Solving Equations

FinleyS, Sep 1, 2025

Review of Solving Equations progressing from 4th-8th grade skills

Table of Contents

  1. Review Skills Part 1
    1. Key Information for a Golf Scorecard
    2. Information in Parts of a Puzzle
    3. Describing the Meaning of a Variable in an Equation
    4. Solving One-Step Equations
    5. Solving One-Step Equations with a Tape Diagram
  2. Review Skills Part 2
    1. Visualizing Algebraic Equations Using a Balance Beam
    2. Solving Two-Step Equations
  3. Justification and Word Problems
    1. Solving Multi-Step Number Problems
    2. Solving Multi-Step Word Problems
    3. Translating Scenarios into Numeric Expressions
    4. Building One Variable Algebraic Expressions
    5. Modeling One Variable Algebraic Expressions
    6. Describing Expressions with a Curtain Reveal
    7. Using Substitution to Evaluate Expressions
    8. Describing Algebraic Expressions
    9. Solution and Justification Steps
    10. Constructing Step-by-Step Solutions
    11. Writing Algebraic Equations
    12. Writing Equations for Word Problems
  4. One Solution, No Solutions, and Infinite Solutions
    1. Solving One-Variable Equations: Hot and Cold Activity
    2. Exploring Number of Solutions of Equations
    3. Number of Solutions of Equations
    4. Building One-Variable Equations
  5. Literal Equations
    1. Solving Direct Variation Word Problems
    2. Visualizing Algebraic Rules Using Tile Patterns
    3. Equation of Ordered Pairs in Tile Patterns
    4. Finding the Multiplication Rule for Points on a Graph
    5. Writing Linear Equations Using Visual Patterns
    6. Variables as Numerical Expressions
  6. Inequalities
    1. Positive and Negative Numbers in a Bank Account
    2. Writing Word Problems for One-Step Inequalities
    3. Graphing Inequalities from Mathematical Notation
    4. Translating and Solving Real World Inequalities

1.

Review Skills Part 1

  • 1. Key Information for a Golf Scorecard
  • 2. Information in Parts of a Puzzle
  • 3. Describing the Meaning of a Variable in an Equation
  • 4. Solving One-Step Equations
  • 5. Solving One-Step Equations with a Tape Diagram

1.1.

Key Information for a Golf Scorecard

Identify important values and the unknown variable in word problems about a game of golf.
Putting It All Together
[i]Answer these open ended questions on your own or with others to form deeper math connections. [/i]
How can you find the unknown in a word problem?
How can you determine what the unknown represents in a word problem?
How can you find the important values in a word problem?
– GeoGebra Content Team

1.2.

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1.3.

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1.4.

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1.5.

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2.

Review Skills Part 2

  • 1. Visualizing Algebraic Equations Using a Balance Beam
  • 2. Solving Two-Step Equations

2.1.

Visualizing Algebraic Equations Using a Balance Beam

Build a model of an equation and see the connection between the model and the solution steps in this activity.
Putting It All Together
[i]Answer these open ended questions on your own or with others to form deeper math connections. [/i]
These equations are often called "two-step equations". Why do you think that is true?
What strategies would you use to solve the equation [math]5x-7=13[/math]?
– GeoGebra Content Team

2.2.

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3.

Justification and Word Problems

  • 1. Solving Multi-Step Number Problems
  • 2. Solving Multi-Step Word Problems
  • 3. Translating Scenarios into Numeric Expressions
  • 4. Building One Variable Algebraic Expressions
  • 5. Modeling One Variable Algebraic Expressions
  • 6. Describing Expressions with a Curtain Reveal
  • 7. Using Substitution to Evaluate Expressions
  • 8. Describing Algebraic Expressions
  • 9. Solution and Justification Steps
  • 10. Constructing Step-by-Step Solutions
  • 11. Writing Algebraic Equations
  • 12. Writing Equations for Word Problems

3.1.

Solving Multi-Step Number Problems

Practice solving number problems that require multiple operations to be performed one after another.
– GeoGebra Content Team

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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3.12.

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4.

One Solution, No Solutions, and Infinite Solutions

8th grade

  • 1. Solving One-Variable Equations: Hot and Cold Activity
  • 2. Exploring Number of Solutions of Equations
  • 3. Number of Solutions of Equations
  • 4. Building One-Variable Equations

4.1.

Solving One-Variable Equations: Hot and Cold Activity

Experiment with substituting different values into an equation. Determine whether there are 0, 1, or an infinite number of solutions.
Putting It All Together
[i]Answer these open ended questions on your own or with others to form deeper math connections.[/i]
How can you tell if an equation has one solution? Give an example.
How can you tell if an equation has no solution? Give an example.
How can you tell if an equation has infinitely many solutions? Give an example.
– GeoGebra Content Team

4.2.

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4.3.

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4.4.

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5.

Literal Equations

  • 1. Solving Direct Variation Word Problems
  • 2. Visualizing Algebraic Rules Using Tile Patterns
  • 3. Equation of Ordered Pairs in Tile Patterns
  • 4. Finding the Multiplication Rule for Points on a Graph
  • 5. Writing Linear Equations Using Visual Patterns
  • 6. Variables as Numerical Expressions

5.1.

Solving Direct Variation Word Problems

Build direct variation equations and use them to solve word problems in this interactive practice activity.
– GeoGebra Content Team

5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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6.

Inequalities

  • 1. Positive and Negative Numbers in a Bank Account
  • 2. Writing Word Problems for One-Step Inequalities
  • 3. Graphing Inequalities from Mathematical Notation
  • 4. Translating and Solving Real World Inequalities

6.1.

Positive and Negative Numbers in a Bank Account

Explore the use of positive and negative numbers in the context of money deposits and withdrawals.
Putting It All Together
[i]Answer these open ended questions on your own or with others to form deeper math connections. [/i]
What do the negative numbers on this number line represent in this scenario?
– GeoGebra Content Team

6.2.

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6.3.

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6.4.

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Information