GRADE 4
Mathematics Learning Expectations
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
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)
Estimates and divides (up to a three digit number with a single divisor) with and without remainders
Understands fractions with denominators through 12 and mixed numbers
Identifies and represent 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 identifies properties of addition and multiplication on whole numbers in computations and problem situations May 2009
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 2D and 3D shapes (e.g. acute angles, parallel, parallelograms, and pyramids)
Compares and analyzes attributes and other features (e.g. number of sides, faces, corners, right angles, diagonals, and lines of symmetry) of 2-D and 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 order pairs of numbers and/or letters, graph, locate, 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
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/or 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 an analog and digital clock using a.m. and p.m.
May 2009
May 2009
Computes elapsed time using a clock and a calendar
Estimates and finds area of perimeter of a rectangle, triangle, or irregular shape, using diagrams, models, and grids, or by measuring
Data Analysis, Statistics, and Probability
Constructs, interprets and matches data on tables and graphs
Collects and organizes data using observations, measurements, surveys, or experiments, and identifies appropriate ways to display the data
Constructs and draws conclusions from representation of data sets in the forms of tables, line plots, line graphs, pictographs, tallies, and bar graphs
Matches representations of a data set in the forms of lists, tables, or graphs (including circle graphs) with the actual data
Lists and counts the number of possible combinations of objects from three sets (e.g. How many different outfits can one make from a set of 3 sweaters, a set of 2 skirts and 4 shoes?)
Classifies outcomes as certain, likely, unlikely, or impossible by designing and conducting experiments using concrete objects such as counters, number cubes, spinners, and coins
