Grade 5
  1. Number Sense and Place Value  1.1. Understanding Large Numbers  1.2. Place Value up to Millions  1.3. Comparing and Ordering Numbers  1.4. Rounding Whole Numbers  1.5. Expanded Form and Standard Form  1.6. Estimation in Calculations
  2. Operations with Whole Numbers  2.1. Addition of Large Numbers  2.2. Subtraction of Large Numbers  2.3. Multiplication Concepts and Strategies  2.4. Division Concepts and Strategies  2.5. Multi-Digit Multiplication  2.6. Long Division  2.7. Order of Operations
  3. Fractions  3.1. Introduction to Fractions  3.2. Equivalent Fractions  3.3. Simplifying Fractions  3.4. Comparing and Ordering Fractions  3.5. Addition and Subtraction of Fractions  3.6. Multiplication of Fractions  3.7. Division of Fractions  3.8. Mixed Numbers and Improper Fractions  3.9. Converting Between Improper Fractions and Mixed Numbers
  4. Decimals  4.1. Understanding Decimals  4.2. Place Value in Decimals  4.3. Comparing and Ordering Decimals  4.4. Rounding Decimals  4.5. Addition and Subtraction of Decimals  4.6. Multiplication of Decimals  4.7. Division of Decimals  4.8. Converting Decimals to Fractions and Vice Versa
  5. Measurement  5.1. Length Measurement (Metric and Customary Units)  5.2. Weight and Mass Measurement  5.3. Volume and Capacity Measurement  5.4. Area of Squares and Rectangles  5.5. Perimeter of Polygons  5.6. Time and Elapsed Time  5.7. Temperature  5.8. Understanding Metric Conversions
  6. Geometry  6.1. Types of Lines and Angles  6.2. Measuring Angles  6.3. Classifying Triangles  6.4. Properties of Quadrilaterals  6.5. Symmetry and Reflection  6.6. Transformations (Translation, Rotation, Reflection)  6.7. Coordinate Plane and Plotting Points  6.8. 3D Shapes and Their Properties  6.9. Nets of 3D Shapes  6.10. Understanding Congruence and Similarity
  7. Data and Probability  7.1. Introduction to Data Collection  7.2. Organizing Data (Tables and Tally Charts)  7.3. Graphs (Bar Graphs, Line Plots, Pictographs)  7.4. Mean, Median, and Mode  7.5. Range of Data  7.6. Introduction to Probability  7.7. Simple Events and Outcomes  7.8. Probability of Independent Events
  8. Ratios and Proportions  8.1. Understanding Ratios  8.2. Writing and Simplifying Ratios  8.3. Equivalent Ratios  8.4. Introduction to Proportions  8.5. Solving Proportion Problems
  9. Algebraic Thinking  9.1. Understanding Variables and Expressions  9.2. Writing Algebraic Expressions  9.3. Simplifying Expressions  9.4. Solving One-Step Equations  9.5. Understanding Patterns and Sequences  9.6. Using the Distributive Property
  10. Financial Literacy  10.1. Introduction to Money and Currency  10.2. Budgeting Basics  10.3. Saving and Spending  10.4. Understanding Interest  10.5. Basic Financial Planning  10.6. Simple vs. Compound Interest

Grade 5 → Algebraic Thinking ↓


Solving One-Step Equations


Solving one-step equations is an important concept in algebraic thinking. It is one of the building blocks that makes it easier to solve more complex equations later on. In math, an equation is a statement that equates two expressions. For example, in the equation x + 3 = 7, the expression x + 3 equals 7. In one-step equations, you only need to perform one operation to solve for the unknown variable.

Understanding one-step equations

One-step equations usually involve a single mathematical operation: addition, subtraction, multiplication, or division. To solve these equations, you must perform the inverse (opposite) operation to isolate the variable. Let's look at each type of one-step equation in detail.

Sum equations

In a summation equation, the variable is added to a number. Its opposite operation is subtraction. For example, consider the equation:

x + 5 = 12

To solve for x, we need to subtract 5 from both sides of the equation to keep it balanced. Let's subtract 5 from each side:

x + 5 - 5 = 12 - 5 x = 7

So, the solution is x = 7. Let's use a simple visual representation to show this:

X + 5 = 12

Subtraction equations

In a subtraction equation, a number is subtracted from the variable. The inverse operation is addition. Consider the equation:

x - 4 = 9

We add 4 to both sides to solve for x:

x - 4 + 4 = 9 + 4 x = 13

The solution is x = 13. Here's a visual approach:

X - 4 = 9

Multiplication equations

In a multiplication equation, the variable is multiplied by a number. The inverse operation is division. Check the equation:

3x = 15

To isolate x, divide both sides by 3:

3x / 3 = 15 / 3 x = 5

The answer is x = 5. Visual demonstration:

3x = 15

Division equation

In division equations, the variable is divided by a number. The inverse operation is multiplication. See example:

x / 4 = 3

Multiply both sides by 4 to find the value of x:

(x / 4) * 4 = 3 * 4 x = 12

Thus, x = 12. Visualize this:

X/4 = 3

Use of skills

Let's apply what we've learned with more examples:

Example 1: Solving x + 6 = 14

Subtract 6 to find x:

x + 6 - 6 = 14 - 6 x = 8

Example 2: Solving x - 5 = 6

Add 5 to both sides to solve:

x - 5 + 5 = 6 + 5 x = 11

Example 3: Solving 4x = 8

Divide both sides by 4:

4x / 4 = 8 / 4 x = 2

Example 4: Solving x / 3 = 7

Multiply both sides by 3:

(x / 3) * 3 = 7 * 3 x = 21

Common challenges

Students often make mistakes when they forget to perform the inverse operation on both sides of the equation. It is important to keep the equation balanced to find the correct solution.

Practice problems

Here are some practice problems for you to solve. Remember to perform the inverse operation on both sides of each equation to isolate the variable.

  1. x + 8 = 15
  2. x - 10 = 5
  3. 5x = 20
  4. x / 2 = 9

Conclusion

Solving one-step equations is an important skill in algebra that simplifies the process of solving complex equations. By understanding how to perform inverse operations, students gain confidence and accuracy in handling mathematical problems. Continue to practice these techniques to master the art of solving equations.

Additional resources

For more information, explore educational resources such as textbooks, worksheets, and online tutorials focused on equation solving strategies in algebra.


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Simplifying Expressions
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Solving One-Step Equations

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