Zeroing in on Number and Operations, Grades 7-8 : Key Ideas and Common Misconceptions

When you talk with students about their number sense and computational skills, you're bound to uncover some surprising gaps in their understanding. Knowing how to identify and bridge those gaps is essential for helping students at all levels advance as mathematical thinkers. The Zeroing in on Number and Operations series, which aligns with the Common Core State Standards and the NCTM Standards and Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained in decades of mathematics teaching and research, Anne Collins and Linda Dacey help you focus on what students really need to know and understand at each grade level. The 30 modules in the grades 7 and 8 flipchart are designed to engage all students in mathematical learning that develops conceptual understanding, addresses common misconceptions, and builds key ideas essential to future learning. The modules are organized into three sections: Number Theory and Integers; Fractions, Decimals and Percents; and Ratio and Proportionality. Each module begins with the identification of its Mathematical Focus and the Potential Challenges and Misconceptions associated with those ideas. In the Classroom then suggests instructional strategies and specific activities to implement with students. Meeting Individual Needs offers ideas for adjusting the activities to reach a broader range of learners. Each activity is supported by a reproducible (located in the appendix), and References/Further Reading provides resources for enriching your knowledge of the topic and gathering more ideas. At grades 7 and 8, the authors focus on the key ideas that are essential for success at these levels: Fundamental Theorem of Arithmetic using the uniqueness of the prime factorization for any given composite number Characteristics of whole numbers including primes, composites, evens, odds, square, cubic, and triangular numbers Properties of integers to include commutative, associative, distributive, identity, and inverse Rational numbers to include equivalencies among fraction, decimal, and percent representations and location of rational numbers on the number line Operations on all rational numbers to include fractions, decimal, integers, positive and negative exponents to include the multiplicative identity property Rational numbers to include division to represent any fraction as a decimal including fractions that represent infinite decimals Ratio and proportionality including rates and scaling Ratio as rate of change and its connection to slope Ratio tables and their connection to multiplication