Successive Percentages Worksheet/Game

Successive Percentages Worksheet/Game Quiz/Worksheet
Welcome to Successive Percentages Worksheet/Game. This game, Successive Percentages, is designed to help you master “Chain Discounts” or “Compound Markups.” In the real world, this is like finding the price of an item that is on sale, but then has sales tax added at the register. Scroll down the page for a more detailed explanation.

 

 

How to play the Successive Percentages Worksheet/Game

1. The Goal
   Your objective is to calculate the Final Price after two different percentage changes are applied in a row. You start with an Original Value (usually $100 to make the mental math smoother) and must apply two adjustments shown in the colored boxes.
   

2. The Logic: Step-by-Step vs. The Chain Rule
   The most common mistake is adding the two percentages together (e.g., thinking -20% and -10% equals -30%). This is incorrect because the second percentage applies to the new price, not the original $100.
   Method A: The Step-by-Step
   Apply Adjustment 1: Calculate the new price after the first change.
   Example: $100 with -20% OFF = $80.
   Apply Adjustment 2: Take that $80 and apply the second change.
   Example: $80 with +10% MARKUP = $80 + $8.00 = $88.
   
   Method B: The Chain Rule
   Multiply the original price by the complements of both rates.
   Final Price = 100 × 0.80 × 1.10 = 88
   

3. Reading the Colors
   The game uses color coding to help you identify the math operation quickly:
   Rose (Red): This is a Discount. You subtract the percentage from 100%. (e.g., -20% means you multiply by 0.80).
   Emerald/Blue: This is a Markup. You add the percentage to 100%. (e.g., +10% means you multiply by 1.10).
   

4. Gameplay Mechanics
   The Streak: Every correct answer adds to your 🔥 Streak.
   The Shake: If you get an answer wrong, the screen will shake, your streak will reset to 0, and the game will show you the correct answer. Use this to see where you went off track.
   Input: Type your final number (you don’t need the dollar sign) and hit the Finalize Price button or press Enter.
   

Tip:
Order Doesn’t Matter for multiplication. You can multiply in any order that is easier.

Successive Percentage Changes

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