Number and Operations Standard for Grades 35
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 placevalue structure of the baseten 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;
 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.

Understand meanings of operations and how they relate to one
another 
 understand various meanings of multiplication and division;
 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;
 understand and use properties of operations, such as the distributivity of
multiplication over addition.

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 wholenumber
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;
 use visual models, benchmarks, and equivalent forms to add and subtract
commonly used fractions and decimals;
 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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