In this lesson:
By the end of this lesson, you should be able to:
Is a solution to ?
The solution is the value that makes the equation true.
What value of works? Think before the next slide.
An equation is like a balance scale — both sides are equal.
The goal: isolate — get it alone on one side.
To isolate , subtract from both sides:
Addition is undone by subtraction.
Example 1:
Check: ✓
Example 2:
Solve:
Try it before the next slide.
To isolate in , divide both sides by :
Multiplication is undone by division.
Complete the solution, then check your answer.
The coefficient is . Divide both sides by :
Misconception: ✗
Correct: Subtract from both sides:
Why it fails: Dividing the coefficient by instead of by the coefficient.
Correct approach: Divide by the coefficient:
Identify the type first — it determines the operation.
We can now solve equations. Next: write them.
Real-world problems describe situations. Our job:
Use this cycle for every word problem.
Emma spent $12.50 on lunch, leaving her $7.25. How much did she start with?
Define: Let = Emma's starting amount (dollars)
Write:
Interpret: Emma started with $19.75.
A recipe uses cup per batch. How many batches from 4 cups?
Define: Let = number of batches
Interpret: 6 batches can be made.
There are 40 books split equally among 5 shelves. How many books per shelf?
Define: Let = books per shelf
Interpret: 8 books per shelf.
Wrong: ✗ ($12.50 is known — not the unknown)
Correct: Define roles first, then write:
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.
Define: Let = number of bags
Interpret: You can buy 4 bags.
Solve each equation. Show the inverse operation and check step.
Work all three before the next slide.
1. · Check: ✓
2. · Check: ✓
3. · 5 items ✓
✓ 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
Today: One unknown, one solution
Next — 6.EE.C.9: Two variables, one relationship
A pattern between quantities, not a single unknown.
Click to begin the narrated lesson
Solve real-world and mathematical problems by writing and solving equations