Writing and Solving One-Step Equations

Grade 6 · 6.EE.B.7

In this lesson:

• Solve equations of the form and
• Write equations from real-world situations
• Verify solutions by substituting back

Learning Objectives for This Lesson

By the end of this lesson, you should be able to:

1. Write an equation of the form or from a real-world situation
2. Solve using the inverse operation: subtraction
3. Solve using the inverse operation: division
4. Verify solutions by substituting back into the equation

What Do You Already Know?

Is a solution to ?

• Substitute : — so no

The solution is the value that makes the equation true.

What value of works? Think before the next slide.

Equations as a Balance Scale

An equation is like a balance scale — both sides are equal.

The goal: isolate — get it alone on one side.

Solving : Use Subtraction

To isolate , subtract from both sides:

• Check: ✓

Addition is undone by subtraction.

Worked Examples with Addition Equations

Example 1:

Check: ✓

Example 2:

Check: ✓

Quick Check: Solve an Addition Equation

Solve:

• What operation is in the equation?
• What is the inverse operation?
• Apply it to both sides
• What is the check step?

Try it before the next slide.

Quick Check Answer: Solve x Plus 9

Solve:

Check: ✓

Solving : Use Division

To isolate in , divide both sides by :

• Check: ✓

Multiplication is undone by division.

Worked Examples with Multiplication Equations

Example 1:

Check: ✓

Example 2:

Check: ✓

Guided Practice: Solve a Multiplication Equation

Solve:

• The coefficient of is ___
• Divide both sides by ___
• ___

Complete the solution, then check your answer.

Guided Practice Answer: Five Times Seven

Solve:

The coefficient is . Divide both sides by :

Check: ✓

Watch Out: Subtracting the Wrong Side

Misconception: ✗

Correct: Subtract from both sides:

Check: ✓

Watch Out: Dividing in the Wrong Order

Misconception: ✗

Why it fails: Dividing the coefficient by instead of by the coefficient.

Correct approach: Divide by the coefficient:

Check: ✓

Identify the Equation Type Before Solving

Identify the type first — it determines the operation.

From Solving to Real-World Problems

We can now solve equations. Next: write them.

Real-world problems describe situations. Our job:

• Read the situation carefully
• Identify the unknown — give it a variable name
• Write an equation that models the situation
• Then solve and interpret

A Five-Step Protocol for Word Problems

Use this cycle for every word problem.

Word Problem 1: Emma's Savings (Additive)

Emma spent $12.50 on lunch, leaving her $7.25. How much did she start with?

Define: Let = Emma's starting amount (dollars)

Write:

Solve:

Check: ✓

Interpret: Emma started with $19.75.

Word Problem 2: Recipe Oil (Multiplicative)

A recipe uses cup per batch. How many batches from 4 cups?

Define: Let = number of batches

Write:

Solve:

Check: ✓

Interpret: 6 batches can be made.

Word Problem 3: Books on Shelves

There are 40 books split equally among 5 shelves. How many books per shelf?

Define: Let = books per shelf

Write:

Solve:

Check: ✓

Interpret: 8 books per shelf.

Watch Out: Setting Up Equations Backward

Wrong: ✗ ($12.50 is known — not the unknown)

Correct: Define roles first, then write:

• Starting amount = unknown →
• Equation:

Guided Practice: Write and Solve

A bag of apples costs $3.75. How many bags for $15.00?

Step 1: Define — let = ___

Step 2: Write — equation: ___

Step 3: Solve, check, and interpret

Work each step before the next slide.

Guided Practice Answer: Four Bags Total

A bag of apples costs $3.75. How many bags for $15.00?

Define: Let = number of bags

Write:

Solve:

Check: ✓

Interpret: You can buy 4 bags.

Independent Practice: Three Mixed Problems

Solve each equation. Show the inverse operation and check step.

3. A store charges $8.50 per item. How many items cost $42.50 total?

Work all three before the next slide.

Independent Practice: Answers and Check Steps

1. · Check: ✓

2. · Check: ✓

3. · 5 items ✓

Key Takeaways for This Lesson

✓ Addition equation: subtract from both sides

✓ Multiplication equation: divide both sides

✓ Always substitute back to check

Subtract from , not

Divide by the coefficient, not the reverse

Define the variable before writing the equation

What Comes Next: Two-Variable Equations

Today: One unknown, one solution

Next — 6.EE.C.9: Two variables, one relationship

A pattern between quantities, not a single unknown.