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Wednesday, March 28, 2012

3-28-2012 One Variable Equations and Inequalities

Teching the CCCS for Grade 6 Mathematics

Expressions & Equations
The goal:
Students will be able to apply and extend previous understandings of arithmetic to algebraic expressions, reason about and solve one-variable equations and inequalities, and represent and analyze quantitative relationships between dependent and independent variables.
More specifically, students will understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students will understand that expressions in different forms can be equivalent, and they will use the properties of operations to rewrite expressions in equivalent forms. Students will learn that the solutions of an equation are the values of the variables that make the equation true. Students will use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students will construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they use equations (such as 3x = y) to describe relationships between quantities.
Reason about and solve one-variable equations and inequalities.

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.
1 Step Equations (add and subtract)
1 Step Equations (divide)

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.

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q andpx = q for cases in which pq and xare all nonnegative rational numbers.

Write an inequality of the form x > cor x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x< c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

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