Number+Sense+and+Operations

**Number Sense and Operations**
Students demonstrate number sense, including an understanding of number systems and operations and how they relate to one another. Students compute fluently and

**By the end of the 3-4 program:**
 * Use place value structure of the base-ten number system to read, write, represent and compare whole numbers and decimals.


 * Recognize and generate equivalent representations for whole numbers, fractions and decimals.


 * Represent commonly used fractions and mixed numbers using words and physical models.


 * Use models, points of reference and equivalent forms of commonly used fractions to judge the size of fractions and to compare, describe and order them.


 * Recognize and classify numbers as prime or composite and list factors.


 * Count money and make change using coins and paper bills to ten dollars.
 * By the end of the 5-7 program:**


 * Represent and compare numbers less than 0 through familiar applications and extending the number line.


 * Compare, order and convert among fractions, decimals and percents.


 * Develop meaning for percents, including percents greater than 100 and less than 1.


 * Use models and pictures to relate concepts of ratio, proportion and percent.


 * Use order of operations, including use of parenthesis and exponents to solve multi-step problems, and verify and interpret the results.


 * Apply number system properties when performing computations.


 * By the end of the 8-10 program:**
 * Use scientific notation to express large numbers and numbers less than one.


 * Identify subsets of the real number system.


 * Apply properties of operations and the real number system, and justify when they hold for a set of numbers.


 * Connect physical, verbal and symbolic representations of integers, rational numbers and irrational numbers.


 * Compare, order and determine equivalent forms of real numbers.


 * Explain the effects of operations on the magnitude of quantities.


 * Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions.

Example 3rd grade: Rewrite 3205 in expanded form 3 x 1000 + 2 x 100 + 5 x 1

Example 6th grade Solve the following problem by using order of operations 3(9-4)+5-2(10+3)-8= 3(5)+5-2(13)-8= 15+5-26-8= 20-18= 2