Whole Numbers: Count, read, and write whole numbers to 10,000.
Comparison and Ordering of Whole Numbers: Compare and order whole numbers to 10,000.
Place Value: Identify the place value for each digit in numbers to 10,000.
Rounding and Estimation: Round off numbers to 10,000 to the nearest ten, hundred, and thousand.
Expanded Notation: Use of expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6).
Multiplication tables: Memorize to automaticity the multiplication table for numbers between 1 and 10.
Inverse Relationship of Multiplication and Division: Use the inverse relationship of multiplication and division to compute and check results.
Multiplication:
Solve simple problems involving multiplication of multidigit numbers by one-digit numbers (3,671 x 3 = __).
Division: Solve division problems in which a multidigit number is evenly divided by a one-digit number (135 / 5 = __).
Properties of 0 and 1: Understand the special properties of 0 and 1 in multiplication and division.
Word Problems: Determine the unit cost when given the total cost and number of units and solve problems that require two or more of the skills mentioned above.
Fractions: Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context (e.g., 1/2 of a pizza is the same amount as 2/4 of another pizza that is the same size; show that 3/8 is larger than 1/4).
Addition and Subtraction of fractions: Add and subtract simple fractions (e.g., determine that 1/8 + 3/8 is the same as 1/2).
Money Problems: Solve problems involving addition, subtraction, multiplication, and division of money amounts in decimal notation and multiply and divide money amounts in decimal notation by using whole-number multipliers and divisors.
Fractions and Decimals: Know and understand that fractions and decimals are two different representations of the same concept (e.g., 50 cents is 1/2 of a dollar, 75 cents is 3/4 of a dollar).
Algebra and Functions
Equations and Inequalities: Represent relationships of quantities in the form of mathematical expressions, equations, or inequalities.
Solving Problems: Solve problems involving numeric equations or inequalities.
Operations and Symbols: Select appropriate operational and relational symbols to make an expression true
(e.g., if 4 __ 3 = 12, what operational symbol goes in the blank?).
Commutative and Associative Properties Recognize and use the commutative and associative properties of multiplication
(e.g., if 5 x 7 = 35, then what is 7 x 5? and if 5 x 7 x 3 = 105, then what is 7 x 3 x 5?).
Linear Patterns: Extend and recognize a linear pattern by its rules (e.g., the number of legs on a given number of horses may be calculated by counting by 4s or by multiplying the number of horses by 4).
Measurement and Geometry
Measurement: Choose the appropriate tools and units (metric and U.S.) and estimate and measure the length, liquid volume, and weight/mass of given objects.
Perimeter: Find the perimeter of a polygon with integer sides.
Conversion of Units: Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes).
Classifying Shapes: Identify, describe, and classify polygons (including pentagons, hexagons, and octagons).
Triangles: Identify attributes of triangles (e.g., two equal sides for the isosceles triangle, three equal sides for the equilateral triangle, right angle for the right triangle).
Quadrilaterls: Identify attributes of quadrilaterals (e.g., parallel sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square).
3D Figures: Identify, describe, and classify common three-dimensional geometric objects (e.g., cube, rectangular solid, sphere, prism, pyramid, cone, cylinder).
Statistics, Data Analysis, and Probability
Probability: Identify whether common events are certain, likely, unlikely, or improbable.
Outcomes of events: Record the possible outcomes for a simple event (e.g., tossing a coin) and systematically keep track of the outcomes when the event is repeated many times.
Representation of Results: Summarize and display the results of probability experiments in a clear and organized way (e.g., use a bar graph or a line plot).
Mathematical Reasoning
Reasoning: Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
Estimation: Use estimation to verify the reasonableness of calculated results.
Use of Strategies: Apply strategies and results from simpler problems to more complex problems.
Methods to Explain Reasoning: Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
Use of verbal and Symbolic work: Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
Generalization: Develop generalizations of the results obtained and apply them in other circumstances.
