| NUMBER SENSE |
| NUMBER SENSE 1.0: Students understand the place value of whole numbers:
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| 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 one-digit numbers (3,671 x 3 = __). |
| Number Sense 2.5 - Solve division problems in which a multidigit number is evenly divided by a one-digit 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 whole-number 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?).
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| 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).
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| 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). |
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| 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 three-dimensional 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).
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| 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.
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| 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. |
