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.
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Standard Grade Area/Subject Description
1.NS.1

1

Number Sense

Count to at least 120 by ones, fives, and tens from any given number. In this range, read and write numerals and represent a number of objects with a written numeral.

1.NS.2

1

Number Sense

Understand that 10 can be thought of as a group of ten ones — called a “ten." Understand that the numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. Understand that the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

1.NS.3

1

Number Sense

Match the ordinal numbers first, second, third, etc., with an ordered set up to 10 items.

1.NS.4

1

Number Sense

Use place value understanding to compare two, two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

1.NS.5

1

Number Sense

Find mentally 10 more or 10 less than a given two-digit number without having to count, and explain the thinking process used to get the answer.

1.NS.6

1

Number Sense

Show equivalent forms of whole numbers as groups of tens and ones, and understand that the individual digits of a two-digit number represent amounts of tens and ones.

2.CA.1

2

Computation, Algebra, and Functions

Add and subtract fluently within 100.

2.CA.2

2

Computation, Algebra, and Functions

Solve real-world problems involving addition and subtraction within 100 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 drawings and equations with a symbol for the unknown number to represent the problem). Use estimation to decide whether answers are reasonable in addition problems.

2.CA.3

2

Computation, Algebra, and Functions

Solve real-world problems involving addition and subtraction within 100 in situations involving lengths that are given in the same units (e.g., by using drawings, such as drawings of rulers, and equations with a symbol for the unknown number to represent the problem).

2.CA.4

2

Computation, Algebra, and Functions

Add and subtract within 1000, 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 or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones, and that sometimes it is necessary to compose or decompose tens or hundreds.

2.CA.5

2

Computation, Algebra, and Functions

Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal groups.

2.CA.6

2

Computation, Algebra, and Functions

Show that the order in which two numbers are added (commutative property) and how the numbers are grouped in addition (associative property) will not change the sum. These properties can be used to show that numbers can be added in any order.

2.CA.7

2

Computation, Algebra, and Functions

Create, extend, and give an appropriate rule for number patterns using addition and subtraction within 1000.

2.DA.1

2

Data Analysis, Statistics, and Probability

Draw a picture graph (with single-unit scale) and a bar graph (with single-unit scale) to represent a data set with up to four choices (What is your favorite color? red, blue, yellow, green). Solve simple put-together, take-apart, and compare problems using information presented in the graphs.

2.G.1

2

Geometry and Measurement

Identify, describe, and classify two- and three-dimensional shapes (triangle, square, rectangle, cube, right rectangular prism) according to the number and shape of faces and the number of sides and/or vertices. Draw two-dimensional shapes.

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