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[
{
"slide": 1,
"fragments": [
{
"fragment_index": -1,
"text_description": "Fun With Permutations\nEvery new order unlocks a fresh possibility!",
"image_description": ""
}
]
},
{
"slide": 2,
"fragments": [
{
"fragment_index": -1,
"text_description": "What Is A Permutation?",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "Permutation",
"image_description": ""
},
{
"fragment_index": 2,
"text_description": "An arrangement of objects where their order matters. Example: 1-2-3 and 3-2-1 are different permutations of the digits 1, 2, and 3.",
"image_description": ""
}
]
},
{
"slide": 3,
"fragments": [
{
"fragment_index": -1,
"text_description": "Counting Quickly\nApplications",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "\\[n! = n \\times (n-1) \\times (n-2) \\times \\dots \\times 2 \\times 1\\]\nMultiply the remaining choices at each step to get the total.",
"image_description": ""
},
{
"fragment_index": 2,
"text_description": "Variable Definitions\n\\(n\\)\nnumber of distinct objects\n\\(n!\\)\ntotal different orders (permutations)",
"image_description": ""
},
{
"fragment_index": 3,
"text_description": "Books on a Shelf\nHow many ways to line up \\(n\\) different books.",
"image_description": ""
},
{
"fragment_index": 4,
"text_description": "Race Results\nPossible finishing orders for \\(n\\) runners, each place different.",
"image_description": ""
}
]
},
{
"slide": 4,
"fragments": [
{
"fragment_index": 1,
"text_description": "Easy Example\nUse multiplication rule to count 3-digit codes.",
"image_description": ""
},
{
"fragment_index": -1,
"text_description": "0-9\n0-9\n0-9\nEach wheel can show any digit 0 – 9.",
"image_description": ""
},
{
"fragment_index": 2,
"text_description": "Question\nHow many different 3-digit lock codes can be formed?",
"image_description": ""
},
{
"fragment_index": 3,
"text_description": "1st slot: 10 choices.\n2nd slot: 10 choices.\n3rd slot: 10 choices.\nMultiply: \\(10 \\times 10 \\times 10 = 1\\,000\\) codes.",
"image_description": ""
},
{
"fragment_index": 4,
"text_description": "Multiplication rule: total outcomes = product of choices for each position.",
"image_description": ""
}
]
},
{
"slide": 5,
"fragments": [
{
"fragment_index": 1,
"text_description": "No Repeats Example\nHow many 4-digit numbers have distinct digits?",
"image_description": ""
},
{
"fragment_index": 2,
"text_description": "1\nThousands place\n9 choices: digits 1–9. Zero can’t lead.",
"image_description": ""
},
{
"fragment_index": 3,
"text_description": "2\nHundreds place\n9 remaining digits: 0–9 except the thousand digit.",
"image_description": ""
},
{
"fragment_index": 4,
"text_description": "3\nTens place\n8 digits left.",
"image_description": ""
},
{
"fragment_index": 5,
"text_description": "4\nUnits place\n7 digits left.",
"image_description": ""
},
{
"fragment_index": 6,
"text_description": "5\nMultiply choices\n\\(9\\times9\\times8\\times7 = 4\\,536\\) distinct 4-digit numbers.",
"image_description": ""
},
{
"fragment_index": 7,
"text_description": "Outcome: You can now count arrangements when digits must be different.",
"image_description": ""
}
]
},
{
"slide": 6,
"fragments": [
{
"fragment_index": -1,
"text_description": "Build A Permutation\nHands-on practice: Drag each coloured ball into the three spots, use each ball once, then read the permutation count.\nResults\n// Drag and drop functionality\n const draggableItems = document.querySelectorAll('.draggable-item');\n const dropZones = document.querySelectorAll('.drop-zone');\n const checkAnswersBtn = document.getElementById('checkAnswersBtn');\n const feedbackArea = document.getElementById('feedbackArea');\n const feedbackContent = document.getElementById('feedbackContent');\n\n draggableItems.forEach(item => {\n item.addEventListener('dragstart', handleDragStart);\n item.addEventListener('dragend', handleDragEnd);\n });\n\n dropZones.forEach(zone => {\n zone.addEventListener('dragover', handleDragOver);\n zone.addEventListener('drop', handleDrop);\n zone.addEventListener('dragenter', handleDragEnter);\n zone.addEventListener('dragleave', handleDragLeave);\n });\n\n function handleDragStart(e) {\n e.target.classList.add('opacity-50');\n e.dataTransfer.setData('text/plain', e.target.dataset.id);\n }\n\n function handleDragEnd(e) {\n e.target.classList.remove('opacity-50');\n }\n\n function handleDragOver(e) {\n e.preventDefault();\n }\n\n function handleDragEnter(e) {\n e.preventDefault();\n e.target.closest('.drop-zone').classList.add('border-green-500', 'bg-green-50');\n }\n\n function handleDragLeave(e) {\n e.target.closest('.drop-zone').classList.remove('border-green-500', 'bg-green-50');\n }\n\n function handleDrop(e) {\n e.preventDefault();\n const dropZone = e.target.closest('.drop-zone');\n dropZone.classList.remove('border-green-500', 'bg-green-50');\n\n const itemId = e.dataTransfer.getData('text/plain');\n const draggedItem = document.querySelector(`[data-id=\"\\${itemId}\"]`);\n\n if (draggedItem && dropZone && !dropZone.contains(draggedItem)) {\n dropZone.appendChild(draggedItem);\n dropZone.querySelector('.text-center').style.display = 'none';\n }\n }\n\n // Check answers functionality\n checkAnswersBtn.addEventListener('click', () => {\n const filledZones = Array.from(dropZones).filter(z => z.querySelector('.draggable-item')).length;\n if (filledZones < 3) {\n feedbackContent.innerHTML = '<p class=\"text-red-600\">Fill all three spots first.</p>';\n } else {\n feedbackContent.innerHTML = '<p class=\"text-green-600\">Great! You created one of the 24 possible permutations.</p>';\n }\n feedbackArea.classList.remove('hidden');\n });",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "Draggable Items\nRed\nBlue\nGreen\nYellow",
"image_description": ""
},
{
"fragment_index": 2,
"text_description": "Drop Zones\n1st\n2nd\n3rd",
"image_description": ""
},
{
"fragment_index": 3,
"text_description": "Tip:\nTry all possibilities, then multiply choices!",
"image_description": ""
},
{
"fragment_index": 4,
"text_description": "Show count",
"image_description": ""
}
]
},
{
"slide": 7,
"fragments": [
{
"fragment_index": -1,
"text_description": "Key Takeaways\nThank You!\nYou now recall the core facts and are ready for harder problems.",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "Order matters: 12 and 21 are different.",
"image_description": ""
},
{
"fragment_index": 2,
"text_description": "All different items: count with \\(n!\\).",
"image_description": ""
},
{
"fragment_index": 3,
"text_description": "Fixed spots? Multiply the remaining choices one at a time.",
"image_description": ""
},
{
"fragment_index": 4,
"text_description": "No repeats allowed: available choices drop each step.",
"image_description": ""
},
{
"fragment_index": 5,
"text_description": "Next Steps\nPrepare for tougher problems: try counting circular arrangements.",
"image_description": ""
}
]
}
]