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Guiding Principles of Mathematics Instruction:

  • Mathematical proficiency is defined by conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition (National Research Council, 2001).
  • Mathematical proficiency drives independent thinking, reasoning, and problem-solving.
  • Mathematical proficiency is the foundation for careers in science, technology, engineering and mathematics (STEM), and it is increasingly becoming the foundation for careers outside of STEM (NCTM, 2018)
  • Effective mathematics teaching “engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically” (NCTM, 2014).
  • Standards-based instruction accelerates student gains.
  • Students construct mathematical knowledge through exploration, discussion, and reflection.
  • Teachers are facilitators of student learning, as they engage students in rich tasks. Administrators are change agents and have the power to create and to support a culture of mathematical proficiency.
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Standard Grade Area/Subject Description
5.AT.3

5

 Computation, Algebra, and Functions

Solve real-world problems involving multiplication of fractions, including mixed numbers (e.g., by using visual fraction models and equations to represent the problem).
5.AT.4

5

 Computation, Algebra, and Functions

Solve real-world problems involving division of unit fractions by non-zero whole numbers, and division of whole numbers by unit fractions (e.g., by using visual fraction models and equations to represent the problem).
5.AT.5

5

 Computation, Algebra, and Functions

Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money in decimal notation (e.g. by using equations, models or drawings and strategies based on place value or properties of operations to represent the problem).
5.AT.6

5

 Computation, Algebra, and Functions

Graph points with whole number coordinates on a coordinate plane. Explain how the coordinates relate the point as the distance from the origin on each axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
5.AT.7

5

 Computation, Algebra, and Functions

Represent real-world problems and equations by graphing ordered pairs in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
5.AT.8

5

 Computation, Algebra, and Functions

Define and use up to two variables to write linear expressions that arise from real-world problems, and evaluate them for given values.
5.C.1

5

 Computation, Algebra, and Functions

Multiply multi-digit whole numbers fluently using a standard algorithmic approach.
5.C.2

5

 Computation, Algebra, and Functions

Find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning used.
5.C.3

5

 Computation, Algebra, and Functions

Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
5.C.4

5

 Computation, Algebra, and Functions

Add and subtract fractions with unlike denominators, including mixed numbers.
5.C.5

5

 Computation, Algebra, and Functions

Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number.
5.C.6

5

 Computation, Algebra, and Functions

Explain why multiplying a positive number by a fraction greater than one results in a product greater than the given number. Explain why multiplying a positive number by a fraction less than 1 results in a product smaller than the given number. Relate the principle of fraction equivalence, a/b = (n x a)/(n x b), to the effect of multiplying a/b by one.
5.C.7

5

 Computation, Algebra, and Functions

Use visual fraction models and numbers to divide a unit fraction by a non-zero whole number and to divide a whole number by a unit fraction.
5.C.8

5

 Computation, Algebra, and Functions

Add, subtract, multiply, and divide decimals to hundredths, using models or drawings and strategies based on place value or the properties of operations. Describe the strategy and explain the reasoning.
5.C.9

5

 Computation, Algebra, and Functions

Evaluate expressions with parentheses or brackets involving whole numbers using the commutative properties of addition and multiplication, associative properties of addition and multiplication, and distributive property.

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