Sunday, March 21, 2010

Common standards and the mathematics for each grade (key information for parents)

For parents, the most helpful element of the draft common core mathematics standards may be the opening paragraph 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 and joining and separating sets; (2) describing shapes and space. More learning time in Kindergarten should be devoted to number than to other topics.
Two to four critical areas for each elementary and middle school are listed in similar paragraphs that list these elements:

Grade 1
• Developing understanding of addition, subtraction, and strategies for additions and subtractions within 20
• Developing understanding of whole number relationships, including grouping in tens and ones,
• Developing understanding of linear measurement and measuring lengths
• Composing and decomposing geometric shapes

Grade 2
• Developing understanding of base-ten notation
• Developing fluency with additions and subtractions within 20 and fluency with multi-digit addition and subtraction
• Describing and analyzing shapes

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

Grade 4
• Continuing to develop understanding and fluency with whole number multiplication, and developing understanding of multi-digit whole number division
• Developing an understanding of addition and subtraction of fractions with like denominators, multiplication of fractions by whole numbers, and division of whole numbers with fractional answers
• Developing an understanding of area
• Understanding that geometric figures can be analyzed and classified using properties such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

Grade 5
• Developing fluency with addition and subtraction of fractions, developing understanding of the multiplication of fractions and of division of fractions in limited cases (fractions divided by whole numbers and whole numbers divided by unit fractions)
• Developing understanding of and fluency with division of multi-digit whole numbers
• Developing understanding of and fluency with addition, subtraction, multiplication, and division of decimals
• Developing understanding of volume

Grade 6
• Connecting ratio and rate to whole number multiplication and division
• Developing understanding of and fluency with division of fractions and developing fluency with multiplication of fractions
• Developing understanding of and using formulas to determine areas of two-dimensional shapes and distinguishing between volume and surface area of three-dimensional shapes
• Writing, interpreting, and using expressions and equations

Grade 7
• Developing understanding of and applying proportional relationships
• Developing understanding of operations with rational numbers and solving linear equations
• Analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence
• Drawing inferences about populations based on samples

Grade 8
• Solving linear equations and systems of linear equations
• Grasping the concept of a function and using functions to describe quantitative relationships
• 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 predict that the outline above (with any modifications made in the final edition) will be the version parents find most helpful in understanding their children's studies and in providing home support for students to succeed.


  1. It would be great if we could also publish a "Problems to look out for in critical skills" section for each grade. My son's academic progress in math tanked in the 7th grade, subsequently after testing it was discovered that he had a specific learning disability in math that showed up in his ability to do the second thing listed in Grade 7: " (2) Students develop a unified understanding of number, recognizing fractions, decimals, and percents as different representations of rational numbers." Yet none of his teachers K-6 picked up on the fact that he was struggling.

    It is kind of like the phenomenon that Karen Cheser talks about in Boone County's discovery that difficulty with skills taught in ealier years are often not detected at the time, but by the time the student gets to high school those difficulties have built into much larger problems in learning and are showing up in testing. (Susan, you had a link to a video of Karen talking abou this on Facebook, but couldn't find it.)

  2. Cindy, are there useful publications on the issue?

    (I ask mainly for the blog, but partly for a girl I know who used verbal proficiency to replace spatial skills all the way up to precalculus. A psychologist using mirror-based tasks had diagnosed the problem when the kid was six, but in the 1960s, they figured all they could do was wait until the problem surfaced in school work--and that took another ten years.)


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