Whole Numbers: Read and write whole numbers in the millions.
Order of Number: Order and compare whole numbers and decimals to two decimal places.
Rounding Numbers: Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand.
Fractions: Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions.
Decimals and Fractions: Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 or .50; 7/4 = 1 3/4 = 1.75).
Negative Numbers: Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, in "owing").
Estimation: Estimate and compute the sum or difference of whole numbers and positive decimals to two places.
Algorithms: Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multi digit numbers.
Multiplication: Solve problems involving multiplication of multi digit numbers by two-digit numbers.
Division: Solve problems involving division of multi digit numbers by one-digit numbers.
Factors: Know that numbers such as 2, 3, 5, 7, and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers.
Algebra and Functions
Use of Symbols: Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable).
Solving Expressions: Interpret and evaluate mathematical expressions that now use parentheses.
Use of Formulae: Use and interpret formulas (e.g., area = length x width or A = lw) to answer questions about quantities and their relationships.
Measurement and Geometry
Measurement: Measure the area of rectangular shapes by using appropriate units, such as square centimeter (cm2), square meter (m2), square kilometer (km2), square inch (in2), square yard (yd2), or square mile (mi2).
Rectangles: Recognize that rectangles that have the same area can have different perimeters.
Use of Formulae: Understand and use formulas to solve problems involving perimeters and areas of rectangles and squares. Use those formulas to find the areas of more complex figures by dividing the figures into basic shapes.
Plotting Graphs: Draw the points corresponding to linear relationships on graph paper (e.g., draw 10 points on the graph of the equation y = 3 x and connect them by using a straight line).
Line Segment: Understand that the length of a horizontal line segment equals the difference of the x- coordinates and that the length of a vertical line segment equals the difference of the y- coordinates.
Solving Problems: Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems:
Parallel and Perpendicular Lines: Identify lines that are parallel and perpendicular.
Circle: Identify the radius and diameter of a circle.
Congruent Figures: Identify congruent figures.
Symmetry: Identify figures that have bilateral and rotational symmetry.
Angles: Know the definitions of a right angle, an acute angle, and an obtuse angle. Understand that 90°, 180°, 270°, and 360° are associated, respectively, with 1/4, 1/2, 3/4, and full turns.
2-D and 3-D Figures: Visualize, describe, and make models of geometric solids (e.g., prisms, pyramids) in terms of the number and shape of faces, edges, and vertices; interpret two-dimensional representations of three-dimensional objects; and draw patterns (of faces) for a solid that, when cut and folded, will make a model of the solid.
Triangles: Know the definitions of different triangles (e.g., equilateral, isosceles, scalene) and identify their attributes.
Quadrilaterls: Know the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid).
Statistics, Data Analysis, and Probability
Data Colletion: Formulate survey questions; systematically collect and represent data on a number line; and coordinate graphs, tables, and charts.
Mean, Median and Mode: Identify the mode(s) for sets of categorical data and the mode(s), median, and any apparent outliers for numerical data sets.
Outcomes of an event: Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams).
Mathematical Reasoning
Analysis of Problem: Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
Breaking a Problem: Determine when and how to break a problem into simpler parts.
Use of Strategies: Apply strategies and results from simpler problems to more complex problems.
Methods to Explain Mathematical Reasoning: Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
Approximations: Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
Checking Result: Make precise calculations and check the validity of the results from the context of the problem.
Reasoning: Evaluate the reasonableness of the solution in the context of the original situation.
Generalization of Results: Develop generalizations of the results obtained and apply them in other circumstances.
