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Number and Operations Standard for Grades 3–5
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Expectations |
| Instructional
programs from prekindergarten through grade 12 should enable
all students to— |
In grades 3–5 all students should— |
| Understand
numbers, ways of representing numbers, relationships among
numbers, and number systems |
| • |
understand the place-value structure of the base-ten number
system and be able to represent and compare whole numbers
and decimals; |
| • |
recognize equivalent representations for the same number
and generate them by decomposing and composing numbers;
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| • |
develop
understanding of fractions as parts of unit wholes, as
parts of a collection, as locations on number lines, and
as divisions of whole numbers; |
| • |
use models, benchmarks, and equivalent forms to judge
the size of fractions; |
| • |
recognize and generate equivalent forms of commonly used
fractions, decimals, and percents; |
| • |
explore numbers less than 0 by extending the number line
and through familiar applications; |
| • |
describe classes of numbers according to characteristics
such as the nature of their factors. |
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| Understand
meanings of operations and how they relate to one another |
| • |
understand various meanings of multiplication and division;
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| • |
understand the effects of multiplying and dividing whole
numbers; |
| • |
identify
and use relationships between operations, such as division
as the inverse of multiplication, to solve problems; |
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understand and use properties of operations, such as the
distributivity of multiplication over addition. |
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| Compute
fluently and make reasonable estimates |
| • |
develop fluency with basic number combinations for multiplication
and division and use these combinations to mentally compute
related problems, such as 30 50; |
| • |
develop fluency in adding, subtracting, multiplying, and
dividing whole numbers; |
| • |
develop and use strategies to estimate the results of
whole-number computations and to judge the reasonableness
of such results; |
| • |
develop and use strategies to estimate computations involving
fractions and decimals in situations relevant to students'
experience; |
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use visual models, benchmarks, and equivalent forms to
add and subtract commonly used fractions and decimals;
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select appropriate methods and tools for computing with
whole numbers from among mental computation, estimation,
calculators, and paper and pencil according to the context
and nature of the computation and use the selected method
or tools. |
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