The following eight standards for mathematical practice apply to students at all levels (K-12) as they seek to develop their mathematical expertise:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Illinois Learning Standards/Common Core State Standards (CCSS)
Illinois, along with over 40 other states, have adopted the Common Core State Standards (CCSS) in mathematics to improve student college and career readiness. The standards provide clear, consistent and rigorous expectations for students by grade level. The New Illinois Learning Standards focus on fewer topics at each grade level, allowing students to develop deeper conceptual understanding and math fact fluency.
The Illinois Learning Standards for math are based on the CCSS and define what students should understand and be able to do in their study of mathematics. Clicking on the hyperlinks below will take you to the Illinois Learning Standards for each grade level. While there are many mathematical standards, instructional time focuses on the following critical areas by grade:
• Describing shapes and space
• Representing, relating and operating on whole numbers, initially with sets of objects
• Developing understanding of strategies for addition and subtraction within 10
• Developing understanding of whole number relationships, including grouping in tens and ones
• Developing and understanding of strategies for addition and subtraction within 20
• Developing understanding of place value for tens and ones
• Developing understanding of measurement
• Developing understanding of two-dimensional and three-dimensional shapes
• Extending understanding of base-ten notation
• Building fluency with addition and subtraction
• Using standard units of measure
• Describing and analyzing shapes
• Developing understanding of multiplication and division problems within 100
• Developing understanding of fractions
• Developing understanding of the concepts of area and perimeter
• Attains fluency in addition and subtraction problems within 1000
• Developing understanding and fluency with multi-digit multiplication
• Developing understanding of dividing to find quotients involving multi-digit dividends
• Developing an understanding of fraction equivalence, addition and subtraction of fractions, and multiplication of fractions by whole numbers
• Understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry
• Solving multi-step word problems
• Determining the area and perimeter of a polygon
• Converting between units of measure
• Understanding decimals: tenths, hundredths, and thousandths; addition and subtraction; multiplication and division; ordering
• Write and interpret numerical expressions
• Analyze patterns and relationships
• Understand the place value system
• Perform operations with multi-digit whole numbers and with decimals to hundredths
• Use equivalent fractions as a strategy to add and subtract fractions
• Apply and extend previous understandings of multiplication and division to multiply and divide fractions
• Convert like measurement units withing a given measurement system
• Represent and interpret data
• Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition
• Graph points on the coordinate plane to solve real-world and mathematical problems
• Classify two-dimensional figures into categories based on their properties
• Using ratios and rates to solve problems
• Deepening understanding of rational numbers, including negative rational numbers
• Writing, interpreting, and using expressions and equations
• Developing understanding of statistical thinking
• Developing an understanding and applying proportional relationships
• Developing an understanding of operations with rational numbers
• Formulating expressions and equations in one variable and use these equations to solve problems
• Solving problems involving scale drawings and geometric constructions
• Using three-dimensional shapes to solve problems involving area, surface area, and volume
• Drawing inferences about populations based on samples
• Using linear equations and systems of linear equations to represent, analyze, and solve a variety of problems
• Developing an understanding of functions and using functions to describe quantitative relationships
• Analyzing two-dimensional and three-dimensional space and figures using distance, angle, similarity, and congruence
• Understanding and applying the Pythagorean Theorem