Math Mammoth Linear Equations 1

123 pages
(includes answers)

Sample pages (PDF)
Contents
Two-Step Equations, Part 1

Word Problems and Equations, Part 1

Equations with Fractions 1
Inequalities

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Este libro en español

Math Mammoth Linear Equations 1 focuses on the linear equations of the types px + q = r and p(x + q) = r and best suits 7th grade mathematics studies. The book assumes that the student has already learned to solve simple one-step equations (for example −6x = 24 or x + 9 = −2). The equations in this book go one step further from that, into equations that typically require two steps (occasionally more) to solve and may contain parentheses.

The next step after this book (in 8th grade or in an algebra 1 course) is to learn to solve complex, multi-step linear equations — yet the beauty of mathematics is that even those complex equations will be able to be reduced to these simpler forms covered in this book.

The book contains several lessons where we focus writing an equation for a word problem. Students solve these word problems both using arithmetic and using an equation, comparing the solution steps.

There is also a lesson on patterns of growth, which may seem to be simply a fascinating topic, but in reality presents the fundamentals of a very important concept in algebra―that of linear functions (although they are not mentioned by that name).

After the section about equations, the text presents the basics of inequalities and how to graph them on a number line. Students apply the principles for solving equations to solve simple inequalities and word problems that involve inequalities.

The equations in this book are limited in complexity, with the variable on one side only, and usually only requiring two (sometimes three) steps to solve. In 8th grade, or in an algebra course, students solve multi-step linear equations, including those with the variable on both sides of the equation, thus completing their understanding of how to solve linear equations.

You will find free videos covering many topics of this book at https://www.mathmammoth.com/videos/ (choose 7th grade).
 

Good Mathematical Practices

• Many of the word problems ask students to compare an algebraic solution to a word problem with an arithmetic solution. This allows them to see the differences and similarities in the two approaches, and to wisely choose later on which approach or “tool” is more efficient.
• Encourage students to check each solution to an equation that they find. Checking and reflecting on your own work is an important habit, and is especially important in mathematics, where we often seek a precise answer to a question.
• Choosing a variable for the unknown in a word problem and writing an equation for the situation (in other words, representing a situation abstractly and symbolically) is an important skill practiced in this book. It is, in fact, an important subskill when modeling with mathematics.

The PDF version of this book can be filled in on a computer, phone, or tablet, using the annotation tools found in many PDF apps. See more.

A sequel to this book, Math Mammoth Linear Equations 2 delves into more complex linear equations, and into how many solutions a linear equation can have.