U.S. National Standards
N.1. Number and Operations (NCTM)
1.1. Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
1.1.3. Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.
1.3. Compute fluently and make reasonable estimates.
1.3.5. Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals.
N.2. Algebra (NCTM)
2.3. Use mathematical models to represent and understand quantitative relationships.
2.3.1. Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.
N.11. Grade 5 Curriculum Focal Points (NCTM)
11.2. Number and Operations: Developing an understanding of and fluency with addition and subtraction of fractions and decimals
11.2.1. Students apply their understandings of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They apply their understandings of decimal models, place value, and properties to add and subtract decimals. They develop fluency with standard procedures for adding and subtracting fractions and decimals. They make reasonable estimates of fraction and decimal sums and differences. Students add and subtract fractions and decimals to solve problems, including problems involving measurement.
N.12. Connections to the Grade 5 Focal Points (NCTM)
12.1. Algebra: Students use patterns, models, and relationships as contexts for writing and solving simple equations and inequalities. They create graphs of simple equations. They explore prime and composite numbers and discover concepts related to the addition and subtraction of fractions as they use factors and multiples, including applications of common factors and common multiples. They develop an understanding of the order of operations and use it for all operations.