Grade 6 Math Workbook with Answers

What is sixth grade math? The goal is to become more fluent in arithmetic (including fractions, decimals, percents, exponents, and negative numbers) and also to prepare prealgebra skills. Not all schools and teachers around the world cover the same topics in the same depth in 6th grade, yet at this stage the student is generally learning a variety of arithmetic and prealgebra skills. This sixth grade math workbook includes:

• order of operations
• ratios and proportions
• prime factorization (including factor trees and ladder diagrams)
• fractions, decimals, and percents
• data analysis (including histograms, box-and-whisker, stem-and-leaf, and dot plots)
• negative numbers
• exponents and squareroots
• geometric figures and the coordinate plane
• direct and inverse relationships
• a first introduction to working with variables
• financial mathematics
• and other sixth grade math and prealgebra skills

What does this workbook include?
With over 300 pages divided into 10 chapters, this book is packed with content. Each section presents a concise introduction to the pertinent concepts and includes examples to help serve as a guide. Exercises in each section offer practice. Answers are tabulated at the back of the book. Each chapter also ends with multiple choice questions that help assess how well the student has learned the material from the chapter.
This book covers a wide variety of sixth grade topics. A few of the main goals of sixth grade math are to become fluent in arithmetic, understand different operations and the order of operations, and to prepare for algebra.
Chapter 1 begins with arithmetic operations. Some sections are designed to improve fluency with multiplication and division, others introduce important ideas like the distributive property or the order of operations, and a couple of sections offer a preview of algebra skills like how to factor a perfect square out of a square root.
Chapters 2-3 provide a thorough review of essential skills involving fractions, decimals, and percents, including repeating decimals.
Chapter 4 covers ratios, proportions, and the rate equation. Ratios and rates involve important reasoning skills and are commonly encountered in word problems.
Chapter 5 introduces the idea of a variable and introduces basic algebra skills. The idea of this chapter is to help bridge the gap between sixth grade math and algebra. Topics include combining like terms, isolating the unknown, the connection between words and variables, solving simple equations, rules for exponents, and inequalities. A few sections offer a taste of algebra techniques such as working with square roots of variables or how to cross multiply. (Remember that the idea here is to give students some early exposure to algebra. The student should not be expected to become fluent in algebra until the student actually takes an algebra course. A little preview of algebra sometimes makes the transition easier.)
Chapter 6 discusses additive, multiplicative, and linear relationships, with emphasis on modeling and applications.
Chapter 7 covers data analysis, including the mean, median, range, standard deviation, interquartile range, frequency, relative frequency, and mode. Graphs include box-and-whisker plots, dot plots, histograms, stem-and-leaf plots, percent bar graphs, and pie charts.
Chapter 8 focuses on coordinate graphs with the algebraic variables x and y. This includes ordered pairs, the four quadrants, finding slope, the y-intercept, and the equation for a straight line.
Chapter 9 includes some basic geometric principles, like the angle sum theorem for triangles, complementary angles, supplementary angles, the triangle inequality, the Pythagorean theorem, quadrilaterals, perimeter, area, and volume.
Chapter 10 introduces a few important aspects of finance. Many schools include a little financial math in the curriculum because this is a practical aspect of mathematics.