OSEI - One-Step Equations and Inequalities Module Overview

Math_MS6Banner.png One-Step Equations and Inequalities Module Overview

Introduction

image of scale on top of math based wordsSometimes when we make a bad decision, we wish we could "undo" it. Solving equations gives you that luxury. In this unit, you will discover ways to look at graphs and equations together instead of separately. You will see that solving equations using algebra is not as hard as you may have thought. It is just the act of undoing what was done by doing the opposite to both sides of the equation. You will see that the key of solving equations is keeping the equation "balanced."

Essential Questions

  • How is an equation like a balance?
  • How can the idea of balance help me solve an equation?
  • What strategies can I use to help me understand and represent real situations using proportions, equations, and inequalities?
  • How can I write, interpret and manipulate proportions, equations, and inequalities?
  • How can I solve a proportion, equation, or inequality?
  • How can I tell the difference between an expression, equation, and inequality?
  • How can proportions be used to solve problems?
  • How can proportional relationships be described using the equation y = kx?
  • How can proportional relationships be represented using rules, tables, and graphs?
  • How can the graph of y = kx be interpreted for different contexts?
  • How does a change in one variable affect the other variable in a given situation?
  • Which tells me more about the relationship I am investigating, a table, a graph, or a formula?

Key Terms

The following key terms will help you understand the content in this module.

  • Addition Property of Equality: Adding the same number to each side of an equation produces an equivalent expression.
  • Constant of Proportionality: The constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the constant of proportionality. In a proportional relationship, y = kx, k is the constant of proportionality, which is the value of the ratio between y and x.
  • Direct Proportion (Direct Variation): The relation between two quantities whose ratio remains constant. When one variable increases the other increases proportionally: When one variable doubles the other doubles, when one variable triples the other triples, and so on. When A changes by some factor, then B changes by the same factor: A=kB, where k is the constant of proportionality.
  • Division Property of Equality: States that when both sides of an equation are divided by the same number, the remaining expressions are still equal.
  • Equation: A mathematical sentence that contains an equal sign.
  • Inequality: A mathematical sentence that contains the symbols >, <, ≥, or ≤.
  • Inverse Operation: A mathematical process that combines two or more numbers such that its product or sum equals the identity.
  • Multiplication Property of Equality: States that when both sides of an equation are multiplied by the same number, the remaining expressions are still equal.
  • Proportion: An equation that states that two ratios are equal.
  • Subtraction Property of Equality: States that when both sides of an equation have the same number subtracted from them, the remaining expressions are still equal.
  • Term: A number, a variable, or a product of numbers and variables.
  • Variable: A letter or symbol used to represent a number or quantities that vary.

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