NUMBER SENSE 
NUMBER SENSE 1.0: Students understand the place value of whole numbers:

Number Sense 1.1  Count, read, and write whole numbers to 10,000. 
Number Sense 1.2  Compare and order whole numbers to 10,000. 
Number Sense 1.3  Identify the place value for each digit in numbers to 10,000. 
Number Sense 1.4  Round off numbers to 10,000 to the nearest ten, hundred, and thousand. 
Number Sense 1.5  Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6). 
NUMBER SENSE 2.0: Students calculate and solve problems involving addition, subtraction, multiplication, and division: 
Number Sense 2.1  Find the sum or difference of two whole numbers between 0 and 10,000. 
Number Sense 2.2  Memorize to automaticity the multiplication table for numbers between 1 and 10. 
Number Sense 2.3  Use the inverse relationship of multiplication and division to compute and check results. 
Number Sense 2.4  Solve simple problems involving multiplication of multidigit numbers by onedigit numbers (3,671 x 3 = __). 
Number Sense 2.5  Solve division problems in which a multidigit number is evenly divided by a onedigit number (135 รท 5 = __). 
Number Sense 2.6  Understand the special properties of 0 and 1 in multiplication and division. 
Number Sense 2.7  Determine the unit cost when given the total cost and number of units. 
Number Sense 2.8  Solve problems that require two or more of the skills mentioned above. 
NUMBER SENSE 3.0: Students understand the relationship between whole numbers, simple fractions, and decimals: 
Number Sense 3.1  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). 
Number Sense 3.2  Add and subtract simple fractions (e.g., determine that 1/8 + 3/8 is the same as 1/2). 
Number Sense 3.3  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 wholenumber multipliers and divisors. 
Number Sense 3.4  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 1.0: Students select appropriate symbols, operations, and properties to represent, describe, simplify, and solve simple number relationships: 
Algebra and Functions 1.1  Represent relationships of quantities in the form of mathematical expressions, equations, or inequalities. 
Algebra and Functions 1.2  Solve problems involving numeric equations or inequalities. 
Algebra and Functions 1.3  Select appropriate operational and relational symbols to make an expression true (e.g., if 4 __ 3 = 12, what operational symbol goes in the blank?).

Algebra and Functions 1.4  Express simple unit conversions in symbolic form (e.g., __ inches = __ feet x 12). 
Algebra and Functions 1.5  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?). 
ALGEBRA AND FUNCTIONS 2.0: Students represent simple functional relationships: 
Algebra and Functions 2.1  Solve simple problems involving a functional relationship between two quantities (e.g., find the total cost of multiple items given the cost per unit).

Algebra and Functions 2.2  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 1.0: Students choose and use appropriate units and measurement tools to quantify the properties of objects: 
Measurement and Geometry 1.1  Choose the appropriate tools and units (metric and U.S.) and estimate and measure the length, liquid volume, and weight/mass of given objects. 
Measurement and Geometry 1.2  Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them. 
Measurement and Geometry 1.3  Find the perimeter of a polygon with integer sides. 
Measurement and Geometry 1.4  Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes). 
MEASUREMENT AND GEOMETRY 2.0: Students describe and compare the attributes of plane and solid geometric figures and use their understanding to show relationships and solve problems: 
Measurement and Geometry 2.1  Identify, describe, and classify polygons (including pentagons, hexagons, and octagons). 
Measurement and Geometry 2.2  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). 
Measurement and Geometry 2.3  Identify attributes of quadrilaterals (e.g., parallel sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square). 
Measurement and Geometry 2.4  Identify right angles in geometric figures or in appropriate objects and determine whether other angles are greater or less than a right angle. 
Measurement and Geometry 2.5  Identify, describe, and classify common threedimensional geometric objects (e.g., cube, rectangular solid, sphere, prism, pyramid, cone, cylinder). 
Measurement and Geometry 2.6  Identify common solid objects that are the components needed to make a more complex solid object. 
STATISTICS, DATA ANALYSIS, PROBABILITY 1.0: Students conduct simple probability experiments by determining the number of possible outcomes and make simple predictions: 
Statistics, Data Analysis, and Probability 1.1  Identify whether common events are certain, likely, unlikely, or improbable. 
Statistics, Data Analysis, and Probability 1.2  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. 
Statistics, Data Analysis, and Probability 1.3  Summarize and display the results of probability experiments in a clear and organized way (e.g., use a bar graph or a line plot).

Statistics, Data Analysis, and Probability 1.4  Use the results of probability experiments to predict future events (e.g., use a line plot to predict the temperature forecast for the next day). 
MATHEMATICAL REASONING 1.0: Students make decisions about how to approach problems: 
Mathematical Reasoning 1.1  Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. 
Mathematical Reasoning 1.2  Determine when and how to break a problem into simpler parts. 
MATHEMATICAL REASONING 2.0: Students use strategies, skills, and concepts in finding solutions: 
Mathematical Reasoning 2.1  Use estimation to verify the reasonableness of calculated results. 
Mathematical Reasoning 2.2  Apply strategies and results from simpler problems to more complex problems. 
Mathematical Reasoning 2.3  Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

Mathematical Reasoning 2.4  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. 
Mathematical Reasoning 2.5  Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy. 
Mathematical Reasoning 2.6  Make precise calculations and check the validity of the results from the context of the problem. 
MATHEMATICAL REASONING 3.0: Students move beyond a particular problem by generalizing to other situations: 
Mathematical Reasoning 3.1  Evaluate the reasonableness of the solution in the context of the original situation. 
Mathematical Reasoning 3.2  Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems. 
Mathematical Reasoning 3.3  Develop generalizations of the results obtained and apply them in other circumstances. 