# 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.

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### Description

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 k...read more

### About the Author(s)

#### Anne M. Collins

Anne Collins has thirty years of teaching experience having taught all grade levels K-12 including undergraduate and graduate level courses. She has been providing mathematics content professional development institutes and courses for teachers for the past fourteen years.

#### Linda Dacey

Linda Dacey, professor of mathematics and education at Lesley University, began her career teaching at the elementary level and early in her career, received an NSF grant to develop a model program for preparing middle school teachers.

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Contents
Introduction
I. NUMBER THEORY AND INTEGERS
Prime Factorization
Factor Lattices
Special Numbers
Fun with Numbers
Number Line Integers
Chip Board Integers
Integers on the Cartesian Coordinate Plane
Order of Operations
II. FRACTIONS, DECIMALS, AND PERCENTS
Solving Problems with Fractions
Estimating with Decimals
Density of Radical Numbers
Ordering Fractions and Decimals
Dealing with Remainders
Exponents and Scientific Notation
The Look of Square Roots
Finding Factors with Square Roots
Benchmark Percents and Equivalencies
Operating with Percents
Percent of Increase or Decrease
Solving Problems with Rational Numbers
III. RATIO AND PROPORTIONALITY
Operating on Ratios
Representing Ratios on Graphs
Working with Ratios
Rate Tables
Interpreting Ratios
Unit Rates
Analyzing Change
Reasoning Proportionality
Solving Problems with Proportionality
Inverse Proportions
Appendix