NUMBER SENSE 
NUMBER SENSE 1.0: Students understand the place value of whole numbers: 
NUMBER SENSE 1.0: Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers: 
Number Sense 1.1  Estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths) numbers. 
Number Sense 1.2  Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number. 
Number Sense 1.3  Understand and compute positive integer powers of nonnegative integers; compute examples as repeated multiplication. 
Number Sense 1.4  Determine the prime factors of all numbers through 50 and write the numbers as the product of their prime factors by using exponents to show multiples of a factor (e.g., 24 = 2 x 2 x 2 x 3 = 23 x 3). 
Number Sense 1.5  Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers. 


NUMBER SENSE 2.0: Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals: 
Number Sense 2.1  Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results. 
Number Sense 2.2  Demonstrate proficiency with division, including division with positive decimals and long division with multidigit divisors. 
Number Sense 2.3  Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions and mixed numbers (like and unlike denominators of 20 or less), and express answers in the simplest form. 
Number Sense 2.4  Understand the concept of multiplication and division of fractions. 
Number Sense 2.5  Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems. 


ALGEBRA AND FUNCTIONS 
ALGEBRA AND FUNCTIONS 1.0: Students use variables in simple expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results: 
Algebra and Functions 1.1  Use information taken from a graph or equation to answer questions about a problem situation. 
Algebra and Functions 1.2  Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution. 
Algebra and Functions 1.3  Know and use the distributive property in equations and expressions with variables. 
Algebra and Functions 1.4  Identify and graph ordered pairs in the four quadrants of the coordinate plane. 
Algebra and Functions 1.5  Solve problems involving linear functions with integer values; write the equation; and graph the resulting ordered pairs of integers on a grid.



MEASUREMENT AND GEOMETRY 
MEASUREMENT AND GEOMETRY 1.0: Students understand and compute the volumes and areas of simple objects: 
Measurement and Geometry 1.1  Derive and use the formula for the area of a triangle and of a parallelogram by comparing it with the formula for the area of a rectangle (i.e., two of the same triangles make a parallelogram with twice the area; a parallelogram is compared with a rectangle of the same area by cutting and pasting a right triangle on the parallelogram). 
Measurement and Geometry 1.2  Construct a cube and rectangular box from twodimensional patterns and use these patterns to compute the surface area for these objects.

Measurement and Geometry 1.3  Understand the concept of volume and use the appropriate units in common measuring systems (i.e., cubic centimeter [cm3], cubic meter [m3], cubic inch [in3], cubic yard [yd3]) to compute the volume of rectangular solids. 
Measurement and Geometry 1.4  Differentiate between, and use appropriate units of measures for, twoand threedimensional objects (i.e., find the perimeter, area, volume).



MEASUREMENT AND GEOMETRY 2.0: Students identify, describe, and classify the properties of, and the relationships between, plane and solid geometric figures: 
Measurement and Geometry 2.1  Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor, drawing software). 
Measurement and Geometry 2.2  Know that the sum of the angles of any triangle is 180° and the sum of the angles of any quadrilateral is 360° and use this information to solve problems. 
Measurement and Geometry 2.3  Visualize and draw twodimensional views of threedimensional objects made from rectangular solids. 


STATISTICS, DATA ANALYSIS, AND PROBABILITY 
STATISTICS, DATA ANALYSIS, AND PROBABILITY 1.0: Students display, analyze, compare, and interpret different data sets, including data sets of different sizes:

Statistics, Data Analysis, and Probability 1.1  Know the concepts of mean, median, and mode; compute and compare simple examples to show that they may differ. 
Statistics, Data Analysis, and Probability 1.2  Organize and display singlevariable data in appropriate graphs and representations (e.g., histogram, circle graphs) and explain which types of graphs are appropriate for various data sets. 
Statistics, Data Analysis, and Probability 1.3  Use fractions and percentages to compare data sets of different sizes. 
Statistics, Data Analysis, and Probability 1.4  Identify ordered pairs of data from a graph and interpret the meaning of the data in terms of the situation depicted by the graph. 
Statistics, Data Analysis, and Probability 1.5  Know how to write ordered pairs correctly; for example, (x, y). 


MATHEMATICAL REASONING 
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. 
