MATHEMATICS PROFICIENCY STRANDS The proficiency strands are an integral part of mathematics content across all strands. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics Understanding Problem Solving Reasoning Fluency Foundation Understanding includes connecting Fluency includes readily counting Problem Solving includes using Reasoning includes explaining names, numerals and quantities numbers in sequences, continuing materials to model authentic comparisons of quantities, creating patterns, and comparing the lengths problems, sorting objects, using patterns, and explaining processes of objects familiar counting sequences to for indirect comparison of length solve unfamiliar problems, and discussing the reasonableness of the answer Level 1 Understanding includes connecting Fluency includes counting number Problem Solving includes using Reasoning includes explaining direct names, numerals and quantities, in sequences readily forward and materials to model authentic and indirect comparisons of length and partitioning numbers in various backwards, locating numbers on a problems, giving and receiving using uniform informal units, ways line, and naming the days of the directions to unfamiliar places, justifying representations of data, week and using familiar counting and explaining patterns that have sequences to solve unfamiliar been created problems and discussing the reasonableness of the answer Level 2 Understanding includes connecting Fluency includes counting numbers Problem Solving includes Reasoning includes using known number calculations with counting in sequences readily, using informal formulating problems from facts to derive strategies for sequences, partitioning and units iteratively to compare authentic situations, making unfamiliar calculations, comparing combining numbers flexibly, measurements, using the language models and using number and contrasting related models of identifying and describing the of chance to describe outcomes of sentences that represent problem operations, and creating and relationship between addition and familiar chance events and situations, and matching interpreting simple representations subtraction and between describing and comparing time transformations with their of data multiplication and division durations original shape
MATHEMATICS PROFICIENCY STRANDS The proficiency strands are an integral part of mathematics content across all strands. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics Understanding Fluency Problem Solving Reasoning Foundation Understanding includes connecting names, numerals and quantities Fluency includes readily counting numbers in sequences, continuing patterns, and comparing the lengths of objects Problem Solving includes using materials to model authentic problems, sorting objects, using familiar counting sequences to solve unfamiliar problems, and discussing the reasonableness of the answer Reasoning includes explaining comparisons of quantities, creating patterns, and explaining processes for indirect comparison of length Level 1 Understanding includes connecting names, numerals and quantities, and partitioning numbers in various ways Fluency includes counting number in sequences readily forward and backwards, locating numbers on a line, and naming the days of the week Problem Solving includes using materials to model authentic problems, giving and receiving directions to unfamiliar places, and using familiar counting sequences to solve unfamiliar problems and discussing the reasonableness of the answer Reasoning includes explaining direct and indirect comparisons of length using uniform informal units, justifying representations of data, and explaining patterns that have been created Level 2 Understanding includes connecting number calculations with counting sequences, partitioning and combining numbers flexibly, identifying and describing the relationship between addition and subtraction and between multiplication and division Fluency includes counting numbers in sequences readily, using informal units iteratively to compare measurements, using the language of chance to describe outcomes of familiar chance events and describing and comparing time durations Problem Solving includes formulating problems from authentic situations, making models and using number sentences that represent problem situations, and matching transformations with their original shape Reasoning includes using known facts to derive strategies for unfamiliar calculations, comparing and contrasting related models of operations, and creating and interpreting simple representations of data