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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Select one Content Area or High School course at a time.
Search for key words within each standard's description.
Standard Grade Area/Subject Description
1.CA.1

1

Computation, Algebra, and Functions

Demonstrate fluency with addition facts and the corresponding subtraction facts within 20. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). Understand the role of 0 in addition and subtraction.

1.CA.2

1

Computation, Algebra, and Functions

Solve real-world problems involving addition and subtraction within 20 in situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all parts of the addition or subtraction problem (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem).

1.CA.3

1

Computation, Algebra, and Functions

Create a real-world problem to represent a given equation involving addition and subtraction within 20.

1.CA.4

1

Computation, Algebra, and Functions

Solve real-world problems that call for addition of three whole numbers whose sum is within 20 (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem).

1.CA.5

1

Computation, Algebra, and Functions

Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; describe the strategy and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones, and that sometimes it is necessary to compose a ten.

1.CA.6

1

Computation, Algebra, and Functions

Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false (e.g., Which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2).

1.CA.7

1

Computation, Algebra, and Functions

Create, extend, and give an appropriate rule for number patterns using addition within 100.

1.DA.1

1

Data Analysis, Statistics, and Probability

Organize and interpret data with up to three choices (What is your favorite fruit? apples, bananas, oranges); ask and answer questions about the total number of data points, how many in each choice, and how many more or less in one choice compared to another.

1.G.1

1

Geometry and Measurement

Identify objects as two-dimensional or three-dimensional. Classify and sort two-dimensional and three-dimensional objects by shape, size, roundness and other attributes. Describe how two-dimensional shapes make up the faces of three-dimensional objects.

1.G.2

1

Geometry and Measurement

Distinguish between defining attributes of two- and three-dimensional shapes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size). Create and draw two-dimensional shapes with defining attributes.

1.G.3

1

Geometry and Measurement

Use two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. [In grade 1, students do not need to learn formal names such as "right rectangular prism."]

1.G.4

1

Geometry and Measurement

Partition circles and rectangles into two and four equal parts; describe the parts using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of, the parts. Understand for partitioning circles and rectangles into two and four equal parts that decomposing into equal parts creates smaller parts.

1.M.1

1

Geometry and Measurement

Use direct comparison or a nonstandard unit to compare and order objects according to length, area, capacity, weight, and temperature.

1.M.2

1

Geometry and Measurement

Tell and write time to the nearest half-hour and relate time to events (before/after, shorter/longer) using analog clocks. Understand how to read hours and minutes using digital clocks.

1.M.3

1

Geometry and Measurement

Find the value of a collection of pennies, nickels, and dimes.

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