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I remember looking once at what chikdren in Kindergarten were expected to know, and it was quite a bit. I have a young son, and would like to know:

What is a Kindergartener expected to know about numbers and shapes and other mathematical concepts?

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  • $\begingroup$ basic differential geometry $\endgroup$ – galois Nov 22 '15 at 1:49
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From http://www.corestandards.org/Math/Content/K/introduction/:

Counting and Cardinality

  • Know number names and the count sequence.
  • Count to tell the number of objects.
  • Compare numbers.

Operations and Algebraic Thinking

  • Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Number and Operations in Base Ten

  • Work with numbers 11-19 to gain foundations for place value.

Measurement and Data

  • Describe and compare measurable attributes.
  • Classify objects and count the number of objects in each category

Geometry

  • Identify and describe shapes.
  • Analyze, compare, create, and compose shapes.

Mathematical Practices

  • Make sense of problems and persevere in solving them.
  • Reason abstractly and quantitatively.
  • Construct viable arguments and critique the reasoning of others.
  • Model with mathematics.
  • Use appropriate tools strategically.
  • Attend to precision.
  • Look for and make use of structure.
  • Look for and express regularity in repeated reasoning.
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http://www.corestandards.org/Math/Content/K/introduction/

I am not aware of incoming requirements for Kindergarten but the link above details the learning goals for CC math at grade K.

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    $\begingroup$ May I suggest that you make the answer more self-contained by summarizing how the link answers the question. $\endgroup$ – Thomas Mar 14 '14 at 1:22
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Here is a github page that details connections between all standards: CCSSM Flow View

For example, you can hover over the standards for K and see how they relate to others. Moreover, you can click through to see the description of the standard, its prerequisites, and its dependent strands.

Site description:

Hover over a standard to see what it depends on (blue) and what depends on it (red). The colors fade as the dependency chain to the standard becomes longer. Click on a standard for more detail on the standard and its prerequisites and dependent standards. The dependencies are derived from a shared spreadsheet, referenced from a document by Jason Zimba.

Hopefully this helps clarify both what is to be known for CCSSM, and also how the covered material will be built upon in subsequent years.

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