U.S. National Standards
N.1. Number and Operations (NCTM)
1.1. Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
1.1.7. Develop meaning for integers and represent and compare quantities with them.
1.2. Understand meanings of operations and how they relate to one another.
1.2.2. Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals.
1.3. Compute fluently and make reasonable estimates.
1.3.2. Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.
N.11. Grade 7 Curriculum Focal Points (NCTM)
11.3. Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations
11.3.1. Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.