Illinois State Standards Alignments Grades Three through Eleven


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1 Illinois State Standards Alignments Grades Three through Eleven Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending registration in the United States and other countries. P.O. Box 8036 Wisconsin Rapids, WI Phone: (800) Fax: (715)
2 Illinois State Standards Alignments Standards list with Aligned Product Skills The Standards list with Aligned Product Skills Report is a standardsoriented document showing the entire list of standards for the subject and grade on the left side of the report with the aligning product objectives on the right side. This alignment report shows the breadth of standards coverage for the purpose and focus of this product. Note to Educator...iii Grade Grade Grade Grade Grade Grade Grade by Renaissance Learning, Inc. All rights reserved. No portion of this document may be reproduced, by any process or technique, without the express written consent of Renaissance Learning, Inc. ii
3 P.O. Box 8036 Wisconsin Rapids, WI Phone: (800) Fax: (715) Note to Educator: Thank you for your interest in Renaissance Learning technology. The attached document contains the alignment between the software and/or instructional materials and the skills described in the state standards documentation. At Renaissance Learning, we recognize the impact that the standardsbased reform movement and highstakes standardized testing have on schools, and we share the concerns of educators and administrators that students perform well on highstakes assessments. We hope this report answers your questions regarding the alignment of Renaissance Learning technology and materials to your state standards. If you have any questions about the attached document, please feel free to call us at (800) Sincerely, Renaissance Sales and Funding Staff iii
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5 Grade 3 Illinois, Math, 2005, Grade 3, IL 6  Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions. IL 6A  Representations and Ordering  Read, Write, and Represent Numbers IL Read, write, recognize, Skill Area 3  Numeration and model equivalent representations Concepts of whole numbers and their place values up to 100,000. Skill 13  N08  Hundreds: Identify place value of digits Skill 14  N09  Hundreds: Write numerals in expanded form Skill 17  N13  Thousands: Identify place value of digits Skill 18  N14  Thousands: Write numerals in expanded form Skill 21  N18  Ten thousands, hundred thousands, millions, billions: Identify place value of digits Skill 22  N19  Ten thousands, hundred thousands, millions, billions: Write numerals in expanded form IL Identify and write (in words and standard form) whole numbers up to 100,000. IL Recognize a fraction represented with a pictorial model. IL Represent multiplication as repeated addition.  Order and Compare Numbers IL Order and compare whole numbers up to 10,000 using symbols (>, <, or =) and words (e.g., greater (more) than, less than, equal to, between). Page 1 of 58 Skill Area 3  Numeration Concepts Skill Area 3  Numeration Concepts Skill 3  NA3  Ones: Relate numerals and number words Skill 8  N03  Tens: Relate numeral and number word Skill 12  N07  Hundreds: Relate numeral and number word Skill 16  N12  Thousands: Relate numeral and number word Skill 20  N17  Ten thousands, hundred thousands, millions, billions: Relate numeral and number word Skill 6  N01  Tens: Place numerals (1099) in order of value
6 Grade 3 Illinois, Math, 2005, Grade 3, IL Order and compare decimals expressed using monetary units.  Number Line IL Identify and locate whole numbers and halves on a number line.  Classifications of Numbers IL Solve problems involving descriptions of numbers, including characteristics and relationships (e.g., odd/even, factors/multiples, greater than, less than). IL 6B 6C  Computation, Operations, Estimation, and Properties Skill Area 3  Numeration Concepts Skill Area 3  Numeration Concepts Skill 11  N06  Hundreds: Place numerals in order of value Skill 15  N11  Thousands: Place numerals in order of value Skill 5  N00  Ones: Locate numbers on a number line Skill 6  N01  Tens: Place numerals (1099) in order of value Skill 9  N04  Tens: Identify one more/one less across decades Skill 15  N11  Thousands: Place numerals in order of value  Number Operations IL Solve problems and number sentences involving addition and subtraction with regrouping. Skill Area 4  Computation Processes Skill 8  C08  Addition beyond basic facts with regrouping (2d+1d, 2d+2d) Skill Area 9  Word Problems IL Solve problems involving the value of a collection of bills and coins whose total value is $10.00 or less, and make change. IL Model and apply basic Skill Area 4  Computation multiplication facts (up to 10 10), and Processes apply them to related multiples of 10 (e.g., 3 4=12, 30 4=120). Page 2 of 58 Skill 9  C09  Subtraction beyond basic facts with regrouping (2d1d, 2d 2d) Skill 10  C10  Addition beyond basic facts with double regrouping (3d+2d, 3d+3d) Skill 11  C11  Subtraction beyond basic facts with double regrouping (3d2d, 3d3d) Skill 4  W08  Word problems: Addition beyond basic facts with regrouping (2d+1d, 2d+2d) Skill 5  W09  Word problems: Subtraction beyond basic facts with regrouping (2d1d, 2d2d) Skill 12  C12  Multiplication basic facts
7 Grade 3 Illinois, Math, 2005, Grade 3,  Properties IL Use the inverse relationships between addition and subtraction to complete basic fact sentences and solve problems (e.g., = 8 and 83 = ). IL Solve problems involving the multiplicative identity of one (e.g., 3 1 =3) and the additive identity of zero (e.g., 3+0 =3).  Estimation IL Make estimates appropriate to a given situation with whole numbers. IL 6D  Ratios, Proportions, and Percents  Identify and Express Ratios  Proportional Reasoning  Percents IL 7  Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy. Skill Area 9  Word Problems Skill Area 3  Numeration Concepts Skill Area 7  Measurement Skill 6  W12  Word problems: Multiplication of basic facts Skill 10  N05  Tens: Understand the concept of zero Skill 10  M02  Customary measures: Estimating linear measures IL 7A 7B 7C  Units, Tools, Estimation, and Applications  Elapsed Time IL Solve problems involving simple elapsed time in compound units (e.g., hours, minutes, days).  Measurement Tools IL Select and use appropriate standard units and tools to measure length (to the nearest inch or cm), time (to the nearest minute), and temperature (to the nearest degree).  Area, Perimeter, and Circumference IL Solve problems involving the perimeter of a polygon with given side lengths or a given nonstandard unit (e.g., paperclip). Skill Area 6  Geometry Skill 15  M08  Estimating linear measure in metric units. Skill 11  G03  Perimeter: square Skill 12  G04  Perimeter: rectangle Skill 13  G05  Perimeter: triangle Page 3 of 58
8 Grade 3 Illinois, Math, 2005, Grade 3, IL Solve problems involving the area of a figure when whole and half square units are shown within the figure.  Estimation IL Compare and estimate length (including perimeter), area, and weight/mass using referents.  Volume and Surface Area IL Determine the volume of a solid figure that shows cubic units.  Measurement Conversions IL Solve problems involving simple unit conversions within the same measurement system for time and length.  Indirect Measurements and Scale Drawings IL 8  Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results. IL 8A  Representations, Patterns, and Expressions  Patterns IL Determine a missing term in a pattern (sequence), describe a pattern (sequence), and extend a pattern (sequence) when given a description or pattern (sequence). Skill Area 7  Measurement Skill Area 6  Geometry Skill 9  M01  Customary measures: Inches, feet, yards Skill 9  G01  Identify numeric patterns  Write and Simplify Expressions Skill Area 10  Algebra Skill 1  A00  Can skip count by 2, 5, 10 in ascending order IL Write an expression to represent a given situation.  Evaluate Algebraic Expressions IL 8B  Connections Using Tables, Graphs, and Symbols  Describing Change  Coordinate System  Representations  Inequalities IL 8C 8D  Writing, Interpreting, and Solving Equations  Write Equations and Inequalities Page 4 of 58
9 Grade 3 Illinois, Math, 2005, Grade 3, IL Represent simple mathematical relationships with number sentences (equations and inequalities).  Solve Equations and Inequalities IL Solve onestep addition Skill Area 10  Algebra and subtraction equations that have a missing number or missing operation sign (e.g., 3 + = 5, 6 1 = 7). IL Solve word problems involving unknown quantities. IL 9  Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space. IL 9A  Properties of Single Figures and Coordinate Geometry  Properties of Single Figures IL Identify, describe, and Skill Area 6  Geometry sketch twodimensional shapes (triangles, squares, rectangles, pentagons, hexagons, and octagons) according to the number of sides, length of sides, and number of vertices. IL Identify and describe threeskildimensional shapes (cubes, spheres, Area 6  Geometry cones, cylinders, prisms, and pyramids) according to their characteristics (faces, edges, vertices).  Circles  Coordinate Geometry IL Locate and identify points using numbers and symbols on a grid, and describe how points relate to each other on a grid (e.g., "heart symbol" is 2 units below "sun symbol", point A is 3 units to the right of point B).  Symmetry IL Identify whether or not a Skill Area 6  Geometry figure has a line of symmetry, and sketch or identify the line of symmetry.  Transformations IL Identify images resulting Skill Area 6  Geometry from flips (reflections), slides (translations), or turns (rotations). Page 5 of 58 Skill 2  A01  Simple number sentence Skill 6  GA6  Recognize elements of basic shapes Skill 7  GA7  Identify common solid shapes Skill 5  GA5  Understand basic symmetry Skill 3  GA3  Identify common plane shapes when rotated
10 Grade 3 Illinois, Math, 2005, Grade 3,  Lines, Segments, Rays, and Angles IL Identify parallel lines. Skill Area 6  Geometry Skill 21  G14  Identify parallel lines IL 9B  Relationships Between and Among Multiple Figures  Relationships Between Two and ThreeDimensional Objects IL Identify the twodimensional components of a threedimensional object (e.g., a cube has square faces). IL Identify a threedimensional object from its net.  Composing and Decomposing Figures IL Predict the result of putting shapes together (composing) and taking them apart (decomposing).  Congruency and Similarity IL Identify congruent and similar figures by visual inspection.  Distance IL Determine the distance between two points on the number line in whole numbers. IL 9C  Justifications of Conjectures and Conclusions IL 9D  Trigonometry IL 10  Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability. IL 10A 10B  Data Analysis and Statistics  Read and Interpret Displays IL Read and interpret data represented in a pictograph, bar graph, Venn diagram (with two circles), tally chart, or table.  Complete and Create Displays Skill Area 8  Data Analysis and Statistics Skill 1  SA1  Read tally charts Skill 2  S00  Read simple pictographs Skill 3  S01  Read table Skill 4  S02  Read bar graph Skill 6  S04  Interpret table Skill 7  S05  Interpret bar graph Page 6 of 58
11 Grade 3 Illinois, Math, 2005, Grade 3, IL Complete missing parts of a pictograph, bar graph, tally chart, or table for a given set of data.  Line of Best Fit  Statistics IL Determine the mode, given a set of data or a graph. IL 10C  Probability  Probability IL Classify events using words such as certain, most likely, equally likely, least likely, possible, and impossible. IL Describe the chances associated with a context presented visually, including using the response format "3 out of 4."  Outcomes and Counting Principles Page 7 of 58
12 Grade 4 Illinois, Math, 2005, Grade 4, IL 6  Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions. IL 6A  Representations and Ordering  Read, Write, and Represent Numbers IL Read, write, recognize, Skill Area 3  Numeration and model equivalent representations Concepts of whole numbers and their place values up to 1,000,000. Skill 13  N08  Hundreds: Identify place value of digits Skill 14  N09  Hundreds: Write numerals in expanded form Skill 17  N13  Thousands: Identify place value of digits Skill 18  N14  Thousands: Write numerals in expanded form Skill 21  N18  Ten thousands, hundred thousands, millions, billions: Identify place value of digits Skill 22  N19  Ten thousands, hundred thousands, millions, billions: Write numerals in expanded form IL Identify and write (in words and standard form) whole numbers up to 1,000,000. Skill Area 3  Numeration Concepts IL Read, write, recognize, Skill Area 3  Numeration and model equivalent representations Concepts of fractions; divide regions or sets to represent a fraction. IL Represent multiplication as repeated addition.  Order and Compare Numbers IL Order and compare whole numbers up to 100,000. Skill Area 3  Numeration Concepts Skill 12  N07  Hundreds: Relate numeral and number word Skill 16  N12  Thousands: Relate numeral and number word Skill 23  N21  Fractions and decimals: Convert fraction to equivalent fraction Skill 15  N11  Thousands: Place numerals in order of value Skill 19  N16  Ten thousands, hundred thousands, millions, billions: Place numerals in order of value IL Order and compare decimals through hundredths. Page 8 of 58
13 Grade 4 Illinois, Math, 2005, Grade 4, IL Order and compare fractions having like denominators with or without models.  Number Line IL Identify and locate whole numbers, halves, and fourths on a number line.  Classifications of Numbers IL Solve problems involving descriptions of numbers, including characteristics and relationships (e.g., odd/even, factors/multiples, greater than, less than). IL 6B 6C  Computation, Operations, Estimation, and Properties Skill Area 3  Numeration Concepts Skill Area 3  Numeration Concepts Skill 5  N00  Ones: Locate numbers on a number line Skill 9  N04  Tens: Identify one more/one less across decades  Number Operations IL Solve problems and Skill Area 4  Computation number sentences involving addition Processes and subtraction with regrouping and multiplication (up to threedigit by onedigit). Skill Area 9  Word Problems Skill 8  C08  Addition beyond basic facts with regrouping (2d+1d, 2d+2d) Skill 9  C09  Subtraction beyond basic facts with regrouping (2d1d, 2d 2d) Skill 10  C10  Addition beyond basic facts with double regrouping (3d+2d, 3d+3d) Skill 11  C11  Subtraction beyond basic facts with double regrouping (3d2d, 3d3d) Skill 14  C14  Multiplication beyond basic facts, no regrouping (2dx1d) Skill 18  C18  Addition of whole numbers: any difficulty Skill 19  C19  Subtraction whole numbers: any difficulty Skill 4  W08  Word problems: Addition beyond basic facts with regrouping (2d+1d, 2d+2d) Skill 5  W09  Word problems: Subtraction beyond basic facts with regrouping (2d1d, 2d2d) Skill 8  W14  Word problems: Multiplication beyond basic facts, no regrouping (2dx1d) Skill 12  W18  Word problems: Addition of whole numbers, any difficulty Page 9 of 58
14 Grade 4 Illinois, Math, 2005, Grade 4, IL Solve problems involving the value of a collection of bills and coins whose total value is $ or less, and make change. IL Model and apply basic multiplication and division facts (up to 12 12), and apply them to related multiples of 10 (e.g., 3 9=27, 30 9=270, 6 3=2, 600 3=200). Skill 13  W19  Word problems: Subtraction of whole numbers, any difficulty IL Model situations involving addition and subtraction of fractions with like denominators.  Properties IL Solve problems involving the commutative and distributive properties of operations on whole numbers [e.g., = 7 + 8, 27 5 = (20 5) + (7 5)]. IL Use the inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences and solve problems (e.g., 4 3=12, 12 3= ).  Estimation IL Make estimates appropriate to a given situation with whole numbers. IL 6D  Ratios, Proportions, and Percents  Identify and Express Ratios  Proportional Reasoning  Percents IL 7  Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy. IL 7A 7B 7C  Units, Tools, Estimation, and Applications  Elapsed Time IL Solve problems involving elapsed time in compound units (e.g., 1 hour and 40 minutes) that occur in the same half day (a.m. only or p.m. only). Page 10 of 58 Skill Area 7  Measurement Skill 10  M02  Customary measures: Estimating linear measures Skill 15  M08  Estimating linear measure in metric units.
15 Grade 4 Illinois, Math, 2005, Grade 4,  Measurement Tools IL Select and use appropriate standard units and tools to measure length (to the nearest ½ inch or ½ cm), time, and temperature.  Area, Perimeter, and Circumference IL Solve problems involving the perimeter of a polygon with given side lengths and the area of a square, rectangle, or irregular shape composed of rectangles using diagrams, models, and grids or by measuring (may include sketching a figure from its description).  Estimation IL Compare and estimate length (including perimeter), area, volume, and weight/mass using referents.  Volume and Surface Area IL Determine the volume of a solid figure that shows cubic units.  Measurement Conversions IL Solve problems involving unit conversions within the same measurement system for time, length, and weight/mass.  Indirect Measurements and Scale Drawings IL 8  Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results. IL 8A  Representations, Patterns, and Expressions  Patterns IL Determine a missing term in a pattern (sequence), describe a pattern (sequence), and extend a pattern (sequence) when given a description or pattern (sequence).  Write and Simplify Expressions Page 11 of 58 Skill Area 6  Geometry Skill Area 6  Geometry Skill 11  G03  Perimeter: square Skill 12  G04  Perimeter: rectangle Skill 13  G05  Perimeter: triangle Skill 14  G06  Area: square Skill 9  G01  Identify numeric patterns
16 Grade 4 Illinois, Math, 2005, Grade 4, IL Write an expression using letters or symbols to represent an unknown quantity.  Evaluate Algebraic Expressions IL Evaluate algebraic expressions with a whole number variable value (e.g., evaluate 3 + m when m = 4). IL 8B  Connections Using Tables, Graphs, and Symbols  Describing Change IL Identify or represent situations with welldefined patterns using words, tables, and graphs (e.g., represent temperature and time in a line graph).  Coordinate System  Representations IL Translate between different representations (table, written, or pictorial) of whole number relationships.  Inequalities IL 8C 8D  Writing, Interpreting, and Solving Equations  Write Equations and Inequalities IL Represent simple mathematical relationships with number sentences (equations and inequalities).  Solve Equations and Inequalities IL Solve for the unknown in an equation with one operation (e.g., 10= +3+2, 1=3). IL Solve word problems involving unknown quantities. IL 9  Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space. IL 9A  Properties of Single Figures and Coordinate Geometry  Properties of Single Figures Skill Area 10  Algebra Skill Area 10  Algebra Skill Area 9  Word Problems Skill 3  A02  Translate word problem to equation Skill 2  A01  Simple number sentence Skill 31  W42  Word problems: Ratios Page 12 of 58
17 Grade 4 Illinois, Math, 2005, Grade 4, IL Identify, describe, and sketch twodimensional shapes (triangles, quadrilaterals, pentagons, hexagons, and octagons) according to the number of sides, length of sides, number of vertices, and right angles. IL Identify and describe threeskildimensional shapes (cubes, spheres, Area 6  Geometry cones, cylinders, prisms, and pyramids) according to their characteristics (faces, edges, vertices). IL Differentiate between polygons and nonpolygons  Circles  Coordinate Geometry IL Graph, locate, identify points, and describe paths using ordered pairs (first quadrant).  Symmetry IL Identify whether or not a figure has one or more lines of symmetry, and sketch or identify all lines of symmetry.  Transformations IL Identify images resulting from flips (reflections), slides (translations), or turns (rotations). Skill 7  GA7  Identify common solid shapes  Lines, Segments, Rays, and Angles IL Identify and sketch parallel Skill Area 6  Geometry and perpendicular lines. IL Identify and sketch right angles. IL 9B  Relationships Between and Among Multiple Figures  Relationships Between Two and ThreeDimensional Objects IL Identify the twodimensional components of a threedimensional object. IL Identify a threedimensional object from its net.  Composing and Decomposing Figures IL Predict the result of composing or decomposing shapes or figures. Page 13 of 58 Skill 21  G14  Identify parallel lines Skill 23  G16  Identify perpendicular lines
18 Grade 4 Illinois, Math, 2005, Grade 4,  Congruency and Similarity IL Identify congruent and similar figures by visual inspection.  Distance IL Determine the distance between two points on the number line in whole numbers. IL 9C  Justifications of Conjectures and Conclusions IL 9D  Trigonometry IL 10  Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability. IL 10A 10B  Data Analysis and Statistics  Read and Interpret Displays IL Read and interpret data represented in a pictograph, bar graph, line (dot) plot, Venn diagram (with two circles), tally chart, table, line graph, or circle graph.  Complete and Create Displays IL Create a pictograph, bar graph, tally chart, or table for a given set of data.  Line of Best Fit  Statistics IL Determine the mode and range, given a set of data or a graph. IL 10C  Probability  Probability IL Classify events using words such as certain, most likely, equally likely, least likely, possible, and impossible. IL Describe the chances associated with a context presented visually, including using the response format "3 out of 4" or ¾.  Outcomes and Counting Principles Skill Area 8  Data Analysis and Statistics Skill 2  S00  Read simple pictographs Skill 4  S02  Read bar graph Skill 6  S04  Interpret table Skill 7  S05  Interpret bar graph Skill 8  S06  Interpret pie graph Page 14 of 58
19 Grade 5 Illinois, Math, 2005, Grade 5, IL 6  Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions. IL 6A  Representations and Ordering  Read, Write, and Represent Numbers IL Read, write, recognize, Skill Area 3  Numeration and model equivalent representations Concepts of whole numbers and their place values up to 100,000,000. Skill 21  N18  Ten thousands, hundred thousands, millions, billions: Identify place value of digits Skill 22  N19  Ten thousands, hundred thousands, millions, billions: Write numerals in expanded form IL Read, write, recognize, model, and interpret numerical expressions from a given description or situation. IL Read, write, recognize, Skill Area 3  Numeration and model equivalent representations Concepts of fractions, including improper fractions and mixed numbers. IL Recognize, translate between, and model multiple representations of decimals, fractions less than one (halves, quarters, fifths, and tenths), and percents (0%, 25%, 50%, 75%, and 100%). IL Read, write, recognize, and model decimals and their place values through thousandths. IL Represent multiplication as repeated addition.  Order and Compare Numbers IL Order and compare whole numbers up to 1,000,000. Skill Area 3  Numeration Concepts Skill Area 3  Numeration Concepts Skill 23  N21  Fractions and decimals: Convert fraction to equivalent fraction Skill 30  N28  Fractions and decimals: Convert improper fraction to mixed number Skill 27  N25  Fractions and decimals: Identify place value of digits in decimals Skill 19  N16  Ten thousands, hundred thousands, millions, billions: Place numerals in order of value IL Order and compare decimals through hundredths. Page 15 of 58
20 Grade 5 Illinois, Math, 2005, Grade 5, IL Order and compare fractions having like or unlike denominators with or without models.  Number Line IL Identify and locate whole numbers, halves, fourths, and thirds on a number line.  Classifications of Numbers IL Solve problems involving descriptions of numbers, including characteristics and relationships (e.g., odd/even, factors/multiples, greater than, less than, square numbers). IL 6B 6C  Computation, Operations, Estimation, and Properties Skill Area 3  Numeration Concepts Skill 41  N39  Advanced concepts: Can determine greatest common factor Skill 42  N40  Advanced concepts: Can determine least common multiple  Number Operations IL Solve problems and number sentences involving addition, subtraction, multiplication, and division using whole numbers. Skill Area 4  Computation Processes Skill 10  C10  Addition beyond basic facts with double regrouping (3d+2d, 3d+3d) Page 16 of 58 Skill Area 9  Word Problems Skill 11  C11  Subtraction beyond basic facts with double regrouping (3d2d, 3d3d) Skill 16  C16  Multiplication with regrouping (2dx1d, 2dx2d) Skill 17  C17  Division with remainders (2d/1d, 3d/1d) Skill 18  C18  Addition of whole numbers: any difficulty Skill 19  C19  Subtraction whole numbers: any difficulty Skill 20  C21  Division of whole numbers: any difficulty Skill 4  W08  Word problems: Addition beyond basic facts with regrouping (2d+1d, 2d+2d) Skill 5  W09  Word problems: Subtraction beyond basic facts with regrouping (2d1d, 2d2d) Skill 8  W14  Word problems: Multiplication beyond basic facts, no regrouping (2dx1d) Skill 9  W15  Word problems: Division beyond basic facts, no remainders (2d/1d)
21 Grade 5 Illinois, Math, 2005, Grade 5, Skill 10  W16  Word problems: Multiplication with regrouping (2dx1d, 2dx2d) Skill 11  W17  Word problems: Division with remainders (2d/1d, 3d/1d) Skill 12  W18  Word problems: Addition of whole numbers, any difficulty Skill 13  W19  Word problems: Subtraction of whole numbers, any difficulty Skill 14  W20  Word problems: Multiplication of whole numbers, any difficulty Skill 15  W21  Word problems: Division of whole numbers, any IL Solve problems and number sentences involving addition and subtraction of decimals through hundredths (with or without monetary labels). IL Model situations involving addition and subtraction of fractions.  Properties IL Solve problems involving the commutative, distributive, and identity properties of operations on whole numbers (e.g., = 46 37, 270 5= (200 5) + (70 5)].  Estimation IL Make estimates appropriate to a given situation with whole numbers, fractions, and decimals. IL 6D  Ratios, Proportions, and Percents  Identify and Express Ratios IL Identify and express ratios using appropriate notation (i.e., a/b, a to b), and identify equivalent ratios. Skill Area 4  Computation Processes Skill Area 9  Word Problems difficulty Skill 31  C33  Addition of decimals, place change (e.g ) Skill 32  C35  Subtraction of decimals, place change (e.g. 5.4) Skill 23  W33  Word problems: Addition of decimals, place change (e.g ) Skill 24  W35  Word problems: Subtraction of decimals, place change (e.g. 5.4) Page 17 of 58
22 Grade 5 Illinois, Math, 2005, Grade 5,  Proportional Reasoning IL Solve problems involving proportional relationships, including unit pricing (e.g., one apple costs 20, so four apples cost 80 ).  Percents IL Read, write, recognize, and model percents (0%, 25%, 50%, 75%, and 100%). IL 7  Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy. IL 7A 7B 7C  Units, Tools, Estimation, and Applications  Elapsed Time IL Solve problems involving elapsed time in compound units.  Measurement Tools IL Select and use appropriate standard units and tools to measure length (to the nearest ¼ inch or mm), mass/weight, capacity, and angles. Skill Area 4  Computation Processes Skill Area 9  Word Problems Skill 38  C41  Proportions Skill 39  C42  Ratios Skill 31  W42  Word problems: Ratios  Area, Perimeter, and Circumference IL Solve problems involving the perimeter and area of a triangle, rectangle, or irregular shape using diagrams, models, and grids or by measuring or using given formulas (may include sketching a figure from its description). Skill Area 6  Geometry Skill 12  G04  Perimeter: rectangle  Estimation IL Compare and estimate length (including perimeter), area, volume, weight/mass, and angles (0 to 180 ) using referents.  Volume and Surface Area IL Determine the volume of a right rectangular prism using an appropriate formula or strategy.  Measurement Conversions Page 18 of 58 Skill Area 6  Geometry Skill 13  G05  Perimeter: triangle Skill 15  G07  Area: rectangle Skill 16  G08  Area: right triangle Skill 18  G10  Volume: rectangular prism
23 Grade 5 Illinois, Math, 2005, Grade 5, IL Solve problems involving unit conversions within the same measurement system for time, length, and weight/mass, including compound units (e.g., 5ft 5in, 2lbs 2oz).  Indirect Measurements and Scale Drawings IL Solve problems involving map interpretation (e.g., one inch represents five miles, so two inches represent ten miles). IL 8  Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results. IL 8A  Representations, Patterns, and Expressions  Patterns IL Determine a missing term in a sequence, extend a sequence, and identify errors in a sequence when given a description or sequence. IL Construct and identify a rule that can generate the terms of a given sequence.  Write and Simplify Expressions IL Write an expression using variables to represent unknown quantities.  Evaluate Algebraic Expressions Skill Area 7  Measurement Skill Area 6  Geometry Skill 9  M01  Customary measures: Inches, feet, yards Skill 9  G01  Identify numeric patterns IL Evaluate algebraic expressions with a whole number variable value (e.g., evaluate m + m + 3 when m = 4). IL 8B  Connections Using Tables, Graphs, and Symbols  Describing Change IL Demonstrate, in simple situations, how a change in one quantity results in a change in another quantity (e.g., inputoutput tables).  Coordinate System  Representations IL Translate between different representations (table, written, or pictorial) of whole number relationships. Page 19 of 58
24 Grade 5 Illinois, Math, 2005, Grade 5,  Inequalities IL 8C 8D  Writing, Interpreting, and Solving Equations  Write Equations and Inequalities IL Represent problems with equations and inequalities.  Solve Equations and Inequalities IL Solve for the unknown in an equation with one operation (e.g., 2+n=20, n 2=6). IL Solve word problems involving unknown quantities. IL 9  Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space. IL 9A  Properties of Single Figures and Coordinate Geometry  Properties of Single Figures IL Classify, describe, and sketch twodimensional shapes (triangles, quadrilaterals, pentagons, hexagons, and octagons) according to the number of sides, length of sides, number of vertices, and interior angles (right, acute, obtuse). IL Identify and describe threeskildimensional shapes (cubes, spheres, Area 6  Geometry cones, cylinders, prisms, and pyramids) according to their characteristics (faces, edges, vertices). IL Solve problems using properties of triangles (e.g., sum of interior angles of a triangle is 180 ).  Circles IL Identify, describe, and sketch circles, including radius and diameter.  Coordinate Geometry IL Graph, locate, identify points, and describe paths using ordered pairs (first quadrant).  Symmetry IL Identify whether or not a figure has one or more lines of symmetry, and sketch or identify all lines of symmetry. Page 20 of 58 Skill 7  GA7  Identify common solid shapes
25 Grade 5 Illinois, Math, 2005, Grade 5,  Transformations IL Identify, describe, and predict results of reflections, translations, and rotations of twodimensional shapes.  Lines, Segments, Rays, and Angles IL Identify and sketch parallel, perpendicular, and intersecting lines. Skill Area 6  Geometry Skill 21  G14  Identify parallel lines Skill 23  G16  Identify perpendicular IL Identify and sketch acute, Skill Area 6  Geometry right, and obtuse angles. IL 9B  Relationships Between and Among Multiple Figures  Relationships Between Two and ThreeDimensional Objects IL Identify the twodimensional components of a threedimensional object. IL Identify a threedimensional object from its net.  Composing and Decomposing Figures IL Predict the result of composing or decomposing shapes or figures.  Congruency and Similarity IL Identify congruent and similar figures by visual inspection. IL Determine if figures are similar, and identify relationships between corresponding parts of similar figures.  Distance IL Determine the distance between two points on a horizontal or vertical number line in whole numbers. IL 9C  Justifications of Conjectures and Conclusions IL 9D  Trigonometry IL 10  Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability. IL 10A 10B  Data Analysis and Statistics  Read and Interpret Displays lines Skill 28  G21  Classify angles (obtuse, etc.) Page 21 of 58
26 Grade 5 Illinois, Math, 2005, Grade 5, IL Read, interpret, and make predictions from data represented in a pictograph, bar graph, line (dot) plot, Venn diagram (with two circles), chart/table, line graph, or circle graph.  Complete and Create Displays IL Create a pictograph, bar graph, chart/table, or line graph for a given set of data.  Line of Best Fit  Statistics IL Determine the mode, range, median (with an odd number of data points), and mean, given a set of data or a graph. IL 10C  Probability  Probability IL Solve problems involving the probability of a simple event, including representing the probability as a fraction between zero and one.  Outcomes and Counting Principles IL Apply the fundamental counting principle in a simple problem (e.g., How many different combinations of onescoop ice cream cones can be made with 3 flavors and 2 types of cones?). Skill Area 8  Data Analysis and Statistics Skill Area 8  Data Analysis and Statistics Skill Area 8  Data Analysis and Statistics Skill 3  S01  Read table Skill 4  S02  Read bar graph Skill 5  S03  Read pie graph Skill 6  S04  Interpret table Skill 7  S05  Interpret bar graph Skill 8  S06  Interpret pie graph Skill 9  S07  Statistics: Mean Skill 11  S11  Probability: Simple Page 22 of 58
27 Grade 6 Illinois, Math, 2005, Grade 6, IL 6  Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions. IL 6A  Representations and Ordering  Read, Write, and Represent Numbers IL Read, write, recognize, Skill Area 3  Numeration and model equivalent representations Concepts of whole numbers and their place values. Skill 20  N17  Ten thousands, hundred thousands, millions, billions: Relate numeral and number word Skill 21  N18  Ten thousands, hundred thousands, millions, billions: Identify place value of digits Skill 22  N19  Ten thousands, hundred thousands, millions, billions: Write numerals in expanded form IL Read, write, recognize, model, and interpret numerical expressions from a given description or situation. IL Read, write, recognize, Skill Area 3  Numeration and model equivalent representations Concepts of fractions, including improper fractions and mixed numbers. IL Recognize, translate between, and apply multiple representations of decimals, fractions, percents (less than 100%), and mixed numbers (halves, quarters, fifths, and tenths). Skill Area 3  Numeration Concepts Skill 23  N21  Fractions and decimals: Convert fraction to equivalent fraction Skill 30  N28  Fractions and decimals: Convert improper fraction to mixed number Skill 24  N22  Fractions and decimals: Convert fraction to decimal Skill 25  N23  Fractions and decimals: Convert decimal to fraction IL Read, write, recognize, Skill Area 3  Numeration and model equivalent representations Concepts of decimals and their place values through thousandths. Page 23 of 58 Skill 32  N30  Fractions and decimals: Relate decimals to percents Skill 26  N24  Fractions and decimals: Read word names for decimals to thousandths
28 Grade 6 Illinois, Math, 2005, Grade 6, IL Represent repeated factors using exponents.  Order and Compare Numbers IL Order and compare whole numbers. Skill Area 3  Numeration Concepts Skill 27  N25  Fractions and decimals: Identify place value of digits in decimals Skill 19  N16  Ten thousands, hundred thousands, millions, billions: Place numerals in order of value IL Order and compare decimals through thousandths. IL Order and compare fractions and mixed numbers having like or unlike denominators.  Number Line IL Identify and locate decimals, fractions, and mixed numbers on a number line.  Classifications of Numbers IL Solve problems involving descriptions of numbers, including characteristics and relationships (e.g., odd/even, factors/multiples, greater than, less than, square numbers, primes). IL 6B 6C  Computation, Operations, Estimation, and Properties Skill Area 3  Numeration Concepts Skill Area 3  Numeration Concepts Skill 28  N26  Fractions and decimals: Identify position of decimals on number line Skill 29  N27  Fractions and decimals: Identify position of fractions on number line Skill 40  N38  Advanced concepts: Knows meaning of primes and composites Skill 41  N39  Advanced concepts: Can determine greatest common factor Skill 42  N40  Advanced concepts: Can determine least common multiple  Number Operations IL Solve problems and number sentences involving addition, subtraction, multiplication, and division using whole numbers. Page 24 of 58 Skill Area 4  Computation Processes Skill 16  C16  Multiplication with regrouping (2dx1d, 2dx2d) Skill 17  C17  Division with remainders (2d/1d, 3d/1d) Skill 18  C18  Addition of whole numbers: any difficulty Skill 19  C19  Subtraction whole numbers: any difficulty Skill 20  C21  Division of whole numbers: any difficulty
29 Grade 6 Illinois, Math, 2005, Grade 6, Skill Area 9  Word Problems Skill 9  W15  Word problems: Division beyond basic facts, no remainders (2d/1d) Skill 10  W16  Word problems: Multiplication with regrouping (2dx1d, 2dx2d) Skill 11  W17  Word problems: Division with remainders (2d/1d, 3d/1d) Skill 12  W18  Word problems: Addition of whole numbers, any difficulty Skill 13  W19  Word problems: Subtraction of whole numbers, any difficulty Skill 14  W20  Word problems: Multiplication of whole numbers, any difficulty Skill 15  W21  Word problems: Division of whole numbers, any difficulty Skill 22  W2S  Word problems: IL Solve problems and number sentences involving addition, subtraction, and multiplication of decimals. IL Solve problems involving addition and subtraction of fractions and mixed numbers, and express answers in simplest form. Skill Area 4  Computation Processes Skill Area 9  Word Problems Skill Area 4  Computation Processes Twostep Skill 31  C33  Addition of decimals, place change (e.g ) Skill 32  C35  Subtraction of decimals, place change (e.g. 5.4) Skill 33  C36  Multiplication of decimals Skill 23  W33  Word problems: Addition of decimals, place change (e.g ) Skill 24  W35  Word problems: Subtraction of decimals, place change (e.g. 5.4) Skill 25  W36  Word problems: Multiplication of decimals Skill 21  C22  Addition of fractions: like single digit denominators Skill 22  C23  Subtraction of fractions: like single digit denominators Skill 23  C24  Addition of fractions: unlike single digit denominators Page 25 of 58 Skill 24  C25  Subtraction of fractions: unlike single digit denominators
30 Grade 6 Illinois, Math, 2005, Grade 6, Skill 27  C28  Addition of mixed numbers Skill 28  C29  Subtraction of mixed IL Identify and apply order of operations to simplify numeric expressions involving whole numbers.  Properties IL Solve problems involving the commutative, distributive, and associative properties of operations on whole numbers [e.g., (5 7) 2 = 5 (7 2)].  Estimation IL Make estimates appropriate to a given situation, and analyze what effect the estimation method used has on the accuracy of results. IL 6D  Ratios, Proportions, and Percents  Identify and Express Ratios IL Identify and express ratios using appropriate notation (i.e., a/b, a to b, a:b), identify equivalent ratios, and explain ratios that represent a given situation.  Proportional Reasoning IL Solve problems involving proportional relationships, including unit pricing (e.g., seven apples cost $1.40, so nine apples cost $1.80). Skill Area 9  Word Problems Skill Area 4  Computation Processes numbers Skill 18  W24  Word problems: Addition of fractions, unlike single digit denominators Skill 19  W25  Word problems: Subtraction of fractions, unlike single digit denominators Skill 20  W28  Word problems: Addition of mixed numbers Skill 21  W29  Word problems: Subtraction of mixed numbers Skill 38  C41  Proportions  Percents IL Read, write, recognize, and model percents from 0% to 100%. Skill Area 9  Word Problems Skill 30  W41  Word problems: Proportions Page 26 of 58
31 Grade 6 Illinois, Math, 2005, Grade 6, IL Solve number sentences and problems involving percents. Skill Area 5  Estimation Skill 17  E38  Estimation problems: Percent A (10 is what % of 40) Skill 18  E39  Estimation problems: Percent B (20% of 50 is what) Skill 19  E40  Estimation problems: Percent C (30 is 50% of what) IL 7  Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy. IL 7A 7B 7C  Units, Tools, Estimation, and Applications  Elapsed Time  Measurement Tools IL Select and use appropriate standard units and tools to measure length, mass/weight, capacity, and angles. Skill Area 9  Word Problems Skill Area 7  Measurement Skill 27  W38  Word problems: Percent A (10 is what % of 40) Skill 28  W39  Word problems: Percent B (20% of 50 is what) Skill 29  W40  Word problems: Percent C (30 is 50% of what) Skill 15  M08  Estimating linear measure in metric units.  Area, Perimeter, and Circumference IL Solve problems involving Skill Area 6  Geometry the perimeter and area of a triangle, parallelogram, or irregular shape using diagrams, models, and grids or by measuring or using given formulas (may include sketching a figure from its description).  Estimation IL Compare and estimate length (including perimeter), area, volume, weight/mass, and angles (0 to 180 ) using referents.  Volume and Surface Area IL Determine the volume of a right rectangular prism using an appropriate formula or strategy.  Measurement Conversions Page 27 of 58 Skill Area 6  Geometry Skill 14  G06  Area: square Skill 15  G07  Area: rectangle Skill 16  G08  Area: right triangle Skill 18  G10  Volume: rectangular prism
32 Grade 6 Illinois, Math, 2005, Grade 6, IL Solve problems involving unit conversions within the same measurement system for time, length, and weight/mass, including compound units (e.g., 5ft 5in, 2lbs 2oz).  Indirect Measurements and Scale Drawings IL Solve problems involving scale drawings and maps. IL 8  Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results. IL 8A  Representations, Patterns, and Expressions  Patterns IL Determine a missing term in a sequence, extend a sequence, and construct and identify a rule that can generate the terms of a given sequence (e.g., 3, 6, 9,... is explained by the rule 3n, for n is greater than or equal to 1).  Write and Simplify Expressions IL Write an expression using variables to represent unknown quantities.  Evaluate Algebraic Expressions IL Evaluate algebraic expressions with up to two whole number variable values (e.g., evaluate 3m + n + 3 when m = 4 and n = 2). IL 8B  Connections Using Tables, Graphs, and Symbols  Describing Change IL Determine a rule having two operations from an inputoutput table (e.g., multiply by 3 and add 2).  Coordinate System IL Select a table of values that satisfies a linear equation, and recognize the ordered pairs on a rectangular coordinate system.  Representations Page 28 of 58
33 Grade 6 Illinois, Math, 2005, Grade 6, IL Translate between different representations (table, written, or pictorial) of whole number relationships.  Inequalities IL Identify graphs of inequalities on a number line. IL 8C 8D  Writing, Interpreting, and Solving Equations  Write Equations and Inequalities Skill Area 10  Algebra Skill 10  A09  Graph linear inequalities IL Represent problems with equations and inequalities.  Solve Equations and Inequalities Skill Area 10  Algebra Skill 3  A02  Translate word problem to equation IL Solve for the unknown in an equation with one operation (e.g., 8x = 24, m 2=25). IL Solve word problems involving unknown quantities. IL 9  Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space. IL 9A  Properties of Single Figures and Coordinate Geometry  Properties of Single Figures IL Classify, describe, and sketch regular and irregular twodimensional shapes according to the number of sides, length of sides, number of vertices, and interior angles. IL Identify and describe threedimensional shapes (cubes, spheres, cones, cylinders, prisms, and pyramids) according to their characteristics (faces, edges, vertices). IL Solve problems using Skill Area 6  Geometry properties of triangles and quadrilaterals (e.g., sum of interior angles of a quadrilateral is 360 ).  Circles IL Identify, describe, and sketch circles, including radius, diameter, and chord.  Coordinate Geometry IL Graph, locate, identify points, describe paths, and plot figures using ordered pairs (first quadrant). Page 29 of 58 Skill 29  G22  Using parts of a triangle
34 Grade 6 Illinois, Math, 2005, Grade 6,  Symmetry  Transformations IL Identify, describe, and predict results of reflections, translations, and rotations of twodimensional shapes.  Lines, Segments, Rays, and Angles IL Identify and sketch parallel, perpendicular, and intersecting lines. Skill Area 6  Geometry IL Identify and sketch acute, Skill Area 6  Geometry right, and obtuse angles. IL 9B  Relationships Between and Among Multiple Figures  Relationships Between Two and ThreeDimensional Objects IL Identify a threedimensional object from its net.  Composing and Decomposing Figures IL Recognize which attributes (such as shape, perimeter, and area) change or don't change when plane figures are composed, decomposed, or rearranged.  Congruency and Similarity IL Identify congruent and similar figures by visual inspection. IL Determine if figures are similar, and identify relationships between corresponding parts of similar figures.  Distance IL Determine the distance between two points on a horizontal or vertical number line. IL 9C  Justifications of Conjectures and Conclusions IL 9D  Trigonometry IL 10  Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability. Skill 21  G14  Identify parallel lines Skill 22  G15  Identify intersecting lines Skill 23  G16  Identify perpendicular lines Skill 28  G21  Classify angles (obtuse, etc.) IL 10A 10B  Data Analysis and Statistics Page 30 of 58
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