Number Sense and Operations
Understands numbers to at least 99,999 (e.g. square numbers, multiples, rounding
and expanded notation )
• Reads, writes, models, orders, and compares numbers to 99,999
• Understands the values of the digits in the base ten number system
• Represents, orders, and compares large numbers using various forms, including
expanded notation (2753=2x1,000 + 7x100 + 5x10 + 3x1)
• Recognizes classes to which a number may belong (odd numbers, even numbers,
squares, factors , and multiples of numbers)
• Rounds whole numbers through 100,000 to the nearest 10, 100, 1,000, 10,000,
and 100,000
Selects and uses appropriate operations to solve word problems, including those
involving money
Estimates and solves up to five digit addition and subtraction problems
Knows multiplication combinations to 144 and division combinations from 144
Estimates and multiplies (up to three digit numbers by two digit numbers)
Divides (up to a three digit number with a single digit divisor) with and
without remainders
Understands fractions with denominators through 12, mixed and equivalent
fractions
•Identifies and represents fractions as parts of unit wholes, parts of groups ,
and as a location on a number line
•Selects, uses, and explains models to relate common fractions and mixed numbers
(1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10, 1/12, and 1 1/2)
• Orders and finds equivalent fractions, mixed numbers, and decimals
•Uses concrete objects and visual models to add and subtract common fractions
Understands decimals up to the hundredths and generates equivalent fractions
•Identifies and generates equivalent forms of common decimals and fractions less
than one whole (halves, quarters, fifths, and tenths)
•Reads, writes, and names decimals between 0 and 1 up to the hundredths
•Uses the commutative (order) and identity properties of addition and
multiplication on whole numbers in computations and problem situations September
2008
Patterns, Relations, and Algebra
Understands, determines, and extends geometric and numeric patterns (e.g.
variables in number sentences)
•Creates, describes, extends, and explains symbolic (geometric) patterns and
numeric patterns, including multiplication patterns
•Uses symbol and letter variables to represent unknowns and inequalities
•Determines values of variables in simple equations (e.g. 4106 - = 37)
•Uses pictures, models, tables, charts, graphs, words, number sentences, and
notations to interpret mathematical relationships
•Solves problems involving proportional relationships , including unit pricing
(e.g. 4 apples cost $.80, so 1 apple costs $.20)
•Determines how change in one variable relates to a change in a second variable
(e.g. input-output tables)
Geometry
Identifies, describes, manipulates, compares and contrasts properties of 2-D
shapes (e.g. acute angles, parallel and symmetrical and parallelograms)
•Compares and analyzes attributes and other features (e.g. number of sides,
faces, corners, right angles, diagonals, and lines of symmetry ) of 2-D shapes
•Describes, models, draws, compares, and classifies 2-D shapes (e.g. circles , and
polygons)
•Recognizes similar figures
•Identifies angles as acute, right, or obtuse
•Describes and draws intersecting, parallel, and perpendicular lines
•Uses ordered pairs of numbers and/or letters to graph, locate, and identify
points, and describe paths (first quadrant)
•Describes and applies techniques such as reflections (flips), rotations (turns),
and translations (slides) for determining if 2 shapes are congruent
•Identifies and describes line symmetry in 2-D shapes
•Predicts and validates the results of partitioning, folding, and combining 2-D
shapes
Identifies, describes, compares and contrasts properties of 3-D shapes (e.g.
cubes, faces, spheres and pyramids)
•Compares and analyzes attributes and other features (e.g. number of sides,
faces, corners, right angles, diagonals, and lines of symmetry) of 3-D shapes
•Describes, models, draws, compares, and classifies 3-D shapes (e.g. cubes,
spheres, and pyramids)
•Predicts and validates the results of partitioning, folding, and combining 3-D
shapes
Measurement
Compares, measures, and converts measurements (length, weight, area, perimeter,
and volume)
•Demonstrates an understanding of the attributes length, area, volume, and weight
•Selects the appropriate type of unit for measuring each attribute using both the
US Customary and the metric systems
•Carries out simple conversions within a system of measurement (e.g. hours to
minutes, cents to dollars)
•Identifies time to the minute on analog and digital clocks using a.m. and p.m.
•Computes elapsed time using a clock and a calendar
•Estimates and finds area or perimeter of a rectangle, triangle, or irregular
shape, using diagrams, models, and grids, or by measuring
Data Analysis, Statistics, and Probability
Organizes, matches, and represents tables and graphs and draws conclusions about
data
•Collects and organizes data using observations, measurements, surveys, or
experiments, and identifies appropriate ways to display the data
•Constructs and draws conclusions from representations of data sets in the forms
of tables, line plots , line graphs, pictographs, tallies, and bar graphs
