111 lines
4.0 KiB
TypeScript
111 lines
4.0 KiB
TypeScript
import type { MathProblem, Difficulty } from "../types";
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import { randomInt, randomChoice } from "@/lib/utils";
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import { simplifyRatio, divideInRatio } from "@/lib/math/ratios";
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let counter = 0;
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function nextId() {
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return `rp-${++counter}-${Date.now()}`;
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}
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export function generateSimplifyRatio(difficulty: Difficulty): MathProblem {
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const gcd = randomChoice(difficulty === 1 ? [2, 3, 4, 5] : difficulty === 2 ? [3, 4, 5, 6, 7] : [4, 6, 8, 9, 12]);
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const a = randomInt(1, difficulty === 1 ? 5 : 10) * gcd;
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const b = randomInt(1, difficulty === 1 ? 5 : 10) * gcd;
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const simplified = simplifyRatio([a, b]);
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return {
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id: nextId(),
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prompt: `\\text{Simplify the ratio } ${a}:${b}`,
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answer: { kind: "ratio", parts: simplified },
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hints: [
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`Find the GCD of ${a} and ${b}`,
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`The GCD is ${gcd}`,
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`Divide both parts by ${gcd}`,
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],
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steps: [
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{ explanation: `GCD of ${a} and ${b} is ${gcd}` },
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{ explanation: `${a} ÷ ${gcd} = ${simplified[0]}, ${b} ÷ ${gcd} = ${simplified[1]}` },
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{ explanation: `Simplified: ${simplified.join(":")}` },
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],
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};
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}
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export function generateDivideInRatio(difficulty: Difficulty): MathProblem {
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const numParts = difficulty === 3 ? 3 : 2;
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const parts: number[] = [];
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for (let i = 0; i < numParts; i++) {
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parts.push(randomInt(1, difficulty === 1 ? 5 : 9));
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}
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const sum = parts.reduce((a, b) => a + b, 0);
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const multiplier = randomChoice(difficulty === 1 ? [2, 3, 4, 5] : [3, 4, 5, 6, 7, 8]);
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const total = sum * multiplier;
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const values = divideInRatio(total, parts);
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const intValues = values.map(Math.round);
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const names = ["first share", "second share", "third share"];
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return {
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id: nextId(),
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prompt: `\\text{Share } ${total} \\text{ in the ratio } ${parts.join(":")}`,
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answer: { kind: "ratio", parts: intValues },
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hints: [
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`Total parts: ${parts.join(" + ")} = ${sum}`,
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`One part = ${total} ÷ ${sum} = ${multiplier}`,
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`Multiply each ratio number by ${multiplier}`,
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],
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steps: [
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{ explanation: `Total parts = ${parts.join(" + ")} = ${sum}` },
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{ explanation: `One part = ${total} ÷ ${sum} = ${multiplier}` },
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...parts.map((p, i) => ({
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explanation: `${names[i]}: ${p} × ${multiplier} = ${intValues[i]}`,
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})),
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],
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};
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}
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export function generateRatioWordProblem(difficulty: Difficulty): MathProblem {
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const a = randomInt(2, 7);
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const b = randomInt(2, 7);
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const diff = Math.abs(a - b);
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if (diff === 0) {
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return generateDivideInRatio(difficulty);
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}
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const contexts = [
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{ item: "sweets", nameA: "Josh", nameB: "Nathan" },
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{ item: "marbles", nameA: "Amy", nameB: "Ben" },
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{ item: "stickers", nameA: "Karen", nameB: "Natasha" },
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];
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const ctx = randomChoice(contexts);
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const onePart = randomChoice(difficulty === 1 ? [5, 10, 12] : [6, 8, 9, 15, 20]);
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const extraAmount = diff * onePart;
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const totalParts = a + b;
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const total = totalParts * onePart;
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const bigger = a > b ? ctx.nameA : ctx.nameB;
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const biggerRatio = Math.max(a, b);
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const smallerRatio = Math.min(a, b);
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return {
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id: nextId(),
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prompt: `\\begin{array}{l}\\text{${ctx.item.charAt(0).toUpperCase() + ctx.item.slice(1)} were shared between ${ctx.nameA} and ${ctx.nameB}}\\\\\\text{in the ratio ${a}:${b}. If ${bigger} received ${extraAmount} more ${ctx.item}, find the total shared.}\\end{array}`,
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answer: { kind: "integer", value: total },
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hints: [
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`The difference in ratio parts is ${biggerRatio} - ${smallerRatio} = ${diff}`,
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`${diff} parts = ${extraAmount}, so 1 part = ${onePart}`,
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`Total parts = ${a} + ${b} = ${totalParts}`,
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],
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steps: [
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{ explanation: `Difference in parts: ${biggerRatio} - ${smallerRatio} = ${diff}` },
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{ explanation: `${diff} parts = ${extraAmount}, so 1 part = ${extraAmount} ÷ ${diff} = ${onePart}` },
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{ explanation: `Total parts: ${a} + ${b} = ${totalParts}` },
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{ explanation: `Total ${ctx.item}: ${totalParts} × ${onePart} = ${total}` },
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],
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};
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}
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