| NUMBER SENSE |
| NUMBER SENSE 1.0: Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers: |
| Number Sense 1.1 - Read and write whole numbers in the millions. |
| Number Sense 1.2 - Order and compare whole numbers and decimals to two decimal places. |
| Number Sense 1.3 - Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand. |
| Number Sense 1.4 - Decide when a rounded solution is called for and explain why such a solution may be appropriate. |
| Number Sense 1.5 - 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 (see Standard 4.0). |
| Number Sense 1.6 - 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). |
| Number Sense 1.7 - Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line. |
| Number Sense 1.8 - Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, in "owing"). |
| Number Sense 1.9 - Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places.
|
|
| NUMBER SENSE 2.0: Students extend their use and understanding of whole numbers to the addition and subtraction of simple decimals: |
| Number Sense 2.1 - Estimate and compute the sum or difference of whole numbers and positive decimals to two places. |
| Number Sense 2.2 - Round two-place decimals to one decimal or the nearest whole number and judge the reasonableness of the rounded answer. |
| NUMBER SENSE 3.0: Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations: |
| Number Sense 3.1 - Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers. |
| Number Sense 3.2 - Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by a one-digit number; use relationships between them to simplify computations and to check results. |
| Number Sense 3.3 - Solve problems involving multiplication of multidigit numbers by two-digit numbers. |
| Number Sense 3.4 - Solve problems involving division of multidigit numbers by one-digit numbers. |
| NUMBER SENSE 4.0: Students know how to factor small whole numbers:
|
| Number Sense 4.1 - Understand that many whole numbers break down in different ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3). |
| Number Sense 4.2 - 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 1.0: Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences: |
| Algebra and Functions 1.1 - 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). |
| Algebra and Functions 1.2 - Interpret and evaluate mathematical expressions that now use parentheses. |
| Algebra and Functions 1.3 - Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations. |
| Algebra and Functions 1.4 - Use and interpret formulas (e.g., area = length x width or A = lw) to answer questions about quantities and their relationships. |
| Algebra and Functions 1.5 - Understand that an equation such as y = 3x + 5 is a prescription for determining a second number when a first number is given. |
|
| ALGEBRA AND FUNCTIONS 2.0: Students know how to manipulate equations: |
| Algebra and Functions 2.1 - Know and understand that equals added to equals are equal. |
| Algebra and Functions 2.2 - Know and understand that equals multiplied by equals are equal. |
|
| MEASUREMENT AND GEOMETRY 1.0: Students understand perimeter and area: |
| Measurement and Geometry 1.1 - 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). |
| Measurement and Geometry 1.2 - Recognize that rectangles that have the same area can have different perimeters. |
| Measurement and Geometry 1.3 - Understand that rectangles that have the same perimeter can have different areas. |
| Measurement and Geometry 1.4 - 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. |
|
| MEASUREMENT AND GEOMETRY 2.0: Students use two-dimensional coordinate grids to represent points and graph lines and simple figures: |
| Measurement and Geometry 2.1 - Draw the points corresponding to linear relationships on graph paper (e.g., draw 10 points on the graph of the equation y = 3x and connect them by using a straight line). |
| Measurement and Geometry 2.2 - Understand that the length of a horizontal line segment equals the difference of the x-coordinates. |
| Measurement and Geometry 2.3 - Understand that the length of a vertical line segment equals the difference of the y-coordinates. |
|
| MEASUREMENT AND GEOMETRY 3.0: Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems: |
| Measurement and Geometry 3.1 - Identify lines that are parallel and perpendicular. |
| Measurement and Geometry 3.2 - Identify the radius and diameter of a circle. |
| Measurement and Geometry 3.3 - Identify congruent figures. |
| Measurement and Geometry 3.4 - Identify figures that have bilateral and rotational symmetry. |
| Measurement and Geometry 3.5 - 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. |
| Measurement and Geometry 3.6 - 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. |
| Measurement and Geometry 3.7 - Know the definitions of different triangles (e.g., equilateral, isosceles, scalene) and identify their attributes. |
| Measurement and Geometry 3.8 - Know the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid). |
|
| STATISTICS, DATA ANALYSIS, AND PROBABILITY 1.0: Students organize, represent, and interpret numerical and categorical data and clearly communicate their findings: |
| Statistics, Data Analysis, and Probability 1.1 - Formulate survey questions; systematically collect and represent data on a number line; and coordinate graphs, tables, and charts. |
| Statistics, Data Analysis, and Probability 1.2 - Identify the mode(s) for sets of categorical data and the mode(s), median, and any apparent outliers for numerical data sets. |
| Statistics, Data Analysis, and Probability 1.3 - Interpret one-and two-variable data graphs to answer questions about a situation. |
|
| STATISTICS, DATA ANALYSIS, AND PROBABILITY 2.0: Students make predictions for simple probability situations: |
| Statistics, Data Analysis, and Probability 2.1 - Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams). |
| Statistics, Data Analysis, and Probability 2.2 - Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4; 3 /4). |
|
| 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. |
