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How to implement complex math equations in Scratch

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MC

MathCoder_Pro

Posted on January 24, 2024 • Intermediate

🧮 Need help converting math equation to Scratch

I’m working on a physics simulation and need to implement this mathematical equation in Scratch:

y = floor(6 × 1.4 × (x/10) × 1.15)

I tried simplifying it myself but I’m getting different results than expected. Can someone help me implement this correctly in Scratch blocks? The floor function and order of operations are confusing me. 😅

ME

MathExpert_Teacher

Replied 2 hours later • ⭐ Best Answer

Great question @MathCoder_Pro! Let me break down how to properly implement mathematical equations in Scratch:

🔢 Equation Analysis Process

Here’s how to approach complex equation implementation:

flowchart TD A[📝 Original Equation] --> B[Identify Components] B --> C[Check Order of Operations] C --> D[🔍 Parse Expression] D --> E[Parentheses First] E --> F[Multiplication/Division] F --> G[Addition/Subtraction] G --> H[Apply Functions] H --> I{Test with Sample Values} I -->|✅ Correct| J[Final Implementation] I -->|❌ Wrong| K[Debug Step by Step] K --> L[Check Each Operation] L --> M[Verify Intermediate Results] M --> N[Fix Issues] N --> I style A fill:#e1f5fe style J fill:#e8f5e8 style K fill:#fff3e0 style L fill:#fce4ec

🧮 Step-by-Step Implementation

Your equation: y = floor(6 × 1.4 × (x/10) × 1.15)

Step 1: Understand Order of Operations

  1. Parentheses: (x/10)
  2. Multiplication: 6 × 1.4 × result × 1.15
  3. Floor function: floor(final result)

Step 2: Direct Implementation

Here’s the exact Scratch implementation:

    // Direct implementation - preserves exact equation structure
set [y v] to ([floor v] of ((6) * ((1.4) * (((x) / (10)) * (1.15)))))

Step 3: Alternative Simplified Version

You can also pre-calculate constants:

    // Pre-calculated constants method
// 6 × 1.4 × 1.15 = 9.66
set [y v] to ([floor v] of ((9.66) * ((x) / (10))))

// Or even simpler:
// 9.66 ÷ 10 = 0.966
set [y v] to ([floor v] of ((0.966) * (x)))

🔍 Debugging Mathematical Equations

Method 1: Step-by-Step Verification

    // Debug version - shows each step
set [step1 v] to ((x) / (10))
set [step2 v] to ((step1) * (1.15))
set [step3 v] to ((1.4) * (step2))
set [step4 v] to ((6) * (step3))
set [y v] to ([floor v] of (step4))

// Display intermediate results for debugging
say (join [Step 1: ] (step1)) for (1) seconds
say (join [Step 2: ] (step2)) for (1) seconds
say (join [Final: ] (y)) for (2) seconds

Method 2: Test with Known Values

    // Test equation with x = 10
// Expected: floor(6 × 1.4 × (10/10) × 1.15) = floor(9.66) = 9

set [x v] to [10]
set [y v] to ([floor v] of ((6) * ((1.4) * (((x) / (10)) * (1.15)))))

if <(y) = [9]> then
say [Equation working correctly!] for (2) seconds
else
say (join [Error! Got: ] (y)) for (2) seconds
end

📊 Common Mathematical Functions in Scratch

Here are essential math functions you’ll need:

    // Floor function (round down)
set [result v] to ([floor v] of (3.7))  // Result: 3

// Ceiling function (round up)
set [result v] to ([ceiling v] of (3.2))  // Result: 4

// Absolute value
set [result v] to ([abs v] of (-5))  // Result: 5

// Square root
set [result v] to ([sqrt v] of (16))  // Result: 4

// Power/Exponent
set [result v] to ((2) ^ (3))  // Result: 8

// Trigonometric functions
set [result v] to ([sin v] of (90))  // Result: 1
set [result v] to ([cos v] of (0))   // Result: 1

⚡ Performance Tips for Complex Equations

  • Pre-calculate constants: Combine multiple constants into single values
  • Use variables for repeated calculations: Store intermediate results
  • Minimize nested operations: Break complex expressions into steps
  • Test edge cases: Verify behavior with extreme values

The key is understanding that Scratch follows standard mathematical order of operations, so your equation will work correctly when properly structured! 🎯

MC

MathCoder_Pro

Replied 1 hour later

@MathExpert_Teacher Perfect explanation! 🎉 The step-by-step debugging method was exactly what I needed!

I was making an error in the order of operations - I had the parentheses wrong. Your direct implementation works flawlessly, and now I understand why the simplified version wasn’t giving me the same results.

The debugging technique with intermediate variables is brilliant - I can see exactly where my calculations were going wrong. Thank you! 🙏

PS

PhysicsSimulator_Dev

Replied 3 hours later

Great thread! 👏 For physics simulations, I’d also recommend:

🔬 Physics-Specific Tips

  • Use meaningful variable names: Instead of ‘x’ and ‘y’, use ‘velocity’, ‘acceleration’, etc.
  • Comment your equations: Add notes explaining what each formula represents
  • Unit consistency: Make sure all your values use consistent units
  • Range validation: Check that results are within expected physical limits
    // Physics equation example with clear naming
set [time v] to (timer)
set [gravity v] to [9.8]
set [initial velocity v] to [50]

// Position equation: y = v₀t + ½gt²
set [position y v] to (((initial velocity) * (time)) + ((0.5) * ((gravity) * ((time) ^ (2)))))

This makes your physics simulations much more readable and maintainable! 🚀

VB

Vibelf_Community

Pinned Message • Moderator

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