Monday, May 13, 2013

Common Core: Bringing focus to math learning

For parents, the most helpful element of the Common Core State Standards in Mathematics may be the opening paragraph of the introduction for each grade.  For example, the section for kindergarten begins this way:
In Kindergarten, instructional time should focus on two critical areas: (1) representing, comparing and ordering whole numbers, initially with sets of objects; (2) describing shapes and space. More learning time in Kindergarten should be devoted to number than to other topics.
For each elementary grade, two to four critical areas are listed in similar paragraphs.  Here's are the focus points:

Grade 1
• Developing understanding of addition, subtraction, and strategies for additions and subtractions within 20
• Developing understanding of whole number relationships and place value, including grouping in tens and ones
• Developing understanding of linear measurement and measuring lengths as iterating length units
• Reasoning about attributes of, and composing and decomposing geometric shapes

Grade 2
• Extending understanding of base-ten notation
• Building fluency with additions and subtractions
• Using standard units of measure
• Describing and analyzing shapes

Grade 3
• Developing understanding of multiplication and division and strategies for multiplication and division within 100
• Developing understanding of fractions, especially unit fractions (fractions with numerator 1)
• Developing understanding of the structure of rectangular arrays and of area
• Describing and analyzing two-dimensional shapes

Grade 4
Developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends
• Developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, 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

Grade 5
• Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions)
• Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations
• Developing understanding of volume

Grade 6
• Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems
• Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers
• Writing, interpreting, and using expressions and equations
• Developing understanding of statistical thinking

Grade 7
• Developing understanding of and applying proportional relationships
• Developing understanding of operations with rational numbers and working with expressions and linear equations
• Solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume
• Drawing inferences about populations based on samples

Grade 8
• Formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations
• Grasping the concept of a function and using functions to describe quantitative relationships
• Analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem

Those paragraphs are followed by a slightly longer explanation each item, and then by the full standards for the grade.  All three levels of detail are helpful, but I think the outline above is the version parents can find most helpful in understanding their children's studies and in providing home support for students to succeed.

[Note to long-time readers: this post updates a March 21, 2010, post that reflected the draft Common Core Standards at a point when the public was invited to comment.  After that comment period, changes were made to clarify the focus of each grade, resulting in the lists above.]

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