Introduction

Solving One-Step Equations is an important Grade 6 math skill because students are moving from simple answers toward explaining how the math works.

In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with solving one-step equations.

What Is Solving One-Step Equations?

Solving One-Step Equations means choosing a model, naming what each number means, and explaining the strategy.

The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.

Understanding Solving One-Step Equations

Before solving, students should slow down and decide what each number, shape, unit, or label represents.

  • Read the question carefully and identify what is being asked.
  • Choose a model, equation, table, or diagram that matches the situation.
  • Solve one step at a time and keep units or labels attached.
  • Use the answer explanation to check that the result makes sense.

Visual Models

Visual Model 1

Question: A balance scale shows \(x+5\) on one side and \(18\) on the other side, and they balance. Which equation describes this?

Visual Model 1

  • A. \(x=5+18\)
  • B. \(5x=18\)
  • C. \(x-5=18\)
  • D. \(x+5=18\)

Why it works: A balanced scale means both sides are equal. The equation is \(x+5=18\), which solves to \(x=13\).

Answer: \(x+5=18\)

Visual Model 2

Question: A tape diagram shows that a length is divided into \(4\) equal parts, each measuring \(6\) cm. Write and solve an equation for the total length \(x\).

Visual Model 2

  • A. \(4x=6\); \(x=1.5\)
  • B. \(x+4=6\); \(x=2\)
  • C. \(x-4=6\); \(x=10\)
  • D. \(\frac{x}{4}=6\); \(x=24\)

Why it works: The total is divided into \(4\) equal parts of \(6\) each, so \(\frac{x}{4}=6\). Multiplying by \(4\) gives \(x=24\) cm.

Answer: \(\frac{x}{4}=6\); \(x=24\)

Worked Examples

Example 1

Question: A bar model shows a number split into two equal parts. Each part is \(9\). Which equation and solution is correct?

Example 1

  • A. \(\frac{x}{2}=9\); \(x=18\)
  • B. \(x+2=9\); \(x=7\)
  • C. \(2x=9\); \(x=4.5\)
  • D. \(\frac{x}{2}=9\); \(x=4.5\)
  1. The number \(x\) is split into two equal parts of \(9\) each, so \(\frac{x}{2}=9\).
  2. Multiplying by \(2\) gives \(x=18\).

Answer: \(\frac{x}{2}=9\); \(x=18\)

Example 2

Question: A balance scale with a block on the left weighing \(x\) grams is balanced against \(2\) blocks on the right each weighing \(8\) grams. Which equation matches?

Example 2

  • A. \(x+2=8\)
  • B. \(2x=8\)
  • C. \(x=8-2\)
  • D. \(x=8+8\)
  1. Two blocks of \(8\) grams balance \(x\).
  2. So \(x=8+8=16\).
  3. Also written as \(x=2\times 8=16\).

Answer: \(x=8+8\)

Example 3

Question: Solve for \(x\): \(x+7=15\)

  • A. \(x=7\)
  • B. \(x=8\)
  • C. \(x=15\)
  • D. \(x=22\)
  1. Subtract \(7\) from both sides: \(x=15-7=8\).

Answer: \(x=8\)

Real-World Word Problems

Problem 1

Question: A student wrote this to solve \(x+8=15\): "I added \(8\) to both sides and got \(x=23\)." What is the error?

  • A. The student should divide by \(8\)
  • B. The student should multiply by \(8\)
  • C. The answer \(x=23\) is correct
  • D. The student should subtract \(8\) instead

Why it works: To undo addition, we subtract. Adding gave the wrong answer. Subtracting \(8\) from both sides gives \(x=7\).

Answer: The student should subtract \(8\) instead

Problem 2

Question: A shop has some apples. After selling \(12\) apples, there are \(28\) left. Write an equation and solve for the original number of apples \(x\).

  • A. \(x+12=28\); \(x=16\)
  • B. \(x-12=28\); \(x=40\)
  • C. \(12x=28\); \(x=2.33\)
  • D. \(\frac{x}{12}=28\); \(x=336\)

Why it works: Starting number minus \(12\) sold equals \(28\) remaining. So \(x-12=28\), giving \(x=40\).

Answer: \(x-12=28\); \(x=40\)

Common Mistakes

  • Rushing before identifying what the numbers represent.
  • Choosing an operation that does not match the situation.
  • Dropping labels, units, or context from the answer.
  • Skipping the estimate or reasonableness check.

Strategy Tips

  • Underline the question being asked.
  • Use a model before jumping to computation.
  • Write an equation that matches the story or picture.
  • Explain the final answer in a sentence.

Practice Questions

Question 1

Solve for \(x\): \(x+9=16\)

  • A. \(x=7\)
  • B. \(x=9\)
  • C. \(x=16\)
  • D. \(x=25\)

Question 2

Solve for \(x\): \(x-5=12\)

  • A. \(x=7\)
  • B. \(x=12\)
  • C. \(x=17\)
  • D. \(x=19\)

Question 3

Solve for \(x\): \(x-8=6\)

  • A. \(x=2\)
  • B. \(x=6\)
  • C. \(x=14\)
  • D. \(x=48\)

Question 4

Solve for \(x\): \(3x=18\)

  • A. \(x=6\)
  • B. \(x=15\)
  • C. \(x=21\)
  • D. \(x=54\)

Question 5

Solve for \(x\): \(5x=40\)

  • A. \(x=8\)
  • B. \(x=35\)
  • C. \(x=45\)
  • D. \(x=200\)

Question 6

Solve for \(x\): \(\frac{x}{4}=6\)

  • A. \(x=1.5\)
  • B. \(x=10\)
  • C. \(x=24\)
  • D. \(x=2.4\)
Full Answer Explanations Click to show all answers and explanations

Question 1

Answer: \(x=7\)

Subtract \(9\) from both sides: \(x=16-9=7\).

Question 2

Answer: \(x=17\)

Add \(5\) to both sides: \(x=12+5=17\).

Question 3

Answer: \(x=14\)

Add \(8\) to both sides: \(x=6+8=14\).

Question 4

Answer: \(x=6\)

Divide both sides by \(3\): \(x=18\div 3=6\).

Question 5

Answer: \(x=8\)

Divide both sides by \(5\): \(x=40\div 5=8\).

Question 6

Answer: \(x=24\)

Multiply both sides by \(4\): \(x=6\times 4=24\).

Timed practice quizzes

Related Quizzes

After studying Solving One-Step Equations, open these two timed quizzes in a new tab for focused extra practice.

Connection to Standards

This lesson supports Grade 6 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.

Summary

Solving One-Step Equations becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.

GOLDEN RULE

Understand the model before choosing the operation.