Illinois State Standards Alignments Grades Three through Six

Transcription

1 Illinois State Standards Alignments Grades Three through Six 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 The 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 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 MathFacts 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, and model equivalent representations of whole numbers and their place values up to 100,000. 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). 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 - Number Operations IL Solve problems and number sentences involving addition and subtraction with regrouping. Page 1 of 30

6 MathFacts Grade 3 Illinois, Math, 2005, Grade 3, 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 Domain 5 - Math Skills - multiplication facts (up to 10 10), and Multiplication (MS) apply them to related multiples of 10 (e.g., 3 4=12, 30 4=120). Skillset 1 - MS17 Multiplication by 0,1 (Multiplying 0 or 1 by numbers 0-10) Skillset 2 - MS18 Multiplication by 2,3 (Multiplying 2 or 3 by numbers 0-10) Skillset 3 - MS19 Multiplication by 4,5 (Multiplying 4 or 5 by numbers 0-10) Skillset 4 - MS20 Alternate Forms: Multiplication by 0 to 5 (Multiplying 0-5 by numbers 0-10 with the Skillset 5 - MS21 Multiplication by 6,7 (Multiplying 6 or 7 by numbers 0-10) Skillset 6 - MS22 Multiplication by 8,9 (Multiplying 8-9 by numbers 0-10) Skillset 7 - MS23 Multiplication by 10 (Multiplying 10 by numbers 0-10) - Properties IL Use the inverse relationships between addition and subtraction to complete basic fact sentences and solve problems (e.g., = 8 and 8-3 = ). Domain 3 - Math Skills - Addition (MS) Domain 4 - Math Skills - Subtraction (MS) Skillset 8 - MS24 Alternate Forms: Multiplication by 6 to 10 (Multiplying 6-10 by numbers 0-10 with the Skillset 4 - MS04 Alternate Forms: Addition of 0 to 5 (Adding 0-5 to numbers 0-10 with the unknown in the operand or answer Skillset 8 - MS08 Alternate Forms: Addition of 6 to 10 (Adding 6-10 to numbers 0-10 with the unknown in the operand or answer Skillset 4 - MS12 Alternate Forms: Subtraction of 0 to 5 (Subtracting 0-5 from numbers 0-15 with the Page 2 of 30

7 MathFacts Grade 3 Illinois, Math, 2005, Grade 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. 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). 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 Skillset 8 - MS16 Alternate Forms: Subtraction of 6 to 10 (Subtracting 6-10 from numbers 6-20 with the Page 3 of 30

8 MathFacts Grade 3 Illinois, Math, 2005, Grade 3, 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). - Write and Simplify Expressions 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 IL Represent simple mathematical relationships with number sentences (equations and inequalities). - Solve Equations and Inequalities IL Solve one-step addition Domain 3 - Math Skills - Addition and subtraction equations that have a (MS) missing number or missing operation sign (e.g., 3 + = 5, 6 1 = 7). Skillset 4 - MS04 Alternate Forms: Addition of 0 to 5 (Adding 0-5 to numbers 0-10 with the unknown in the operand or answer Page 4 of 30

9 MathFacts Grade 3 Illinois, Math, 2005, Grade 3, Skillset 8 - MS08 Alternate Forms: Addition of 6 to 10 (Adding 6-10 to numbers 0-10 with the unknown in the operand or answer 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 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 threedimensional shapes (cubes, spheres, 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 figure has a line of symmetry, and sketch or identify the line of symmetry. - Transformations Page 5 of 30 Domain 4 - Math Skills - Subtraction (MS) Skillset 4 - MS12 Alternate Forms: Subtraction of 0 to 5 (Subtracting 0-5 from numbers 0-15 with the Skillset 8 - MS16 Alternate Forms: Subtraction of 6 to 10 (Subtracting 6-10 from numbers 6-20 with the

10 MathFacts Grade 3 Illinois, Math, 2005, Grade 3, IL Identify images resulting from flips (reflections), slides (translations), or turns (rotations). - Lines, Segments, Rays, and Angles IL 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 IL Complete missing parts of a pictograph, bar graph, tally chart, or table for a given set of data. - Line of Best Fit - Statistics Page 6 of 30

11 MathFacts Grade 3 Illinois, Math, 2005, Grade 3, 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 30

12 MathFacts 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, and model equivalent representations of whole numbers and their place values up to 1,000,000. IL Identify and write (in words and standard form) whole numbers up to 1,000,000. IL Read, write, recognize, and model equivalent representations 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. IL Order and compare decimals through hundredths. 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 - Number Operations IL Solve problems and number sentences involving addition and subtraction with regrouping and multiplication (up to three-digit by onedigit). Page 8 of 30

13 MathFacts 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). Domain 5 - Math Skills - Multiplication (MS) Skillset 1 - MS17 Multiplication by 0,1 (Multiplying 0 or 1 by numbers 0-10) Skillset 2 - MS18 Multiplication by 2,3 (Multiplying 2 or 3 by numbers 0-10) Skillset 3 - MS19 Multiplication by 4,5 (Multiplying 4 or 5 by numbers 0-10) Skillset 4 - MS20 Alternate Forms: Multiplication by 0 to 5 (Multiplying 0-5 by numbers 0-10 with the Skillset 5 - MS21 Multiplication by 6,7 (Multiplying 6 or 7 by numbers 0-10) Skillset 6 - MS22 Multiplication by 8,9 (Multiplying 8-9 by numbers 0-10) Skillset 7 - MS23 Multiplication by 10 (Multiplying 10 by numbers 0-10) Domain 7 - Math Skills - Division (MS) Skillset 8 - MS24 Alternate Forms: Multiplication by 6 to 10 (Multiplying 6-10 by numbers 0-10 with the Skillset 9 - MS25 Multiplication by 11,12 (Multiplying 11 or 12 by numbers 0-12) Skillset 10 - MS26 Alternate Forms: Multiplication by 11 to 12 (Multiplying 11 or 12 by numbers 0-12 with the Skillset 1 - MS27 Division by 1,2 (Dividing numbers 0-20 by 1 or 2) Skillset 2 - MS28 Division by 3,4 (Dividing numbers 0-40 by 3 or 4) Skillset 3 - MS29 Division by 5,6 (Dividing numbers 0-60 by 5 or 6) Page 9 of 30

14 MathFacts Grade 4 Illinois, Math, 2005, Grade 4, Skillset 4 - MS30 Alternate Forms: Division by 1-6 (Dividing numbers 0-60 by 1-6 with the unknown in the operand or answer Skillset 5 - MS31 Division by 7,8 (Dividing numbers 0-80 by 7 or 8) Skillset 6 - MS32 Division by 9,10 (Dividing numbers by 9 or 10) Skillset 7 - MS33 Alternate Forms: Division by 7-10 (Dividing numbers by 7-10 with the unknown in the operand or answer Skillset 8 - MS34 Division by 11,12 (Dividing numbers by 11 or 12) Skillset 9 - MS35 Alternate Forms: Division by 11 to 12 (Dividing numbers by 11 or 12 with unknown in operand 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= ). Domain 3 - Math Skills - Addition (MS) Domain 4 - Math Skills - Subtraction (MS) Skillset 4 - MS04 Alternate Forms: Addition of 0 to 5 (Adding 0-5 to numbers 0-10 with the unknown in the operand or answer Skillset 8 - MS08 Alternate Forms: Addition of 6 to 10 (Adding 6-10 to numbers 0-10 with the unknown in the operand or answer Skillset 4 - MS12 Alternate Forms: Subtraction of 0 to 5 (Subtracting 0-5 from numbers 0-15 with the Page 10 of 30

15 MathFacts Grade 4 Illinois, Math, 2005, Grade 4, Skillset 8 - MS16 Alternate Forms: Subtraction of 6 to 10 (Subtracting 6-10 from numbers 6-20 with the - 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. Domain 5 - Math Skills - Multiplication (MS) Domain 7 - Math Skills - Division (MS) Skillset 4 - MS20 Alternate Forms: Multiplication by 0 to 5 (Multiplying 0-5 by numbers 0-10 with the Skillset 8 - MS24 Alternate Forms: Multiplication by 6 to 10 (Multiplying 6-10 by numbers 0-10 with the Skillset 4 - MS30 Alternate Forms: Division by 1-6 (Dividing numbers 0-60 by 1-6 with the unknown in the operand or answer Skillset 7 - MS33 Alternate Forms: Division by 7-10 (Dividing numbers by 7-10 with the unknown in the operand or answer Skillset 9 - MS35 Alternate Forms: Division by 11 to 12 (Dividing numbers by 11 or 12 with unknown in operand 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 11 of 30

16 MathFacts 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 IL Write an expression using letters or symbols to represent an unknown quantity. Page 12 of 30

17 MathFacts Grade 4 Illinois, Math, 2005, Grade 4, - 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). Page 13 of 30 Domain 3 - Math Skills - Addition (MS) Domain 4 - Math Skills - Subtraction (MS) Skillset 4 - MS04 Alternate Forms: Addition of 0 to 5 (Adding 0-5 to numbers 0-10 with the unknown in the operand or answer Skillset 8 - MS08 Alternate Forms: Addition of 6 to 10 (Adding 6-10 to numbers 0-10 with the unknown in the operand or answer Skillset 4 - MS12 Alternate Forms: Subtraction of 0 to 5 (Subtracting 0-5 from numbers 0-15 with the Skillset 8 - MS16 Alternate Forms: Subtraction of 6 to 10 (Subtracting 6-10 from numbers 6-20 with the

18 MathFacts Grade 4 Illinois, Math, 2005, Grade 4, Domain 5 - Math Skills - Multiplication (MS) Domain 7 - Math Skills - Division (MS) Skillset 4 - MS20 Alternate Forms: Multiplication by 0 to 5 (Multiplying 0-5 by numbers 0-10 with the Skillset 8 - MS24 Alternate Forms: Multiplication by 6 to 10 (Multiplying 6-10 by numbers 0-10 with the Skillset 10 - MS26 Alternate Forms: Multiplication by 11 to 12 (Multiplying 11 or 12 by numbers 0-12 with the Skillset 4 - MS30 Alternate Forms: Division by 1-6 (Dividing numbers 0-60 by 1-6 with the unknown in the operand or answer Skillset 7 - MS33 Alternate Forms: Division by 7-10 (Dividing numbers by 7-10 with the unknown in the operand or answer Skillset 9 - MS35 Alternate Forms: Division by 11 to 12 (Dividing numbers by 11 or 12 with unknown in operand 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 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 threedimensional shapes (cubes, spheres, cones, cylinders, prisms, and pyramids) according to their characteristics (faces, edges, vertices). Page 14 of 30

19 MathFacts Grade 4 Illinois, Math, 2005, Grade 4, 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). - Lines, Segments, Rays, and Angles IL Identify and sketch parallel 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. - 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. Page 15 of 30

20 MathFacts Grade 4 Illinois, Math, 2005, Grade 4, 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 Page 16 of 30

21 MathFacts 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, and model equivalent representations of whole numbers and their place values up to 100,000,000. IL Read, write, recognize, model, and interpret numerical expressions from a given description or situation. IL Read, write, recognize, and model equivalent representations of fractions, including improper fractions and mixed numbers. IL Recognize, translate Domain 8 - Math Skills - between, and model multiple Fractions Decimal Conversion representations of decimals, fractions (MS) less than one (halves, quarters, fifths, and tenths), and percents (0%, 25%, 50%, 75%, and 100%). Skillset 1 - MS37 Fractions to Decimals (Converting fractions with numerators 1-9 and denominator 10 or 100; unit fractions (1/n) with denominators of 2, 3, 4, 5, and 3/4, 2/5, 3/5, 4/5) Domain 9 - Math Skills - Percentage Decimal Conversion (MS) Domain 10 - Fraction Percentage Conversion (MS) Skillset 2 - MS38 Decimals to Fractions (Converting decimals to fractions with values 0.5, , 0.25, 0.75, 0.1, 0.3, 0.7, 0.9., 0.2, 0.4, 0.6, and 0.8) Skillset 1 - MS39 Percentages to Decimals (Converting percentages to decimals with 1%, 2%,...9%; 10%, 20%,...100%; and 50%, 25%, and 75% values) Skillset 2 - MS40 Decimals to Percentages (Converting decimals to percentages with values 0.1, 0.2, 1.0; 0.01, ; and 0.5, 0.25, and 0.75) Skillset 1 - MS41 Fractions to Percentages (Converting fractions to percentages with values 1/10, 2/10, 9/10; 1/100, 2/100 9/100, and 1/2, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5) Page 17 of 30

22 MathFacts Grade 5 Illinois, Math, 2005, Grade 5, 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. IL Order and compare decimals through hundredths. 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 - Number Operations IL Solve problems and number sentences involving addition, subtraction, multiplication, and division using whole numbers. 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 Page 18 of 30

23 MathFacts Grade 5 Illinois, Math, 2005, Grade 5, 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. - 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. - 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). - Estimation IL Compare and estimate length (including perimeter), area, volume, weight/mass, and angles (0 to 180 ) using referents. Page 19 of 30

24 MathFacts Grade 5 Illinois, Math, 2005, Grade 5, - Volume and Surface Area IL Determine the volume of a right rectangular prism using an appropriate formula or strategy. - Measurement Conversions 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 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 Page 20 of 30

25 MathFacts Grade 5 Illinois, Math, 2005, Grade 5, - 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 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 threedimensional shapes (cubes, spheres, 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). Page 21 of 30

26 MathFacts Grade 5 Illinois, Math, 2005, Grade 5, - 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, 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. IL Identify and sketch acute, 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. Page 22 of 30

27 MathFacts Grade 5 Illinois, Math, 2005, Grade 5, IL 10A 10B - Data Analysis and Statistics - Read and Interpret Displays 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?). Page 23 of 30

28 MathFacts 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, and model equivalent representations of whole numbers and their place values. IL Read, write, recognize, model, and interpret numerical expressions from a given description or situation. IL Read, write, recognize, and model equivalent representations 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). Domain 8 - Math Skills - Fractions Decimal Conversion (MS) Skillset 1 - MS37 Fractions to Decimals (Converting fractions with numerators 1-9 and denominator 10 or 100; unit fractions (1/n) with denominators of 2, 3, 4, 5, and 3/4, 2/5, 3/5, 4/5) Domain 9 - Math Skills - Percentage Decimal Conversion (MS) Domain 10 - Fraction Percentage Conversion (MS) Skillset 2 - MS38 Decimals to Fractions (Converting decimals to fractions with values 0.5, , 0.25, 0.75, 0.1, 0.3, 0.7, 0.9., 0.2, 0.4, 0.6, and 0.8) Skillset 1 - MS39 Percentages to Decimals (Converting percentages to decimals with 1%, 2%,...9%; 10%, 20%,...100%; and 50%, 25%, and 75% values) Skillset 2 - MS40 Decimals to Percentages (Converting decimals to percentages with values 0.1, 0.2, 1.0; 0.01, ; and 0.5, 0.25, and 0.75) Skillset 1 - MS41 Fractions to Percentages (Converting fractions to percentages with values 1/10, 2/10, 9/10; 1/100, 2/100 9/100, and 1/2, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5) Page 24 of 30

29 MathFacts Grade 6 Illinois, Math, 2005, Grade 6, IL Read, write, recognize, and model equivalent representations of decimals and their place values through thousandths. IL Represent repeated factors using exponents. - Order and Compare Numbers IL Order and compare whole numbers. 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 - Number Operations IL Solve problems and number sentences involving addition, subtraction, multiplication, and division using whole numbers. 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. IL Identify and apply order of operations to simplify numeric expressions involving whole numbers. - Properties Page 25 of 30

30 MathFacts Grade 6 Illinois, Math, 2005, Grade 6, 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). - Percents IL Read, write, recognize, and model percents from 0% to 100%. IL Solve number sentences and problems involving 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 - Measurement Tools IL Select and use appropriate standard units and tools to measure length, mass/weight, capacity, and angles. - Area, Perimeter, and Circumference Page 26 of 30

31 MathFacts Grade 6 Illinois, Math, 2005, Grade 6, IL Solve problems involving 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 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 Page 27 of 30

32 MathFacts Grade 6 Illinois, Math, 2005, Grade 6, 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 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 IL Represent problems with equations and inequalities. - Solve Equations and Inequalities 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. Page 28 of 30

33 MathFacts Grade 6 Illinois, Math, 2005, Grade 6, IL Identify and describe threedimensional shapes (cubes, spheres, cones, cylinders, prisms, and pyramids) according to their characteristics (faces, edges, vertices). IL Solve problems using 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). - 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. IL Identify and sketch acute, 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. Page 29 of 30

34 MathFacts Grade 6 Illinois, Math, 2005, Grade 6, 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. IL 10A 10B - Data Analysis and Statistics - Read and Interpret Displays IL Read, interpret, and make predictions from data represented in a bar graph, line (dot) plot, Venn diagram (with two circles), chart/table, line graph, or circle graph. IL Compare different representations of the same data. - Complete and Create Displays IL Create a bar graph, chart/table, line graph, or circle graph with common referents (1/4, 50%,.75) for a given set of data. - Line of Best Fit - Statistics IL Determine the mode, range, median, 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, decimal, or percent. - Outcomes and Counting Principles IL Apply the fundamental counting principle in a simple problem (e.g., How many different 3-digit numbers can be made with the digits 1, 2, and 2?). Page 30 of 30