Standard 4:Mathematics

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.
 

A.     Number Sense
 

By the end of Grade 2, students will:
 

 1.         Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 2 pertain to these sets of numbers as well).

·        Whole numbers through hundreds

·        Ordinals

·        Proper fractions (denominators of 2, 3, 4, 8, 10)
 

 2.         Demonstrate an understanding of whole number place value concepts.

 

 3.         Understand that numbers have a variety of uses.

 

 4.         Count and perform simple computations with coins.

·        Amounts up to $1.00 (using cents notation)
 

 5.         Compare and order whole numbers.
 

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

 1.         Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 3 pertain to these sets of numbers as well).

·        Whole numbers through hundred thousands

·        Commonly used fractions (denominators of 2, 3, 4, 5, 6, 8, 10) as part of a whole, as a subset of a set, and as a location on a number line
 

 2.         Demonstrate an understanding of whole number place value concepts.
 

3.         Identify whether any whole number is odd or even.
 

 4.         Explore the extension of the place value system to decimals through hundredths.
 

 5.         Understand the various uses of numbers.

·        Counting, measuring, labeling (e.g., numbers on baseball uniforms)
 

 6.         Compare and order numbers.
 

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

 1.         Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 4 pertain to these sets of numbers as well).

·        Whole numbers through millions

·        Commonly used fractions (denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 16) as part of a whole, as a subset of a set, and as a location on a number line

·        Decimals through hundredths
 

 2.         Demonstrate an understanding of place value concepts.

 

 3.         Demonstrate a sense of the relative magnitudes of numbers.
 

 4.         Understand the various uses of numbers.

·        Counting, measuring, labeling (e.g., numbers on baseball uniforms), locating (e.g., Room 235 is on the second floor)
 

 5.         Use concrete and pictorial models to relate whole numbers, commonly used fractions, and decimals to each other, and to represent equivalent forms of the same number.
 

 6.         Compare and order numbers.

 

 7.         Explore settings that give rise to negative numbers.

·        Temperatures below 0o, debts

·        Extension of the number line

 

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

 1.         Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 5 pertain to these sets of numbers as well).

·        All fractions as part of a whole, as subset of a set, as a location on a number line, and as divisions of whole numbers

·        All decimals

 

 2.         Recognize the decimal nature of United States currency and compute with money.
 

 3.         Demonstrate a sense of the relative magnitudes of numbers.
 

 4.         Use whole numbers, fractions, and decimals to represent equivalent forms of the same number.

 

 5.         Develop and apply number theory concepts in problem solving situations.

·        Primes, factors, multiples
 

 6.         Compare and order numbers.

 

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

 1.         Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 6 pertain to these sets of numbers as well).

·        All integers

·        All fractions as part of a whole, as subset of a set, as a location on a number line, and as divisions of whole numbers

·        All decimals

 

 2.         Recognize the decimal nature of United States currency and compute with money.
 

 3.         Demonstrate a sense of the relative magnitudes of numbers.
 

 4.         Explore the use of ratios and proportions in a variety of situations.
 

 5.         Understand and use whole-number percents between 1 and 100 in a variety of situations.
 

 6.         Use whole numbers, fractions, and decimals to represent equivalent forms of the same number.

 

 7.         Develop and apply number theory concepts in problem solving situations.

·        Primes, factors, multiples

·        Common multiples, common factors
 

 8.         Compare and order numbers.

 

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

 1.         Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 7 pertain to these sets of numbers as well):

·        Rational numbers

·        Percents

·        Whole numbers with exponents

 

 2.         Demonstrate a sense of the relative magnitudes of numbers.
 

 3.         Understand and use ratios, proportions, and percents (including percents greater than 100 and less than 1) in a variety of situations.
 

 4.         Compare and order numbers of all named types.
 

 5.         Use whole numbers, fractions, decimals, and percents to represent equivalent forms of the same number.
 

 6.         Understand that all fractions can be represented as repeating or terminating decimals.
 

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

 1.         Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well):

·        Rational numbers

·        Percents

·        Exponents

·        Roots

·        Absolute values

·        Numbers represented in scientific notation

 

 2.         Demonstrate a sense of the relative magnitudes of numbers.
 

 3.         Understand and use ratios, proportions, and percents (including percents greater than 100 and less than 1) in a variety of situations.
 

 4.         Compare and order numbers of all named types.
 

 5.         Use whole numbers, fractions, decimals, and percents to represent equivalent forms of the same number.
 

 6.         Recognize that repeating decimals correspond to fractions and determine their fractional equivalents.

·        5/7 = 0. 714285714285…  =  0.
 

 7.         Construct meanings for common irrational numbers, such as p (pi) and the square root of 2.
 

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

 1.         Extend understanding of the number system to all real numbers.

 

 2.         Compare and order rational and irrational numbers.
 

 3.         Develop conjectures and informal proofs of properties of number systems and sets of numbers.