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Math for Grade 6
1 Number Sense
1-1 Understanding Place Value
1-2 Comparing and Ordering Numbers
1-3 Rounding Numbers
1-4 Estimating Sums and Differences
2 Operations with Whole Numbers
2-1 Addition and Subtraction
2-2 Multiplication and Division
2-3 Properties of Operations
2-4 Problem Solving with Whole Numbers
3 Fractions
3-1 Understanding Fractions
3-2 Equivalent Fractions
3-3 Comparing and Ordering Fractions
3-4 Adding and Subtracting Fractions
3-5 Multiplying and Dividing Fractions
3-6 Mixed Numbers and Improper Fractions
4 Decimals
4-1 Understanding Decimals
4-2 Comparing and Ordering Decimals
4-3 Adding and Subtracting Decimals
4-4 Multiplying and Dividing Decimals
4-5 Converting Between Fractions and Decimals
5 Algebraic Thinking
5-1 Patterns and Sequences
5-2 Expressions and Equations
5-3 Solving Simple Equations
5-4 Variables and Algebraic Expressions
6 Geometry
6-1 Basic Shapes and Properties
6-2 Angles and Lines
6-3 Perimeter and Area
6-4 Volume and Surface Area
6-5 Symmetry and Transformations
7 Measurement
7-1 Units of Measurement
7-2 Converting Units
7-3 Time and Calendar
7-4 Money and Financial Literacy
8 Data Handling
8-1 Collecting and Organizing Data
8-2 Interpreting Data
8-3 Mean, Median, Mode, and Range
8-4 Graphs and Charts
9 Probability
9-1 Understanding Probability
9-2 Experimental and Theoretical Probability
9-3 Simple Probability Problems
10 Problem Solving Strategies
10-1 Logical Reasoning
10-2 Estimation and Approximation
10-3 Model Building
10-4 Communication of Mathematical Ideas
Solving Simple Equations

Solving Simple Equations

Key Concepts

Solving simple equations involves finding the value of a variable that makes the equation true. The key concepts include:

1. Understanding the Equation

An equation is a mathematical statement that two expressions are equal. The goal is to find the value of the variable that makes the equation true.

Example: In the equation 2x + 3 = 7, 'x' is the variable we need to solve for.

2. Isolating the Variable

To solve an equation, we need to isolate the variable on one side of the equation. This means getting 'x' (or any other variable) by itself on one side of the equal sign.

Example: In the equation 2x + 3 = 7, we want to isolate 'x' by removing the 3 and the 2 from the left side.

3. Using Inverse Operations

Inverse operations are used to undo operations in an equation. For example, addition and subtraction are inverse operations, and multiplication and division are inverse operations.

Example: To solve 2x + 3 = 7, first subtract 3 from both sides to get 2x = 4, then divide both sides by 2 to get x = 2.

4. Checking the Solution

After finding the value of the variable, it's important to check the solution by substituting it back into the original equation to ensure it makes the equation true.

Example: Substitute x = 2 back into the equation 2x + 3 = 7. We get 2(2) + 3 = 4 + 3 = 7, which is true, so x = 2 is the correct solution.

Examples and Analogies

Imagine you have a balance scale with weights on both sides. To find the weight of one object, you need to remove equal weights from both sides until the object is by itself. This is similar to isolating the variable in an equation.

Another analogy is a seesaw. To balance it, you need to add or remove weights from both sides equally. This is like using inverse operations to solve an equation.

Insightful Content

Solving simple equations is like solving a puzzle where you need to find the missing piece. By understanding the equation, isolating the variable, using inverse operations, and checking the solution, you can solve any simple equation with confidence. This skill is foundational for more complex algebraic problems and real-world applications.

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