U.S. National Standards
N.1. Number and Operations (NCTM)
1.1. Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
1.1.1. Work flexibly with fractions, decimals, and percents to solve problems.
1.2. Understand meanings of operations and how they relate to one another.
1.2.1. Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers.
1.3. Compute fluently and make reasonable estimates.
1.3.1. Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods.
1.3.2. Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.
N.11. Grade 6 Curriculum Focal Points (NCTM)
11.1. Number and Operations: Developing an understanding of and fluency with multiplication and division of fractions and decimals
11.1.1. Students use the meanings of fractions, multiplication and division, and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions and explain why they work. They use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain the procedures for multiplying and dividing decimals. Students use common procedures to multiply and divide fractions and decimals efficiently and accurately. They multiply and divide fractions and decimals to solve problems, including multi-step problems and problems involving measurement.
N.12. Connections to the Grade 6 Focal Points (NCTM)
12.1. Number and Operations: Students' work in dividing fractions shows them that they can express the result of dividing two whole numbers as a fraction (viewed as parts of a whole). Students then extend their work in grade 5 with division of whole numbers to give mixed number and decimal solutions to division problems with whole numbers. They recognize that ratio tables not only derive from rows in the multiplication table but also connect with equivalent fractions. Students distinguish multiplicative comparisons from additive comparisons.