Math Mammoth Expressions & Equations

109 pages
(includes answers)

Sample pages (PDF)
Contents
Expressions, Part 1
Writing and simplifying expressions 2: area
The distributive property
Solving equations

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Este libro en español

Math Mammoth Expressions & Equations is a worktext that focuses on the order of operations, equations, expressions, and simplifying expressions in several different ways. It is most suitable for 6th-7th grades. The main principles are explained and practiced both with visual models and in abstract form, and the lessons contain diverse practice problems that approach the concepts from various angles. We also touch on inequalities and graphing on an introductory level. In order to make learning these concepts easier, the expressions and equations in this book do not involve negative numbers (as they typically do when studied in pre-algebra and algebra).

We start out by studying the order of operations. Then the lessons focus on algebraic expressions. Students encounter the exact definition of an expression, a variable, and a formula, and practice writing expressions in many different ways. They study equivalent expressions and simplifying expressions. Length and area are two simple contexts I have used extensively for students to learn to write and simplify expressions.

In the lesson More On Writing and Simplifying Expressions students encounter more terminology: term, coefficient, and constant. In exercise #3, they write an expression for the perimeter of some shapes in two ways. This exercise is preparing the students to understand the distributive property.

In these lessons, students have opportunities to write real-world scenarios in terms of variables. In other words, they decontextualise — they abstract a given situation and represent it symbolically. Then, as they learn algebra, they learn to manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents, and to reason abstractly about those quantities represented by the variables.

The other major topic of the book is equations. Students learn some basics, such as, the solutions of an equation are the values of the variables that make the equation true. They use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. I have also included a few easy two-step equations.

Next, students solve and graph simple inequalities, again practicing the usage of variables to represent quantities. Lastly, they are introduced to the usage of two variables in algebra, including how to graph that relationship on a coordinate plane. This is an important topic, as so many real-life situations involve a relationship between two quantities, and graphing that relationship is an important tool in mathematical modeling.

You will find free videos covering many topics of this book at www.mathmammoth.com/videos/equations_expressions (the first three sections, up to the subtitle “Linear Equations”).

The digital download version (PDF) of this book is enabled for annotation. This means that if you prefer, the student can fill it in on a computer (with Adobe Reader) or on a tablet (requires a PDF app with annotation tools).