Beginning Arithmetic Patterner

Recognizes and uses arithmetic patterns with perceptual or pedagogical support, often first those that involve properties of zero. The child also accepts number sentences not in the form of 3 + 4 = 7 (e.g., 7 = 3 + 4, or even 3 + 4 = 2 + 5). This represents a move from an "equals-as-an answer” notion to recognizing that equals means equivalent numbers.


You may see this:

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Other Examples:

  • Child recognizes and uses patterns (e.g., understands 5 + 3 - 3 = 5).
  • In functional thinking, builds two sets (e.g. in a t-chart) following two sepereate general rules.
  • Given a situation and asked to generate data for a t-chart, children generalize a rule (you add 2 every time) for each column seperately.

Help your student become a(n) Beginning Arithmetic Patterner

Problems, activities, and discussions encourage children to generalize patterns that occur in arithmetic, formulating and justifying rules such as "When you add zero to a number, the result is the same number" or "When you add, you can add numbers any which way" (commutative and associative properties). Activities also ask children to analyze their growing patterns arithmetically. Sharing ideas and representations of all such work is critical. Representation of number sentences are represented flexibly (not only 3 + 5 = 8, but as 8 = 5 + 3, etc.).

Special Thanks To

Institute of Education Sciences
The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through grant numbers R305K050157, R305A120813, R305A110188, and R305A150243. to the University of Denver. The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education.