3a. Solve practical computation problems involving whole numbers, integers and rational numbers.
6.B.3b. Apply primes, factors, divisors, multiples, common factors and common multiples in solving problems.
6.B.3c. Identify and apply properties of real numbers including pi, squares, and square roots.
6.C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.
6.C.3a. Select computational procedures and solve problems with whole numbers, fractions, decimals, percents and proportions.
6.C.3b. Show evidence that computational results using whole numbers, fractions, decimals, percents and proportions are correct and/or that estimates are reasonable.
6.D. Solve problems using comparison of quantities, ratios, proportions and percents.
6.D.3. Apply ratios and proportions to solve practical problems.
IL.7. Estimation and Measurement: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.
7.A. Measure and compare quantities using appropriate units, instruments and methods.
7.A.3a. Measure length, capacity, weight/mass and angles using sophisticated instruments (e.g., compass, protractor, trundle wheel).
7.A.3b. Apply the concepts and attributes of length, capacity, weight/mass, perimeter, area, volume, time, temperature and angle measures in practical situations.
7.B. Estimate measurements and determine acceptable levels of accuracy.
7.B.3. Select and apply instruments including rulers and protractors and units of measure to the degree of accuracy required.
7.C. Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.
7.C.3a. Construct a simple scale drawing for a given situation.
7.C.3b. Use concrete and graphic models and appropriate formulas to find perimeters, areas, surface areas and volumes of two- and three-dimensional regions.
IL.8. Algebra and Analytical Methods: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.
8.A. Describe numerical relationships using variables and patterns.
8.A.3a. Apply the basic properties of commutative, associative, distributive, transitive, inverse, identity, zero, equality and order of operations to solve problems.
8.A.3b. Solve problems using linear expressions, equations and inequalities.
8.B. Interpret and describe numerical relationships using tables, graphs and symbols.
8.B.3. Use graphing technology and algebraic methods to analyze and predict linear relationships and make generalizations from linear patterns.
8.C. Solve problems using systems of numbers and their properties.
8.C.3. Apply the properties of numbers and operations including inverses in algebraic settings derived from economics, business and the sciences.
8.D. Use algebraic concepts and procedures to represent and solve problems.
8.D.3a. Solve problems using numeric, graphic or symbolic representations of variables, expressions, equations and inequalities.
8.D.3b. Propose and solve problems using proportions, formulas and linear functions.
8.D.3c. Apply properties of powers, perfect squares and square roots.
IL.9. Geometry: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.
9.A. Demonstrate and apply geometric concepts involving points, lines, planes and space.
9.A.3a. Draw or construct two- and three- dimensional geometric figures including prisms, pyramids, cylinders and cones.
9.A.3b. Draw transformation images of figures, with and without the use of technology.
9.A.3c. Use concepts of symmetry, congruency, similarity, scale, perspective, and angles to describe and analyze two- and three-dimensional shapes found in practical applications (e.g., geodesic domes, A-frame houses, basketball courts, inclined planes, art forms, blueprints).
9.B. Identify, describe, classify and compare relationships using points, lines, planes and solids.
9.B.3. Identify, describe, classify and compare two- and three- dimensional geometric figures and models according to their properties.
9.C. Construct convincing arguments and proofs to solve problems.
9.C.3a. Construct, develop and communicate logical arguments (informal proofs) about geometric figures and patterns.
9.C.3b. Develop and solve problems using geometric relationships and models, with and without the use of technology.
9.D. Use trigonometric ratios and circular functions to solve problems.
9.D.3. Compute distances, lengths and measures of angles using proportions, the Pythagorean theorem and its converse.
IL.10. Data Analysis and Probability: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.
10.A. Organize, describe and make predictions from existing data.
10.A.3a. Construct, read and interpret tables, graphs (including circle graphs) and charts to organize and represent data.
10.A.3b. Compare the mean, median, mode and range, with and without the use of technology.
10.A.3c. Test the reasonableness of an argument based on data and communicate their findings.
10.B. Formulate questions, design data collection methods, gather and analyze data and communicate findings.
10.B.3. Formulate questions (e.g., relationships between car age and mileage, average incomes and years of schooling), devise and conduct experiments or simulations, gather data, draw conclusions and communicate results to an audience using traditional methods and contemporary technologies.
10.C. Determine, describe and apply the probabilities of events.
10.C.3a. Determine the probability and odds of events using fundamental counting principles.
10.C.3b. Analyze problem situations (e.g., board games, grading scales) and make predictions about results.
IL.6. Number Sense: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.
6.A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.
6.A.3. Represent fractions, decimals, percentages, exponents and scientific notation in equivalent forms.
6.B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.
6.B.3a. Solve practical computation problems involving whole numbers, integers and rational numbers.
6.B.3b. Apply primes, factors, divisors, multiples, common factors and common multiples in solving problems.
6.B.3c. Identify and apply properties of real numbers including pi, squares, and square roots.
6.C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.
6.C.3a. Select computational procedures and solve problems with whole numbers, fractions, decimals, percents and proportions.
6.C.3b. Show evidence that computational results using whole numbers, fractions, decimals, percents and proportions are correct and/or that estimates are reasonable.
6.D. Solve problems using comparison of quantities, ratios, proportions and percents.
6.D.3. Apply ratios and proportions to solve practical problems.
IL.7. Estimation and Measurement: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.
7.A. Measure and compare quantities using appropriate units, instruments and methods.
7.A.3a. Measure length, capacity, weight/mass and angles using sophisticated instruments (e.g., compass, protractor, trundle wheel).
7.A.3b. Apply the concepts and attributes of length, capacity, weight/mass, perimeter, area, volume, time, temperature and angle measures in practical situations.
7.B. Estimate measurements and determine acceptable levels of accuracy.
7.B.3. Select and apply instruments including rulers and protractors and units of measure to the degree of accuracy required.
7.C. Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.
7.C.3a. Construct a simple scale drawing for a given situation.
7.C.3b. Use concrete and graphic models and appropriate formulas to find perimeters, areas, surface areas and volumes of two- and three-dimensional regions.
IL.8. Algebra and Analytical Methods: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.
8.A. Describe numerical relationships using variables and patterns.
8.A.3a. Apply the basic properties of commutative, associative, distributive, transitive, inverse, identity, zero, equality and order of operations to solve problems.
8.A.3b. Solve problems using linear expressions, equations and inequalities.
8.B. Interpret and describe numerical relationships using tables, graphs and symbols.
8.B.3. Use graphing technology and algebraic methods to analyze and predict linear relationships and make generalizations from linear patterns.
8.C. Solve problems using systems of numbers and their properties.
8.C.3. Apply the properties of numbers and operations including inverses in algebraic settings derived from economics, business and the sciences.
8.D. Use algebraic concepts and procedures to represent and solve problems.
8.D.3a. Solve problems using numeric, graphic or symbolic representations of variables, expressions, equations and inequalities.
8.D.3b. Propose and solve problems using proportions, formulas and linear functions.
8.D.3c. Apply properties of powers, perfect squares and square roots.
IL.9. Geometry: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.
9.A. Demonstrate and apply geometric concepts involving points, lines, planes and space.
9.A.3a. Draw or construct two- and three- dimensional geometric figures including prisms, pyramids, cylinders and cones.
9.A.3b. Draw transformation images of figures, with and without the use of technology.
9.A.3c. Use concepts of symmetry, congruency, similarity, scale, perspective, and angles to describe and analyze two- and three-dimensional shapes found in practical applications (e.g., geodesic domes, A-frame houses, basketball courts, inclined planes, art forms, blueprints).
9.B. Identify, describe, classify and compare relationships using points, lines, planes and solids.
9.B.3. Identify, describe, classify and compare two- and three- dimensional geometric figures and models according to their properties.
9.C. Construct convincing arguments and proofs to solve problems.
9.C.3a. Construct, develop and communicate logical arguments (informal proofs) about geometric figures and patterns.
9.C.3b. Develop and solve problems using geometric relationships and models, with and without the use of technology.
9.D. Use trigonometric ratios and circular functions to solve problems.
9.D.3. Compute distances, lengths and measures of angles using proportions, the Pythagorean theorem and its converse.
IL.10. Data Analysis and Probability: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.
10.A. Organize, describe and make predictions from existing data.
10.A.3a. Construct, read and interpret tables, graphs (including circle graphs) and charts to organize and represent data.
10.A.3b. Compare the mean, median, mode and range, with and without the use of technology.
10.A.3c. Test the reasonableness of an argument based on data and communicate their findings.
10.B. Formulate questions, design data collection methods, gather and analyze data and communicate findings.
10.B.3. Formulate questions (e.g., relationships between car age and mileage, average incomes and years of schooling), devise and conduct experiments or simulations, gather data, draw conclusions and communicate results to an audience using traditional methods and contemporary technologies.
10.C. Determine, describe and apply the probabilities of events.
10.C.3a. Determine the probability and odds of events using fundamental counting principles.
10.C.3b. Analyze problem situations (e.g., board games, grading scales) and make predictions about results.
IL.6. Number Sense: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.
6.A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.
6.A.4. Identify and apply the associative, commutative, distributive and identity properties of real numbers, including special numbers such as pi and square roots.
6.B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.
6.B.4. Select and use appropriate arithmetic operations in practical situations including calculating wages after taxes, developing a budget and balancing a checkbook.
6.C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.
6.C.4. Determine whether exact values or approximations are appropriate (e.g., bid a job, determine gas mileage for a trip).
6.D. Solve problems using comparison of quantities, ratios, proportions and percents.
6.D.4. Solve problems involving recipes or mixtures, financial calculations and geometric similarity using ratios, proportions and percents.
IL.7. Estimation and Measurement: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.
7.A. Measure and compare quantities using appropriate units, instruments and methods.
7.A.4a. Apply units and scales to describe and compare numerical data and physical objects.
7.A.4b. Apply formulas in a wide variety of theoretical and practical real-world measurement applications involving perimeter, area, volume, angle, time, temperature, mass, speed, distance, density and monetary values.
7.B. Estimate measurements and determine acceptable levels of accuracy.
7.B.4. Estimate and measure the magnitude and directions of physical quantities (e.g., velocity, force, slope) using rulers, protractors and other scientific instruments including timers, calculators and computers.
7.C. Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.
7.C.4a. Make indirect measurements, including heights and distances, using proportions (e.g., finding the height of a tower by its shadow).
7.C.4b. Interpret scale drawings and models using maps and blueprints.
7.C.4c. Convert within and between measurement systems and monetary systems using technology where appropriate.
IL.8. Algebra and Analytical Methods: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.
8.A. Describe numerical relationships using variables and patterns.
8.A.4a. Use algebraic methods to convert repeating decimals to fractions.
8.A.4b. Represent mathematical patterns and describe their properties using variables and mathematical symbols.
8.B. Interpret and describe numerical relationships using tables, graphs and symbols.
8.B.4a. Represent algebraic concepts with physical materials, words, diagrams, tables, graphs, equations and inequalities and use appropriate technology.
8.B.4b. Use the basic functions of absolute value, square root, linear, quadratic and step to describe numerical relationships.
8.C. Solve problems using systems of numbers and their properties.
8.C.4a. Analyze and report the effects of changing coefficients, exponents and other parameters on functions and their graphs.
8.C.4b. Apply algebraic properties and procedures with matrices, vectors, functions and sequences using data found in business, industry and consumer situations.
8.D. Use algebraic concepts and procedures to represent and solve problems.
8.D.4. Formulate and solve linear and quadratic equations and linear inequalities algebraically and investigate nonlinear inequalities using graphs, tables, calculators and computers.
IL.9. Geometry: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.
9.A. Demonstrate and apply geometric concepts involving points, lines, planes and space.
9.A.4a. Construct a model of a three-dimensional figure from a two-dimensional pattern.
9.A.4b. Make perspective drawings, tessellations and scale drawings, with and without the use of technology.
9.B. Identify, describe, classify and compare relationships using points, lines, planes and solids.
9.B.4. Recognize and apply relationships within and among geometric figures.
9.C. Construct convincing arguments and proofs to solve problems.
9.C.4a. Construct and test logical arguments for geometric situations using technology where appropriate.
9.C.4b. Construct and communicate convincing arguments for geometric situations.
9.C.4c. Develop and communicate mathematical proofs (e.g., two-column, paragraph, indirect) and counter examples for geometric statements.
9.D. Use trigonometric ratios and circular functions to solve problems.
9.D.4. Analyze and solve problems involving triangles (e.g., distances which cannot be measured directly) using trigonometric ratios.
IL.10. Data Analysis and Probability: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.
10.A. Organize, describe and make predictions from existing data.
10.A.4a. Represent and organize data by creating lists, charts, tables, frequency distributions, graphs, scatterplots and box-plots.
10.A.4b. Analyze data using mean, median, mode, range, variance and standard deviation of a data set, with and without the use of technology.
10.A.4c. Predict from data using interpolation, extrapolation and trend lines, with and without the use of technology.
10.B. Formulate questions, design data collection methods, gather and analyze data and communicate findings.
10.B.4. Design and execute surveys or experiments, gather data to answer relevant questions, and communicate results and conclusions to an audience using traditional methods and contemporary technology.
10.C. Determine, describe and apply the probabilities of events.
10.C.4a. Solve problems of chance using the principles of probability including conditional settings.
10.C.4b. Design and conduct simulations (e.g., waiting times at restaurant, probabilities of births, likelihood of game prizes), with and without the use of technology.
10.C.4c. Propose and interpret discrete probability distributions, with and without the use of technology.
IL.6. Number Sense: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.
6.A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.
6.A.4. Identify and apply the associative, commutative, distributive and identity properties of real numbers, including special numbers such as pi and square roots.
6.B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.
6.B.4. Select and use appropriate arithmetic operations in practical situations including calculating wages after taxes, developing a budget and balancing a checkbook.
6.C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.
6.C.4. Determine whether exact values or approximations are appropriate (e.g., bid a job, determine gas mileage for a trip).
6.D. Solve problems using comparison of quantities, ratios, proportions and percents.
6.D.4. Solve problems involving recipes or mixtures, financial calculations and geometric similarity using ratios, proportions and percents.
IL.7. Estimation and Measurement: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.
7.A. Measure and compare quantities using appropriate units, instruments and methods.
7.A.4a. Apply units and scales to describe and compare numerical data and physical objects.
7.A.4b. Apply formulas in a wide variety of theoretical and practical real-world measurement applications involving perimeter, area, volume, angle, time, temperature, mass, speed, distance, density and monetary values.
7.B. Estimate measurements and determine acceptable levels of accuracy.
7.B.4. Estimate and measure the magnitude and directions of physical quantities (e.g., velocity, force, slope) using rulers, protractors and other scientific instruments including timers, calculators and computers.
7.C. Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.
7.C.4a. Make indirect measurements, including heights and distances, using proportions (e.g., finding the height of a tower by its shadow).
7.C.4b. Interpret scale drawings and models using maps and blueprints.
7.C.4c. Convert within and between measurement systems and monetary systems using technology where appropriate.
IL.8. Algebra and Analytical Methods: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.
8.A. Describe numerical relationships using variables and patterns.
8.A.4a. Use algebraic methods to convert repeating decimals to fractions.
8.A.4b. Represent mathematical patterns and describe their properties using variables and mathematical symbols.
8.B. Interpret and describe numerical relationships using tables, graphs and symbols.
8.B.4a. Represent algebraic concepts with physical materials, words, diagrams, tables, graphs, equations and inequalities and use appropriate technology.
8.B.4b. Use the basic functions of absolute value, square root, linear, quadratic and step to describe numerical relationships.
8.C. Solve problems using systems of numbers and their properties.
8.C.4a. Analyze and report the effects of changing coefficients, exponents and other parameters on functions and their graphs.
8.C.4b. Apply algebraic properties and procedures with matrices, vectors, functions and sequences using data found in business, industry and consumer situations.
8.D. Use algebraic concepts and procedures to represent and solve problems.
8.D.4. Formulate and solve linear and quadratic equations and linear inequalities algebraically and investigate nonlinear inequalities using graphs, tables, calculators and computers.
IL.9. Geometry: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.
9.A. Demonstrate and apply geometric concepts involving points, lines, planes and space.
9.A.4a. Construct a model of a three-dimensional figure from a two-dimensional pattern.
9.A.4b. Make perspective drawings, tessellations and scale drawings, with and without the use of technology.
9.B. Identify, describe, classify and compare relationships using points, lines, planes and solids.
9.B.4. Recognize and apply relationships within and among geometric figures.
9.C. Construct convincing arguments and proofs to solve problems.
9.C.4a. Construct and test logical arguments for geometric situations using technology where appropriate.
9.C.4b. Construct and communicate convincing arguments for geometric situations.
9.C.4c. Develop and communicate mathematical proofs (e.g., two-column, paragraph, indirect) and counter examples for geometric statements.
9.D. Use trigonometric ratios and circular functions to solve problems.
9.D.4. Analyze and solve problems involving triangles (e.g., distances which cannot be measured directly) using trigonometric ratios.
IL.10. Data Analysis and Probability: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.
10.A. Organize, describe and make predictions from existing data.
10.A.4a. Represent and organize data by creating lists, charts, tables, frequency distributions, graphs, scatterplots and box-plots.
10.A.4b. Analyze data using mean, median, mode, range, variance and standard deviation of a data set, with and without the use of technology.
10.A.4c. Predict from data using interpolation, extrapolation and trend lines, with and without the use of technology.
10.B. Formulate questions, design data collection methods, gather and analyze data and communicate findings.
10.B.4. Design and execute surveys or experiments, gather data to answer relevant questions, and communicate results and conclusions to an audience using traditional methods and contemporary technology.
10.C. Determine, describe and apply the probabilities of events.
10.C.4a. Solve problems of chance using the principles of probability including conditional settings.
10.C.4b. Design and conduct simulations (e.g., waiting times at restaurant, probabilities of births, likelihood of game prizes), with and without the use of technology.
10.C.4c. Propose and interpret discrete probability distributions, with and without the use of technology.
IL.6. Number Sense: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.
6.A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.
6.A.5. Perform addition, subtraction and multiplication of complex numbers and graph the results in the complex plane.
6.B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.
6.B.5. Identify, represent and apply numbers expressed in exponential, logarithmic and scientific notation using contemporary technology.
6.C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.
6.C.5. Determine the level of accuracy needed for computations involving measurement and irrational numbers.
6.D. Solve problems using comparison of quantities, ratios, proportions and percents.
6.D.5. Solve problems involving loans, mortgages and other practical applications involving geometric patterns of growth.
IL.7. Estimation and Measurement: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.
7.A. Measure and compare quantities using appropriate units, instruments and methods.
7.A.5. Apply nonlinear scales (e.g., Richter, decibel, pH) to solve practical problems.
7.B. Estimate measurements and determine acceptable levels of accuracy.
7.B.5. Estimate perimeter, area, volume, and capacity of irregular shapes, regions and solids and explain the reasoning supporting the estimate.
7.C. Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.
7.C.5a. Use dimensional analysis to determine units and check answers in applied measurement problems.
7.C.5b. Determine how changes in one measure may affect other measures (e.g., what happens to the volume and surface area of a cube when the side of the cube is halved).
IL.8. Algebra and Analytical Methods: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.
8.A. Describe numerical relationships using variables and patterns.
8.A.5. Solve mathematical problems involving recursive patterns and use models that employ such relationships.
8.B. Interpret and describe numerical relationships using tables, graphs and symbols.
8.B.5. Use functions including exponential, polynomial, rational, parametric, logarithmic, and trigonometric to describe numerical relationships.
8.C. Solve problems using systems of numbers and their properties.
8.C.5. Use polynomial, exponential, logarithmic and trigonometric functions to model situations.
8.D. Use algebraic concepts and procedures to represent and solve problems.
8.D.5. Formulate and solve nonlinear equations and systems including problems involving inverse variation and exponential and logarithmic growth and decay.
IL.9. Geometry: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.
9.A. Demonstrate and apply geometric concepts involving points, lines, planes and space.
9.A.5. Use geometric figures and their properties to solve problems in the arts, the physical and life sciences and the building trades, with and without the use of technology.
9.B. Identify, describe, classify and compare relationships using points, lines, planes and solids.
9.B.5. Construct and use two- and three-dimensional models of objects that have practical applications (e.g., blueprints, topographical maps, scale models).
9.C. Construct convincing arguments and proofs to solve problems.
9.C.5a. Perform and describe an original investigation of a geometric problem and verify the analysis and conclusions to an audience.
9.C.5b. Apply physical models, graphs, coordinate systems, networks and vectors to develop solutions in applied contexts (e.g., bus routing, areas of irregular shapes, describing forces and other physical quantities).
9.D. Use trigonometric ratios and circular functions to solve problems.
9.D.5. Analyze and solve problems involving periodic patterns (e.g., sound waves, tide variations) using circular functions and communicate results orally and in writing.
IL.10. Data Analysis and Probability: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.
10.A. Organize, describe and make predictions from existing data.
10.A.5. Construct a statistics-based presentation, individually and as members of a team, to communicate and justify the results of a project.
10.B. Formulate questions, design data collection methods, gather and analyze data and communicate findings.
10.B.5. Design a statistical experiment to answer a question about a realistic situation, conduct the experiment, use statistics to interpret the data, and communicate the results, individually and as members of a team.
10.C. Determine, describe and apply the probabilities of events.
10.C.5a. Compute conditional probabilities and the probabilities of independent events.
10.C.5b. Compute probabilities in counting situations involving permutations and combinations.
10.C.5c. Make predictions using probabilities associated with normally distributed events.
IL.6. Number Sense: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.
6.A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.
6.A.5. Perform addition, subtraction and multiplication of complex numbers and graph the results in the complex plane.
6.B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.
6.B.5. Identify, represent and apply numbers expressed in exponential, logarithmic and scientific notation using contemporary technology.
6.C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.
6.C.5. Determine the level of accuracy needed for computations involving measurement and irrational numbers.
6.D. Solve problems using comparison of quantities, ratios, proportions and percents.
6.D.5. Solve problems involving loans, mortgages and other practical applications involving geometric patterns of growth.
IL.7. Estimation and Measurement: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.
7.A. Measure and compare quantities using appropriate units, instruments and methods.
7.A.5. Apply nonlinear scales (e.g., Richter, decibel, pH) to solve practical problems.
7.B. Estimate measurements and determine acceptable levels of accuracy.
7.B.5. Estimate perimeter, area, volume, and capacity of irregular shapes, regions and solids and explain the reasoning supporting the estimate.
7.C. Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.
7.C.5a. Use dimensional analysis to determine units and check answers in applied measurement problems.
7.C.5b. Determine how changes in one measure may affect other measures (e.g., what happens to the volume and surface area of a cube when the side of the cube is halved).
IL.8. Algebra and Analytical Methods: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.
8.A. Describe numerical relationships using variables and patterns.
8.A.5. Solve mathematical problems involving recursive patterns and use models that employ such relationships.
8.B. Interpret and describe numerical relationships using tables, graphs and symbols.
8.B.5. Use functions including exponential, polynomial, rational, parametric, logarithmic, and trigonometric to describe numerical relationships.
8.C. Solve problems using systems of numbers and their properties.
8.C.5. Use polynomial, exponential, logarithmic and trigonometric functions to model situations.
8.D. Use algebraic concepts and procedures to represent and solve problems.
8.D.5. Formulate and solve nonlinear equations and systems including problems involving inverse variation and exponential and logarithmic growth and decay.
IL.9. Geometry: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.
9.A. Demonstrate and apply geometric concepts involving points, lines, planes and space.
9.A.5. Use geometric figures and their properties to solve problems in the arts, the physical and life sciences and the building trades, with and without the use of technology.
9.B. Identify, describe, classify and compare relationships using points, lines, planes and solids.
9.B.5. Construct and use two- and three-dimensional models of objects that have practical applications (e.g., blueprints, topographical maps, scale models).
9.C. Construct convincing arguments and proofs to solve problems.
9.C.5a. Perform and describe an original investigation of a geometric problem and verify the analysis and conclusions to an audience.
9.C.5b. Apply physical models, graphs, coordinate systems, networks and vectors to develop solutions in applied contexts (e.g., bus routing, areas of irregular shapes, describing forces and other physical quantities).
9.D. Use trigonometric ratios and circular functions to solve problems.
9.D.5. Analyze and solve problems involving periodic patterns (e.g., sound waves, tide variations) using circular functions and communicate results orally and in writing.
IL.10. Data Analysis and Probability: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.
10.A. Organize, describe and make predictions from existing data.
10.A.5. Construct a statistics-based presentation, individually and as members of a team, to communicate and justify the results of a project.
10.B. Formulate questions, design data collection methods, gather and analyze data and communicate findings.
10.B.5. Design a statistical experiment to answer a question about a realistic situation, conduct the experiment, use statistics to interpret the data, and communicate the results, individually and as members of a team.
10.C. Determine, describe and apply the probabilities of events.
10.C.5a. Compute conditional probabilities and the probabilities of independent events.
10.C.5b. Compute probabilities in counting situations involving permutations and combinations.
10.C.5c. Make predictions using probabilities associated with normally distributed events.