U.S. National Standards
N.1. Number and Operations (NCTM)
1.1. Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
1.1.4. Understand and use ratios and proportions to represent quantitative relationships.
1.3. Compute fluently and make reasonable estimates.
1.3.4. Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.
N.11. Grade 6 Curriculum Focal Points (NCTM)
11.2. Number and Operations: Connecting ratio and rate to multiplication and division
11.2.1. Students use simple reasoning about multiplication and division to solve ratio and rate problems (e.g., 'If 5 items cost $3.75 and all items are the same price, then I can find the cost of 12 items by first dividing $3.75 by 5 to find out how much one item costs and then multiplying the cost of a single item by 12'). By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative sizes of quantities, students extend whole number multiplication and division to ratios and rates. Thus, they expand the repertoire of problems that they can solve by using multiplication and division, and they build on their understanding of fractions to understand ratios. Students solve a wide variety of problems involving ratios and rates.