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.

C.     Estimation

By the end of Grade 2, students will:

 1.         Judge without counting whether a set of objects has less than, more than, or the same number of objects as a reference set.

 2.         Determine the reasonableness of an answer by estimating the result of computations (e.g., 15 + 16 is not 211).

 3.         Explore a variety of strategies for estimating both quantities (e.g., the number of marbles in a jar) and results of computation.

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

 1.         Judge without counting whether a set of objects has less than, more than, or the same number of objects as a reference set.

 2.         Construct and use a variety of estimation strategies (e.g., rounding and mental math) for estimating both quantities and the result of computations.

 3.         Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.

 4.         Use estimation to determine whether the result of a computation (either by calculator or by hand) is reasonable.

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

 1.         Judge without counting whether a set of objects has less than, more than, or the same number of objects as a reference set.

 2.         Construct and use a variety of estimation strategies (e.g., rounding and mental math) for estimating both quantities and the results of computations.

 3.         Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.

 4.         Use estimation to determine whether the result of a computation (either by calculator or by hand) is reasonable.

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

 1.         Use a variety of estimation strategies for both number and computation.

 2.         Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.

 3.         Determine the reasonableness of an answer by estimating the result of operations.

 4.         Determine whether a given estimate is an overestimate or an underestimate.

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

 1.         Use a variety of strategies for estimating both quantities and the results of computations.

 2.         Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.

 3.         Determine the reasonableness of an answer by estimating the result of operations.

 4.         Determine whether a given estimate is an overestimate or an underestimate.

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

 1.         Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation.

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

 1.         Estimate square and cube roots of numbers.

 2.         Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation.

 3.         Recognize the limitations of estimation and assess the amount of error resulting from estimation.

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

 1.         Recognize the limitations of estimation, assess the amount of error resulting from estimation, and determine whether the error is within acceptable tolerance limits.