Curriculum Focal Points

Table A.2. Table Grades A.2. 3–5 Grades Curriculum 3–5 Curriculum Focal Points Focal and Points Connections and Connections Compared Compared with with
the Expectations the Expectations of the Content of the Standards Content Standards in Principles Principles and Standards Standards for School for School
Mathematics Mathematics
Curriculum Curriculum Focal Points Focal and Points Connections and Connections
Grade 3
Grade Grade 34
Grade Grade 45
Grade Outside 5 grades 3–5
Outside Not identified grades at3–5
any level, pre-K–8
Not identified at
any level, pre-K–8
Expectations Expectations of the Content of the Content Standards Standards
Grade 3 Curriculum Grade 3 Curriculum Focal Points Focal Points
Number and Number Operations and Operations and Algebra: and Developing Algebra: Developing understandings understandings of of
multiplication multiplication and division and and division strategies and strategies for basic multiplication for basic multiplication facts and facts and
related division related facts division facts
Students understand Students understand the meanings the of meanings multiplication of multiplication and division and of whole division numbers of whole numbers
through the through use of representations the use of representations (e.g., equal-sized (e.g., equal-sized groups, arrays, groups, area arrays, models, area and models, and
equal “jumps” equal on “jumps” number on lines number for multiplication, lines for multiplication, and successive and subtraction, successive subtraction, partitioning,
and sharing ing, and for sharing division). for They division). use properties They use of properties addition of and addition multiplication and multiplication (e.g., (e.g.,
partition-
commutativity, commutativity, associativity, associativity, and the distributive and the distributive property) to property) multiply to whole multiply numbers whole numbers
and apply increasingly and apply increasingly sophisticated sophisticated strategies based strategies on these based properties on these to properties solve to solve
multiplication multiplication and division and problems division involving problems basic involving facts. basic By comparing facts. By comparing a variety of a variety of
solution strategies, solution students strategies, relate students multiplication relate multiplication and division and as inverse division operations. as inverse operations.
Number and Number Operations: and Operations: Developing Developing an understanding understanding of fractions of and fractions and
fraction equivalence
fraction equivalence
Students develop Students an develop understanding understanding of the meanings of the and meanings uses of and fractions uses of to fractions represent to represent
parts of a whole, parts of parts a whole, of a set, parts or points of a set, or or distances points or on distances a number on line. a number They understand line. They understand
that the size that of a the fractional size of a part fractional is relative part to is the relative size of to the whole, size of and the whole, they use and fractions they use fractions
to represent to numbers represent that numbers are equal that to, are less equal than, to, or less greater than, than or greater 1. They than solve 1. problems They solve problems
that involve that comparing involve comparing and ordering and fractions ordering by fractions using models, by using benchmark models, benchmark fractions, or fractions, or
common numerators common numerators denominators. or denominators. They understand They understand use models, and use including models, the including the
number line, number to identify line, equivalent to identify fractions. equivalent fractions.
Geometry: Geometry: Describing Describing and analyzing and analyzing properties properties of two-dimensional of two-dimensional shapes shapes
Students describe, Students analyze, describe, compare, analyze, and compare, classify and two-dimensional classify two-dimensional shapes by their shapes sides by their sides
and angles and connect angles and these connect attributes these to attributes definitions to of definitions shapes. Students of shapes. investigate, Students investigate,
describe, and describe, reason and about reason decomposing, about decomposing, combining, combining, and transforming and transforming polygons to polygons to
make other make polygons. other Through polygons. building, Through drawing, building, and drawing, analyzing and two-dimensional
analyzing two-dimensional
shapes, students shapes, understand students understand attributes and attributes properties and of properties two-dimensional of two-dimensional space and the space and the
use of those use attributes of those and attributes properties and in properties solving problems, in solving including problems, applications including applications
involving congruence involving congruence and symmetry. and symmetry.
Number and Number Operations, and Operations, Grades 3–5 Grades 3–5
Understand Understand the place-value the place-value structure of structure the base-ten of the number base-ten system number system
and be able and to represent be able to and represent compare and whole compare numbers whole and numbers decimals and decimals
Recognize equivalent Recognize representations equivalent representations for the same for number the same and number and
generate them generate by decomposing them by decomposing and composing and composing numbers numbers
Develop understanding Develop understanding of fractions of as fractions parts of unit as parts wholes, of unit as parts wholes, as parts
of a collection, of a as collection, locations as on locations number on lines, number and [in lines, Grade and 6 [in Grade 6
Curriculum Curriculum Focal Points] Focal as divisions Points] as of divisions whole numbers of whole numbers
Use models, Use benchmarks, models, benchmarks, and equivalent and forms equivalent to judge forms the to size judge of the size of
fractions fractions
Recognize and Recognize generate and equivalent generate forms equivalent of commonly forms of commonly used used
fractions, decimals, fractions, and decimals, [in Grade and 7 [in Curriculum Grade 7 Curriculum Focal Points] Focal Points]
percents percents
Explore numbers Explore less numbers than 0 by less extending than 0 by the extending number the line number and line and
through familiar through applications familiar applications
Describe classes Describe of numbers classes of according numbers to according characteristics to characteristics such as the such as the
nature of their nature factors of their factors
Understand Understand various meanings various of meanings multiplication of multiplication and divisionand division
Understand Understand the effects of the multiplying effects of multiplying and dividing and whole dividing whole
numbers numbers
Identify and Identify use relationships and use relationships between operations, between operations, such as division such as division as
the inverse the of multiplication, inverse of multiplication, to solve problems to solve problems
Understand Understand use properties and use of properties operations, of operations, such as the such distributivity
of multiplication ity of multiplication over addition over
as the distributiv-
addition
Develop fluency Develop with fluency basic number with basic combinations number combinations for multiplication for multiplication
and division and division use these and combinations use these combinations to mentally to compute mentally related compute related
problems, such problems, as 30 × such 50 as 30 × 50
(Continued) (Continued)
Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics 29