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Math Mammoth Light Blue Series Grade 6-B Worktext

by Ingram

The two books (worktext part A and part B) deal with

  • review of the basic operations with whole numbers
  • beginning algebra topics: expressions, equations, and inequalities
  • review of all decimal arithmetic
  • introduction to ratios and percent
  • prime factorization, GCF, and LCM
  • a review of fraction arithmetic from 5th grade, plus a focus on division of fractions
  • the concept of integers, coordinate grid, addition & subtraction of integers
  • geometry: review of quadrilaterals & drawing problems; area of triangles & polygons; volume of rectangular prisms with fractional edge lengths; surface area
  • statistics: concept of distribution, measures of center, measures of variation, boxplots, stem-and-leaf plots, histograms

In sixth grade, students encounter the beginnings of algebra, learning about algebraic expressions, one-variable equations and inequalities, integers, and ratios. We also review and deepen the students' understanding of rational numbers: both fractions and decimals are studied in depth, while percent is a new topic for 6th grade. In geometry, students learn to compute the area of various polygons, and also calculate volume and surface area of various solids. The last major area of study is statistics, where students learn to summarize and describe distributions using both measures of center and variability.

The year starts out with a review of the four operations with whole numbers (including long division), place value, and rounding. Students are also introduced to exponents and do some problem solving.

Chapter 2 starts the study of algebra topics, delving first into expressions and equations. Students practice writing expressions in many different ways, and use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. We also study briefly inequalities and using two variables.

Chapter 3 has to do with decimals. This is a long chapter, as we review all of decimal arithmetic, just using more decimal digits than in 5th grade. Students also convert measuring units in this chapter.

Ratios is a new topic (chapter 4). Students are already familiar with finding fractional parts from earlier grades, and now it is time to advance that knowledge into the study of ratios, which arise naturally from dividing a quantity into many equal parts. We study such topics as rates, unit rates, equivalent ratios, and problem solving using bar models.

Percent (chapter 5) is an important topic to understand thoroughly, because of it many applications in real life. The goal of this chapter is to develop a basic understanding of percent, to see percentages as decimals, and to learn to calculate discounts.

In chapter 6, we first review prime factorization, and then study the greatest common factor and the least common multiple.

Chapter 7 first presents a thorough review of fraction operations from 5th grade (addition, subtraction, and multiplication). The topic of focus in the chapter is fraction division. Students also do some problem solving with fractions.

In chapter 8, students are introduced to integers. They plot points in all four quadrants of the coordinate plane and learn to add and subtract with negative numbers. Multiplication and division of integers are studied in 7th grade.

In geometry (chapter 9), the focus is on the area of polygons. This is studied in a logical progression: first, the area of right triangles, then the area of parallelograms, then, the area of triangles, and lastly the area of polygons. We also review some topics from earlier grades (quadrilaterals, perimeter, basic drawing). Other major topics in this chapter are calculating surface area of some solids using nets, and volume of rectangular prisms with fractional edge lengths.

Lastly, in chapter 10, students study statistics. The focus idea is that of a statistical distribution. Students learn about measures of center and measures of variability. They learn how to make dot plots, histograms, boxplots, and stem-and-leaf plots. All of these lessons are necessary to summarize and analyze distributions.