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abstraction to solve problems. Students will effectively communicate mathematical ideas,
reasoning, and their implications using multiple representations such as symbols, diagrams,
graphs, computer programs, and language. Students will use mathematical relationships to
generate solutions and make connections and predictions. Students will analyze mathematical
relationships to connect and communicate mathematical ideas. Students will display, explain, or
justify mathematical ideas and arguments using precise mathematical language in written or oral
communication.
(3) For students to become fluent in mathematics, students must develop a robust sense of number.
The National Research Council's report, "Adding It Up," defines procedural fluency as "skill in
carrying out procedures flexibly, accurately, efficiently, and appropriately." As students develop
procedural fluency, they must also realize that true problem solving may take time, effort, and
perseverance. Students in Grade 3 are expected to perform their work without the use of
calculators.
(4) The primary focal areas in Grade 3 are place value, operations of whole numbers, and
understanding fractional units. These focal areas are supported throughout the mathematical
strands of number and operations, algebraic reasoning, geometry and measurement, and data
analysis. In Grades 3-5, the number set is limited to positive rational numbers. In number and
operations, students will focus on applying place value, comparing and ordering whole numbers,
connecting multiplication and division, and understanding and representing fractions as numbers
and equivalent fractions. In algebraic reasoning, students will use multiple representations of
problem situations, determine missing values in number sentences, and represent real-world
relationships using number pairs in a table and verbal descriptions. In geometry and
measurement, students will identify and classify two-dimensional figures according to common
attributes, decompose composite figures formed by rectangles to determine area, determine the
perimeter of polygons, solve problems involving time, and measure liquid volume (capacity) or
weight. In data analysis, students will represent and interpret data.
(5) Statements that contain the word "including" reference content that must be mastered, while those
containing the phrase "such as" are intended as possible illustrative examples.
(b) Knowledge and skills.
(1) Mathematical process standards. The student uses mathematical processes to acquire and
demonstrate mathematical understanding. The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information, formulating
a plan or strategy, determining a solution, justifying the solution, and evaluating the
problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate;