Standard: 6.EE.B5 – 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.
Grade level: Grade 6
Subject: Mathematics
Domain: Expressions & Equations
Teacher Overview
This standard focuses on understanding the process of solving equations and inequalities by using substitution. It is important because it lays the foundation for more complex algebraic thinking and problem-solving skills that students will encounter in higher grades. Before tackling this standard, students should be comfortable with basic arithmetic operations and have a basic understanding of variables and simple algebraic expressions.
After mastering this standard, students will be able to tackle more complex equations and inequalities, graph solutions on a number line, and understand the relationships between different algebraic expressions.
Common Misconception 1
A common misconception is that the same number must always be substituted for a variable on both sides of an equation. This is incorrect because the goal is to find values that make the equation true, which may require different numbers on each side.
Intervention 1
To address this misconception, provide students with examples where different values are substituted on each side of the equation, and explain why the equation remains balanced.
Common Misconception 2
Another misconception is that inequalities can always be solved using the same operations as equations. This is incorrect because inequalities have unique rules, such as reversing the inequality sign when multiplying or dividing by a negative number.
Intervention 2
To correct this, use examples to show the specific rules for solving inequalities, and practice these rules with students until they understand the differences.
Prerequisite Knowledge
Students should have an understanding of basic arithmetic operations, including addition, subtraction, multiplication, and division. They should also be familiar with the concepts of variables and simple algebraic expressions.
Subsequent Knowledge
After mastering this standard, students will develop the ability to solve more complex equations and inequalities. They will also learn to graph solutions on a number line and understand the relationships between different algebraic expressions.
Instructional Activities
- Use balance scales and weights to visually demonstrate the concept of balancing equations.
- Create real-world scenarios where students must solve equations or inequalities to make decisions.
- Provide practice problems that require substitution to determine if a value makes an equation or inequality true.
- Use interactive online tools and games to reinforce the concepts of solving equations and inequalities.
- Organize group activities where students solve equations or inequalities together and explain their reasoning.
