Mathematics

Number & Operations:

• Demonstrates understanding of place value and the magnitude for numbers up to 10,000.
• Composes and decomposes numbers in multiple ways up to 10,000.
• Understands the following number characteristics and their relationships: odd and even; factors and multiples; explore squares, primes and composites.
• Understands and applies divisibility rules for 2, 5 and 10.
• Understands the relationship among halves, fourths, and eighths and among thirds, sixths and twelfths.
• Uses area models and numerical reasoning to judge the relative size of fractions and order and compares fractions.
• Identifies, uses, and generates equivalent forms of commonly used fractions.
• Reads, compares, and orders decimals to tenths.
• Sees multiplication as an accumulation of groups of a number as well as uses and explains an array model for multiplication.
• Understands how division notation can represent a variety of division situations including sharing and partitioning.
• When solving problems, selects and uses appropirate operations to solve addition, subtraction, muliplication, and division problems.
• Understands the effect of an operation on whole numbers.
• Uses efficient, accurate, and flexible mental and written strategies based on numerical reasoning to find: sums and differences of multi-digit numbers (up to 4-digit numbers and including money amounts); products of 2-and 2-digit numbers; and quotients (dividing whole numbers up to 3-digits by 1-digit divisors).
• Develops, records, explains, and compares strategies for estimating and computing multiplication and division problems in more than one way.
• Demonstrates fluency with multiplication facts through 12 x 12 and the related division facts.
• Uses efficient, accurate, and flexible mental and written strategies based on numerical reasoning to add and substract: fractions with like denominators, unlike denominators & mixed numbers (halves, thirds, fourths, sixths, eighths); and decimals (tenths).

Geometry:

• Distinguishes between polygons and shapes that are not polygons and between regular and nonregular polygons.
• Recognizes and names polygons by the number of sides.
• Identifies and describes the results of sliding, flipping and turning 2-D shapes.
• Identifies and describes congruent figures.
• Sorts and classifies triangles and quadrilaterals and uses mathematical vocabulary to describe them.
• Identifies, draws, estimates and measures straight, right, acute and obtuse angels; uses known angles to find measures of other angles.
• Using ordered pairs, locates, graphs, and identifies points and describes paths on coordinate plane.
• Recognizes, identifies, and names 3-D shapes (cube, prism, sphere, cone, cylinder).
• Identifies and builds 3-D objects fro 2-D representations.
• Develops concepts and language needed to be able to think about and communicate about spatial relationships in 3-D environments.

Measurement:

• Estimates, measures, and compares lenght (to the nearest quarter inch & half centimeter).
• Selects and uses benchmarks to estimate measurement.
• Measures the area of a polygon using square and half units.
• Measures the perimeter of geometric figures.

Data & Probability:

• Collects and organizes data using observations, surveys, and experiments.
• Represents data using tables, bar graphs, line graphs, and line plots and circle graphs.
• Chooses and constructs representations that are appropriate for a data set.
• Compares related data sets with emphasis on range, center, and how the data are distributed.
• Describes the shape and important features of a set of data (median, mode, and range).
• Describes events with terms such as likely, unlikely, more likely, and less likely.
• Predicts the probability of outcomes of simple experiments, tests the predictions and records results.
• Recognizes that repeating a probability experiment several times can yeild a variety of results.

Algebra:

• Recognizes, describes, and extends geometric and numeric patterns.
• Explains and applies rules for pattern and functions.
• Recognizes and analyzes patterns and relationships using word, models, tables and graphs.
• Represents the idea of a variable as an unknown quantity using a letter or a symbol.
• Expresses mathematical relationships using equations.

Communication & Representation:

• Creates and uses representations to organize, record, and communicate mathematical ideas.
• Selects and applies appropriate mathematical representations to slove problems and demonstrate solution methods.
• Presents mathematical ideas and solutions in written, oral and visual forms.
• Communicates mathematically thinking coherently to others.
• Uses the language of mathematics to precisely express mathematical ideas and solution methods.
• Analyzes and evaluates the mathematical thinking and strategies of others.

Problem Solving:

• Selects, develops, adapts and applies strategies to solve a wide variety of problems.
• Transfers and generalizes previous experience to new problem solving situations.
• Builds new mathematical knowlege through problem solving.
• Demonstrates persistence in problem solving.
• Verifies results.