Mathematics Curriculum Framework
November 2000

Learning Standards by Strand

Number Sense and Operations
for Grades 5-6

cross symbolUnderstand numbers, ways of representing numbers, relationships among numbers, and number systems
solid circle symbolUnderstand meanings of operations and how they relate to one another
solid triangle symbolCompute fluently and make reasonable estimates

Learning Standards

Students engage in problem solving, communicating, reasoning, connecting, and representing as they:
6.N.1Demonstrate an understanding of positive integer exponents, in particular, when used in powers of ten, e.g., 102, 105. cross symbol
6.N.2Demonstrate an understanding of place value to billions and thousandths. cross symbol
6.N.3Represent and compare very large (billions) and very small (thousandths) positive numbers in various forms such as expanded notation without exponents, e.g., 9724 = 9 x 1000 + 7 x 100 + 2 x 10 + 4. cross symbol
6.N.4Demonstrate an understanding of fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on the number line. cross symbol
6.N.5Identify and determine common equivalent fractions, mixed numbers, decimals, and percents. cross symbol
6.N.6Find and position integers, fractions, mixed numbers, and decimals (both positive and negative) on the number line. cross symbol
6.N.7Compare and order integers (including negative integers), and positive fractions, mixed numbers, decimals, and percents. cross symbol
6.N.8Apply number theory concepts-including prime and composite numbers, prime factorization, greatest common factor, least common multiple, and divisibility rules for 2, 3, 4, 5, 6, 9, and 10-to the solution of problems. cross symbol
6.N.9Select and use appropriate operations to solve problems involving addition, subtraction, multiplication, division, and positive integer exponents with whole numbers, and with positive fractions, mixed numbers, decimals, and percents. solid circle symbol
6.N.10Use the number line to model addition and subtraction of integers, with the exception of subtracting negative integers. solid circle symbol
6.N.11Apply the Order of Operations for expressions involving addition, subtraction, multiplication, and division with grouping symbols (+, -, x, ÷). solid circle symbol
6.N.12Demonstrate an understanding of the inverse relationship of addition and subtraction, and use that understanding to simplify computation and solve problems. solid circle symbol
6.N.13Accurately and efficiently add, subtract, multiply, and divide (with double-digit divisors) whole numbers and positive decimals. solid triangle symbol
6.N.14Accurately and efficiently add, subtract, multiply, and divide positive fractions and mixed numbers. Simplify fractions. solid triangle symbol
6.N.15Add and subtract integers, with the exception of subtracting negative integers. solid triangle symbol
6.N.16Estimate results of computations with whole numbers, and with positive fractions, mixed numbers, decimals, and percents. Describe reasonableness of estimates. solid triangle symbol

Exploratory Concepts and Skills

  • Explore the addition and subtraction of positive and negative fractions.
  • Investigate the concepts of ratio and proportion.
  • Investigate the distributive property of multiplication over addition for double-digit multipliers, e.g., 12 x (10 + 3) is equivalent to 12 x 10 + 12 x 3.
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