Percent Puzzle Lesson Plan Lesson Plan: The Percent Puzzle
Solving Percent Equations & Proportions
Grade 9 | Mathematics
Duration: 65 Minutes
Learning Objectives
Identify the Part, Whole, and Percent in a word problem.
Set up and solve percent equations (\(a = p \cdot w\)).
Set up and solve percent proportions (\(\frac{is}{of} = \frac{\%}{100}\)).
Apply percent solving strategies to real-world scenarios.
Materials Needed
"The Percent Puzzle" Slide Deck
Percent Equation Triangle Reference
Percent Problems Worksheet
Exit Ticket
Calculators (optional but recommended)
Instructional Arc
0-10 min
Introduction & Hook: The Missing Piece
Engage students with a "Mystery Discount" scenario. Present a price tag with a price and a final cost, but the percentage off is missing. Ask: "How do we find the missing piece of this puzzle?"
10-25 min
Direct Instruction: Building the Tools
Introduce the two primary methods for solving percent problems:
The Percent Equation: \(Part = Percent \times Whole\) (convert % to decimal).The Percent Proportion: \(\frac{Part}{Whole} = \frac{Percent}{100}\).
Distribute the Percent Equation Triangle and explain how to use it to isolate the unknown variable.
25-40 min
Guided Practice: Solving the Puzzle
Work through 3 distinct examples as a class:
Finding the Part : What is 15% of 80?
Finding the Percent : 12 is what percent of 40?
Finding the Whole : 18 is 30% of what number?
40-55 min
Independent Practice: Solving Percent Problems
Students work on the Solving Percent Problems Worksheet . Circulate to provide support, specifically focusing on students struggling with setting up the initial equation. Encourage use of the triangle reference.
55-65 min
Wrap-up & Assessment: The Final Solution
Review one challenging problem from the worksheet. Exit Ticket: Students complete two quick problems to demonstrate mastery.
Differentiation Strategies
Support
Provide a pre-filled "Is/Of" table for every problem.
Use the Equation Triangle as a constant visual scaffold.
Extension
Multi-step problems (e.g., price after tax and a discount).
Have students write their own word problems.
Percent Equation Triangle Reference The Percent Equation Triangle
Your Master Key to Solving Percent Puzzles
PART (is) % WHOLE (of)
How to Use:
Cover the variable you are looking for with your hand. The remaining parts show the operation:
To Find PART:
Multiply % by whole.
\(% \cdot Whole\)
To Find %:
Divide part by whole.
\(\frac{Part}{Whole}\)
To Find WHOLE:
Divide part by %.
\(\frac{Part}{\%}\)
Prefer Proportions?
Use this setup for every problem:
is
of
=
%
100
Solving Percent Problems Worksheet Solving Percent Problems
Worksheet: Can you solve the puzzle?
Name:
Date:
Part 1: Identify the Pieces
Label the Part (P), Whole (W), and Percent (%) in each statement below. Use 'x' for the missing piece.
1. 15 is 20% of 75
Part: 15
Whole: 75
Percent: 20%
2. What is 30% of 90?
Part:
Whole:
Percent:
3. 12 is what percent of 40?
Part:
Whole:
Percent:
Part 2: Solving the Puzzle
Show your setup and solve for the unknown.
4. What is 15% of 120?
Answer:
5. 18 is what percent of 72?
Answer:
6. 24 is 40% of what number?
Answer:
7. What percent of 50 is 35?
Answer:
Part 3: Real-World Scenarios
8. The New Jacket: A winter jacket is originally priced at $150. If there is a 25% discount, how much money will you save?
Savings: $
9. Test Results: You answered 17 questions correctly on a math test. If you received an 85%, how many total questions were on the test?
Total Questions:
Percent Puzzle Exit Ticket Exit Ticket: The Final Piece
Lesson: Solving Percent Equations
NAME:
DATE:
1
Challenge: Find the Percent
"What percent of 60 is 15?"
Show Your Work:
Answer:
2
Challenge: Find the Whole
"18 is 30% of what number?"
Show Your Work:
Answer:
Reflection
How confident do you feel about solving percent puzzles?
1 STUCK
2
3 OKAY
4
5 READY
What strategy (Triangle, Proportion, or Equation) was most helpful today? Why?
Percent Puzzle Slides Revised The Percent Puzzle
Solving Percent Equations & Proportions
9th Grade Algebra
Mission Objective
"Today, we will learn to set up and solve percent equations and proportions to find the part, whole, or percent."
The Mystery Discount
Retail Price:
$120.00
SALE!
You Pay:
$90.00
What is the missing piece of this puzzle?
How much of a percentage discount did you actually receive?
The Vocabulary of Percents
The PART
A portion of the whole amount. Often followed by the word "is".
"12 is what percent of 40?"
The WHOLE
The total amount. Often followed by the word "of".
"What is 30% of 80?"
The PERCENT
The ratio per 100. Look for the % symbol or the word "percent".
"50 is 20% of what?"
Strategy #1: The Percent Equation
Part = Percent \(\cdot\) Whole
Critical Note: You MUST convert the percent to a decimal before calculating!
Example: 20% of 50 \(\rightarrow\) \(0.20 \cdot 50 = 10\)
Strategy #2: The Percent Proportion
Part
Whole
=
%
100
Memory Trick:
is
of
=
%
100
Your Cheat Sheet: The Triangle
Part
%
Whole
How to use:
Cover the variable you are looking for with your hand.
Cover PART : \(% \cdot Whole\)
Cover % : \(Part / Whole\)
Cover WHOLE : \(Part / %\)
Guided Practice #1
Finding Part
"What is 15% of 80?"
Equation Method
\(x = 0.15 \cdot 80\)
\(x = \underline{\quad? \quad}\)
Proportion Method
x
80
=
15
100
Guided Practice #2
Finding Percent
"12 is what percent of 40?"
Setup for the %
12
40
=
Percent Problems Answer Key Answer Key: Percent Problems
Teacher Reference Guide
Part 1: Identify the Pieces
1. 15 is 20% of 75
Part: 15
Whole: 75
Percent: 20%
2. What is 30% of 90?
Part: x
Whole: 90
Percent: 30%
3. 12 is what percent of 40?
Part: 12
Whole: 40
Percent: x
Part 2: Solving the Puzzle
4. What is 15% of 120?
\(x = 0.15 \cdot 120\)
Ans: 18
5. 18 is what percent of 72?
\(\frac{18}{72} = \frac{x}{100}\)
Ans: 25%
6. 24 is 40% of what number?
\(24 = 0.40 \cdot x\)
Ans: 60
7. What percent of 50 is 35?
\(\frac{35}{50} = \frac{x}{100}\)
Ans: 70%
Part 3: Word Problems
8. The New Jacket ($150, 25% discount)
Ans: $37.50 saved
9. Test Results (17 correct, 85%)
Ans: 20 questions total
Exit Ticket Answers
1. 25%
2. 60
