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 standards-based reform movement and high-stakes standardized testing have on schools, and we share the concerns of educators and administrators that students perform well on high-stakes 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 (10-99) 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 (10-99) 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 (2d-1d, 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 (3d-2d, 3d-3d) 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 (2d-1d, 2d-2d) 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 8-3 = ). 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 non-standard 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 one-step 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 two-dimensional 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 three-skildimensional 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 Three-Dimensional 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 three-digit 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 (2d-1d, 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 (3d-2d, 3d-3d) 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 (2d-1d, 2d-2d) 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 well-defined 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 two-dimensional 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 three-skildimensional shapes (cubes, spheres, Area 6 - Geometry cones, cylinders, prisms, and pyramids) according to their characteristics (faces, edges, vertices). IL Differentiate between polygons and non-polygons - 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 Three-Dimensional 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 (3d-2d, 3d-3d) 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 (2d-1d, 2d-2d) 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., input-output 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 two-dimensional 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 three-skildimensional 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 Three-Dimensional 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 one-scoop 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 Two-step 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 input-output 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 Three-Dimensional 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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