Illinois State Standards for Mathematics: Grade 4

IL.6. Number Sense: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.

6.A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.

6.A.2. Compare and order whole numbers, fractions and decimals using concrete materials, drawings and mathematical symbols.

6.B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.

6.B.2. Solve one- and two-step problems involving whole numbers, fractions and decimals using addition, subtraction, multiplication and division.

6.C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.

6.C.2a. Select and perform computational procedures to solve problems with whole numbers, fractions and decimals.

6.C.2b. Show evidence that computational results using whole numbers, fractions and decimals are correct and/or that estimates are reasonable.

6.D. Solve problems using comparison of quantities, ratios, proportions and percents.

6.D.2. Describe the relationship between two sets of data using ratios and appropriate notations (e.g., a/b, a to b, a:b).

IL.7. Estimation and Measurement: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.

7.A. Measure and compare quantities using appropriate units, instruments and methods.

7.A.2a. Calculate, compare and convert length, perimeter, area, weight/mass and volume within the customary and metric systems.

7.A.2b. Solve addition, subtraction, multiplication and division problems using currency.

7.B. Estimate measurements and determine acceptable levels of accuracy.

7.B.2a. Determine and communicate possible methods for estimating a given measure, selecting proper units in both customary and metric systems.

7.B.2b. Estimate conversions between measures within the customary and metric systems.

7.C. Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.

7.C.2a. Describe relationships in a simple scale drawing.

7.C.2b. Construct or draw figures with given perimeters and areas.

IL.8. Algebra and Analytical Methods: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.

8.A. Describe numerical relationships using variables and patterns.

8.A.2a. Identify, describe, extend and create geometric and numeric patterns.

8.A.2b. Construct and solve number sentences using a variable to represent an unknown quantity.

8.B. Interpret and describe numerical relationships using tables, graphs and symbols.

8.B.2. Analyze a geometric pattern and express the results numerically.

8.C. Solve problems using systems of numbers and their properties.

8.C.2. Explain operations and number properties including commutative, associative, distributive, transitive, zero, equality and order of operations.

8.D. Use algebraic concepts and procedures to represent and solve problems.

8.D.2. Solve linear equations involving whole numbers.

IL.9. Geometry: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.

9.A. Demonstrate and apply geometric concepts involving points, lines, planes and space.

9.A.2a. Build physical models of two- and three-dimensional shapes.

9.A.2b. Identify and describe how geometric figures are used in practical settings (e.g., construction, art, advertising).

9.A.2c. Describe and draw representations of geometric relationships, patterns, symmetries, and designs in two- and three-dimensions with and without technology.

9.B. Identify, describe, classify and compare relationships using points, lines, planes and solids.

9.B.2. Compare geometric figures and determine their properties including parallel, perpendicular, similar, congruent and line symmetry.

9.C. Construct convincing arguments and proofs to solve problems.

9.C.2. Formulate logical arguments about geometric figures and patterns and communicate reasoning.

IL.10. Data Analysis and Probability: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.

10.A. Organize, describe and make predictions from existing data.

10.A.2a. Organize and display data using pictures, tallies, tables, charts, bar graphs, line graphs, line plots and stem-and-leaf graphs.

10.A.2b. Using a data set, determine mean, median, mode and range, with and without the use of technology.

10.A.2c. Make predictions and decisions based on data and communicate their reasoning.

10.B. Formulate questions, design data collection methods, gather and analyze data and communicate findings.

10.B.2a. Formulate questions of interest and select methods to systematically collect data.

10.B.2b. Collect, organize and display data using tables, charts, bar graphs, line graphs, circle graphs, line plots and stem-and-leaf graphs.

10.B.2c. Analyze the data using mean, median, mode and range, as appropriate, with or without the use of technology.

10.B.2d. Interpret results or make relevant decisions based on the data gathered.

10.C. Determine, describe and apply the probabilities of events.

10.C.2a. Calculate the probability of a simple event.

10.C.2b. Compare the likelihood of events in terms of certain, more likely, less likely or impossible.

10.C.2c. Determine the probability of an event involving 'and', or 'or not'.