# Introduction to Algebra: Grade 6 (Distance Learning)

Created ByMaria Miller
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In the unit Introduction to Algebra: Grade 6, we concentrate on two important concepts: expressions and equations. We also touch on inequalities and graphing on a very introductory level. In order to make the learning of these concepts easier, the expressions and equations in this unit do not involve negative numbers (as they typically do when studied in pre-algebra and algebra).

We start out by learning some basic vocabulary used to describe mathematical expressions verballyโterms such as the sum, the difference, the product, the quotient, and the quantity. Next, we study the order of operations once again. A lot of this lesson is review. The lesson Multiplying and Dividing in Parts is also partially review and leads up to the lesson on distributive property that follows later.

Then, we get into studying expressions in definite terms: students encounter the exact definition of an expression, a variable, and a formula, and practice writing expressions in many different ways.

The concepts of equivalent expressions and simplifying expressions are important. If you can simplify an expression in some way, the new expression you get is equivalent to the first. We study these ideas first using lengthsโ it is a concrete example, and hopefully easy to grasp.

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 once again preparing them to understand the distributive property.

Next, students write and simplify expressions for the area of rectangles and rectangular shapes. Then we study the distributive property, concentrating on the symbolic aspect and tying it in with area models.

The next topic 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 two-step equations as an optional topic.

Lastly, in this unit students get to solve and graph simple inequalities, and study the usage of two variables and graphing.

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This PDF is enabled for annotation.

This means the student can fill it in using a computer or a tablet (distance learning).

The student will need to use either Adobe Reader (on desktop/laptop) or a PDF app that has annotation tools (phones or tablets). Several PDF apps with annotation capabilities exist; see more details here.

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It is recommended that you not share the entire PDF file with students. Instead, it is better to just give the students a few pages at a time. Here is a simple method for extracting a few pages from a PDF file. It is done using Google Chrome.

1. Open the PDF file in Chrome.

2. Go to "Print" (Ctrl+P).

3. Print to PDF, and choose the page range.

4. Click the "Save" button.

Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation ๐ฅ = 65๐ต to represent the relationship between distance and time.
Write an inequality of the form ๐น > ๐ค or ๐น < ๐ค to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form ๐น > ๐ค or ๐น < ๐ค have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
Solve real-world and mathematical problems by writing and solving equations of the form ๐น + ๐ฑ = ๐ฒ and ๐ฑ๐น = ๐ฒ for cases in which ๐ฑ, ๐ฒ and ๐น are all nonnegative rational numbers.
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
Total Pages
80 pages