Mathematics Cumulative Progress Indicators (CPIs) for the end of the designated grade span

Place a "+" for an expectation that represents a strength & a "-" for a weakness

+ or -

STANDARD 4.1     (NUMBER AND NUMERICAL OPERATIONS)     ALL STUDENTS WILL DEVELOP NUMBER SENSE AND WILL PERFORM STANDARD NUMERICAL OPERATIONS AND ESTIMATIONS ON ALL TYPES OF NUMBERS IN A VARIETY OF WAYS.

B.     Numerical Operations

By the end of Grade 2, students will:

 1.         Develop the meanings of addition and subtraction by concretely modeling and discussing a large variety of problems.

·        Joining, separating, and comparing

 2.         Explore the meanings of multiplication and division by modeling and discussing problems.

3.         Develop proficiency with basic addition and subtraction number facts using a variety of fact strategies (such as “counting on” and “near doubles”) and then commit them to memory.

 4.         Construct, use, and explain procedures for performing addition and subtraction calculations with:

·        Pencil-and-paper

·        Mental math

·        Calculator

 5.         Use efficient and accurate pencil-and-paper procedures for computation with whole numbers.

·        Addition of 2-digit numbers

·        Subtraction of 2-digit numbers

 6.         Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.

 7.         Check the reasonableness of results of computations.

 8.         Understand and use the inverse relationship between addition and subtraction.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 3, students will:

 1.         Develop the meanings of the four basic arithmetic operations by modeling and discussing a large variety of problems.

·        Addition and subtraction:  joining, separating, comparing

·        Multiplication:  repeated addition, area/array

·        Division:  repeated subtraction, sharing

 2.         Develop proficiency with basic multiplication and division number facts using a variety of fact strategies (such as “skip counting” and “repeated subtraction”).

 3.         Construct, use, and explain procedures for performing whole number calculations with:

·        Pencil-and-paper

·        Mental math

·        Calculator

 4.         Use efficient and accurate pencil-and-paper procedures for computation with whole numbers.

·        Addition of 3-digit numbers

·        Subtraction of 3-digit numbers

·        Multiplication of 2-digit numbers by 1-digit numbers

5.         Count and perform simple computations with money.

·        Cents notation (¢)

 6.         Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.

 7.         Check the reasonableness of results of computations.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 4, students will:

  1.         Develop the meanings of the four basic arithmetic operations by modeling and discussing a large variety of problems.

·        Addition and subtraction:  joining, separating, comparing

·        Multiplication:  repeated addition, area/array

·        Division: repeated subtraction, sharing

 2.         Develop proficiency with basic multiplication and division number facts using a variety of fact strategies (such as “skip counting” and “repeated subtraction”) and then commit them to memory.

 3.         Construct, use, and explain procedures for performing whole number calculations and with:

·        Pencil-and-paper

·        Mental math

·        Calculator

4.         Use efficient and accurate pencil-and-paper procedures for computation with whole numbers.

·        Addition of 3-digit numbers

·        Subtraction of 3-digit numbers

·        Multiplication of 2-digit numbers

·        Division of 3-digit numbers by 1-digit numbers

 5.         Construct and use procedures for performing decimal addition and subtraction.

 6.         Count and perform simple computations with money.

·        Standard dollars and cents notation

 7.         Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.

 8.         Check the reasonableness of results of computations.

 9.         Use concrete models to explore addition and subtraction with fractions.

 10.     Understand and use the inverse relationships between addition and subtraction and between multiplication and division.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 5, students will:

 1.         Recognize the appropriate use of each arithmetic operation in problem situations.

 2.         Construct, use, and explain procedures for performing addition and subtraction with fractions and decimals with:

·        Pencil-and-paper

·        Mental math

·        Calculator

 3.         Use an efficient and accurate pencil-and-paper procedure for division of a 3-digit number by a 2-digit number.

 4.         Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.

 5.         Check the reasonableness of results of computations.

 6.         Understand and use the various relationships among operations and properties of operations.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 6, students will:

 1.         Recognize the appropriate use of each arithmetic operation in problem situations.

 2.         Construct, use, and explain procedures for performing calculations with fractions and decimals with:

·        Pencil-and-paper

·        Mental math

·        Calculator

3.         Use an efficient and accurate pencil-and-paper procedure for division of a 3-digit number by a 2-digit number.

 4.         Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.

 5.         Find squares and cubes of whole numbers.

 6.         Check the reasonableness of results of computations.

 7.         Understand and use the various relationships among operations and properties of operations.

 8.         Understand and apply the standard algebraic order of operations for the four basic operations, including appropriate use of parentheses.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 7, students will:

 1.         Use and explain procedures for performing calculations with integers and all number types named above with:

·        Pencil-and-paper

·        Mental math

·        Calculator

 2.         Use exponentiation to find whole number powers of numbers.

 3.         Understand and apply the standard algebraic order of operations, including appropriate use of parentheses.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 8, students will:

 1.         Use and explain procedures for performing calculations involving addition, subtraction, multiplication, division, and exponentiation with integers and all number types named above with:

·        Pencil-and-paper

·        Mental math

·        Calculator

 2.         Use exponentiation to find whole number powers of numbers.

 3.         Find square and cube roots of numbers and understand the inverse nature of powers and roots.

 4.         Solve problems involving proportions and percents.

 5.         Understand and apply the standard algebraic order of operations, including appropriate use of parentheses.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 12, students will:

1.         Extend understanding and use of operations to real numbers and algebraic procedures.

 2.         Develop, apply, and explain methods for solving problems involving rational and negative exponents.

 3.         Perform operations on matrices.

·        Addition and subtraction

·        Scalar multiplication

 4.         Understand and apply the laws of exponents to simplify expressions involving numbers raised to power