357 lines
14 KiB
TypeScript
357 lines
14 KiB
TypeScript
"use client";
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import { useState, useCallback } from "react";
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import { Card } from "@/components/ui/card";
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import { ClientOnly } from "@/components/ui/client-only";
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import { StepControls } from "./step-controls";
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import { MathDisplay } from "@/components/math/math-display";
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type Mode = "commutative" | "associative" | "distributive";
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type Op = "+" | "-" | "\\times" | "\\div";
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interface Step {
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label: string;
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math: string;
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match?: boolean; // colour the result green (holds) / red (fails)
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}
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const OP_META: Record<Op, { apply: (a: number, b: number) => number; commutative: boolean; associative: boolean; name: string }> = {
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"+": { apply: (a, b) => a + b, commutative: true, associative: true, name: "Addition" },
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"-": { apply: (a, b) => a - b, commutative: false, associative: false, name: "Subtraction" },
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"\\times": { apply: (a, b) => a * b, commutative: true, associative: true, name: "Multiplication" },
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"\\div": { apply: (a, b) => a / b, commutative: false, associative: false, name: "Division" },
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};
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function fmt(x: number): string {
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if (Number.isInteger(x)) return `${x}`;
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return `${parseFloat(x.toFixed(3))}`;
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}
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function buildCommutativeSteps(a: number, b: number, op: Op): Step[] {
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const meta = OP_META[op];
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const r1 = meta.apply(a, b);
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const r2 = meta.apply(b, a);
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const same = r1 === r2;
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return [
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{
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label: "Commutative law: does the ORDER of the numbers change the answer?",
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math: `${a} ${op} ${b} \\quad \\text{vs} \\quad ${b} ${op} ${a}`,
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},
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{ label: `Work out the first order.`, math: `${a} ${op} ${b} = ${fmt(r1)}` },
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{ label: `Now swap the order.`, math: `${b} ${op} ${a} = ${fmt(r2)}` },
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meta.commutative
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? {
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label: `Same answer! ${meta.name} IS commutative — order does not matter.`,
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math: `a ${op} b = b ${op} a`,
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match: true,
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}
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: {
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label: same
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? `They match here only because the numbers are special. In general, ${meta.name.toLowerCase()} is NOT commutative.`
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: `Different answers! ${meta.name} is NOT commutative — order matters.`,
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math: `a ${op} b \\neq b ${op} a`,
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match: false,
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},
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];
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}
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function buildAssociativeSteps(a: number, b: number, c: number, op: Op): Step[] {
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const meta = OP_META[op];
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const left = meta.apply(meta.apply(a, b), c);
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const right = meta.apply(a, meta.apply(b, c));
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return [
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{
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label: "Associative law: does where we put the BRACKETS change the answer?",
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math: `(${a} ${op} ${b}) ${op} ${c} \\quad \\text{vs} \\quad ${a} ${op} (${b} ${op} ${c})`,
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},
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{ label: "Do the brackets on the LEFT first.", math: `(${a} ${op} ${b}) ${op} ${c} = ${fmt(meta.apply(a, b))} ${op} ${c} = ${fmt(left)}` },
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{ label: "Now do the brackets on the RIGHT first.", math: `${a} ${op} (${b} ${op} ${c}) = ${a} ${op} ${fmt(meta.apply(b, c))} = ${fmt(right)}` },
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meta.associative
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? { label: `Same answer! ${meta.name} IS associative — the grouping does not matter.`, math: `(a ${op} b) ${op} c = a ${op} (b ${op} c)`, match: true }
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: { label: `Different answers! ${meta.name} is NOT associative — the grouping matters.`, math: `(a ${op} b) ${op} c \\neq a ${op} (b ${op} c)`, match: false },
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];
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}
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function buildDistributiveSteps(a: number, b: number, c: number): Step[] {
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const inside = b + c;
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const answer = a * inside;
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return [
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{ label: "Distributive law: a number outside a bracket multiplies EVERYTHING inside.", math: `${a} \\times (${b} + ${c})` },
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{
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label: `Multiply the ${a} by each number inside the bracket separately.`,
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math: `${a} \\times ${b} \\; + \\; ${a} \\times ${c}`,
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},
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{ label: "Working the direct way: add inside the bracket first, then multiply.", math: `${a} \\times (${b} + ${c}) = ${a} \\times ${inside} = ${answer}` },
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{ label: "Working the expanded way gives the same answer.", math: `${a * b} + ${a * c} = ${answer}`, match: true },
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];
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}
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// ── Quick practice ───────────────────────────────────────────────────────────
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interface PracticeQ {
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prompt: string;
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answer: number;
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}
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function randInt(min: number, max: number) {
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return Math.floor(Math.random() * (max - min + 1)) + min;
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}
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function makeQuestion(): PracticeQ {
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const roll = Math.floor(Math.random() * 4);
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if (roll === 0) {
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const a = randInt(2, 9), b = randInt(1, 9), c = randInt(1, 9);
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return { prompt: `Fill the blank: ${a} × (${b} + ${c}) = ${a} × ${b} + ${a} × ▢`, answer: c };
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}
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if (roll === 1) {
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const a = randInt(3, 12), b = randInt(1, a - 1);
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return { prompt: `Subtraction is not commutative. What is ${a} − ${b}?`, answer: a - b };
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}
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if (roll === 2) {
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const a = randInt(2, 8), b = randInt(1, 6), c = randInt(1, 6);
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return { prompt: `Work out ${a} × (${b} + ${c})`, answer: a * (b + c) };
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}
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const a = randInt(2, 9), b = randInt(2, 9);
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return { prompt: `Multiplication is commutative, so ${a} × ${b} equals ${b} × ▢. What is ▢?`, answer: a };
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}
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function QuickPractice() {
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const [q, setQ] = useState<PracticeQ>(() => makeQuestion());
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const [val, setVal] = useState("");
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const [feedback, setFeedback] = useState<"correct" | "incorrect" | null>(null);
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const [score, setScore] = useState({ correct: 0, total: 0 });
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function check() {
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const parsed = parseInt(val, 10);
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if (isNaN(parsed)) return;
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const correct = parsed === q.answer;
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setFeedback(correct ? "correct" : "incorrect");
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setScore((s) => ({ correct: s.correct + (correct ? 1 : 0), total: s.total + 1 }));
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}
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function next() {
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setQ(makeQuestion());
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setVal("");
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setFeedback(null);
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}
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return (
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<Card className="space-y-4">
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<div className="flex items-center justify-between">
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<p className="text-xs font-bold uppercase tracking-wider text-unit-8">Quick Practice</p>
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<span className="rounded-full bg-unit-8-light px-3 py-1 text-xs font-bold text-unit-8-dark">
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{score.correct}/{score.total}
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</span>
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</div>
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<p className="text-center text-lg font-bold">{q.prompt}</p>
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<div className="flex flex-wrap items-center justify-center gap-3">
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<input
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type="number"
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value={val}
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onChange={(e) => {
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setVal(e.target.value);
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setFeedback(null);
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}}
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onKeyDown={(e) => {
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if (e.key === "Enter") {
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if (feedback !== null) next();
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else check();
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}
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}}
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className={`w-24 rounded-lg border-2 px-3 py-2 text-center text-xl font-bold outline-none transition-colors ${
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feedback === "correct"
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? "border-correct bg-correct-light"
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: feedback === "incorrect"
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? "border-incorrect bg-incorrect-light"
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: "border-border focus:border-unit-8"
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}`}
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placeholder="?"
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aria-label="Your answer"
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/>
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{feedback === null ? (
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<button onClick={check} className="rounded-lg bg-unit-8 px-5 py-2.5 text-sm font-bold text-white hover:bg-unit-8-dark">
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Check
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</button>
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) : (
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<button onClick={next} className="rounded-lg bg-foreground px-5 py-2.5 text-sm font-bold text-background hover:bg-foreground/80">
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Next →
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</button>
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)}
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</div>
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{feedback === "correct" && <p className="text-center text-sm font-bold text-correct">Correct!</p>}
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{feedback === "incorrect" && (
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<p className="text-center text-sm font-bold text-incorrect">Not quite — the answer is {q.answer}.</p>
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)}
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</Card>
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);
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}
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// ── Main explorer ────────────────────────────────────────────────────────────
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export function NumberLawsExplorer() {
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const [mode, setMode] = useState<Mode>("commutative");
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const [op, setOp] = useState<Op>("+");
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const [a, setA] = useState("8");
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const [b, setB] = useState("3");
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const [c, setC] = useState("2");
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const [error, setError] = useState("");
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const [steps, setSteps] = useState<Step[] | null>(null);
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const [currentStep, setCurrentStep] = useState(0);
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const [isPlaying, setIsPlaying] = useState(false);
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const done = steps ? currentStep >= steps.length - 1 : false;
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const reset = useCallback(() => {
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setSteps(null);
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setCurrentStep(0);
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setIsPlaying(false);
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}, []);
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function switchMode(m: Mode) {
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setMode(m);
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setError("");
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// distributive is fixed to + inside; keep whatever op for the others
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reset();
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}
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const opChoices: Op[] = mode === "associative" ? ["+", "\\times", "-"] : ["+", "-", "\\times", "\\div"];
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function handleGo() {
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setError("");
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const na = parseInt(a, 10);
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const nb = parseInt(b, 10);
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const nc = parseInt(c, 10);
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if (isNaN(na) || isNaN(nb) || (mode !== "commutative" && isNaN(nc))) {
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return setError("Enter whole numbers in every box.");
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}
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const vals = mode === "commutative" ? [na, nb] : [na, nb, nc];
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if (vals.some((v) => Math.abs(v) > 50)) return setError("Keep the numbers between -50 and 50.");
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if ((op === "\\div") && (nb === 0 || (mode === "associative" && nc === 0))) {
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return setError("Cannot divide by zero — change the numbers.");
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}
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if (mode === "commutative") setSteps(buildCommutativeSteps(na, nb, op));
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else if (mode === "associative") setSteps(buildAssociativeSteps(na, nb, nc, op));
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else setSteps(buildDistributiveSteps(na, nb, nc));
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setCurrentStep(0);
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setIsPlaying(false);
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}
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const stepForward = useCallback(() => {
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if (!steps || currentStep >= steps.length - 1) return;
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setCurrentStep((s) => s + 1);
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if (currentStep + 1 >= steps.length - 1) setIsPlaying(false);
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}, [steps, currentStep]);
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const stepBack = useCallback(() => {
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if (currentStep <= 0) return;
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setCurrentStep((s) => s - 1);
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}, [currentStep]);
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const togglePlay = useCallback(() => setIsPlaying((p) => !p), []);
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const step = steps ? steps[currentStep] : null;
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const showThree = mode !== "commutative";
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const showOp = mode !== "distributive";
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const opLabel: Record<Op, string> = { "+": "+", "-": "−", "\\times": "×", "\\div": "÷" };
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return (
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<div className="space-y-4">
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{/* Mode toggle */}
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<div className="flex flex-wrap gap-2">
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{(["commutative", "associative", "distributive"] as Mode[]).map((m) => (
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<button
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key={m}
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onClick={() => switchMode(m)}
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className={`rounded-full border-2 px-4 py-2 text-sm font-semibold capitalize transition-colors ${
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mode === m
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? "border-unit-8 bg-unit-8 text-white"
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: "border-unit-8/40 text-unit-8 hover:bg-unit-8-light"
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}`}
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>
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{m}
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</button>
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))}
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</div>
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{/* Operation tabs */}
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{showOp && (
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<div className="flex flex-wrap gap-2">
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{opChoices.map((o) => (
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<button
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key={o}
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onClick={() => {
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setOp(o);
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reset();
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}}
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className={`h-10 w-12 rounded-full border-2 text-lg font-bold transition-colors ${
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op === o
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? "border-unit-8-dark bg-unit-8-dark text-white"
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: "border-unit-8/30 text-unit-8-dark hover:bg-unit-8-light"
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}`}
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>
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{opLabel[o]}
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</button>
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))}
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</div>
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)}
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{/* Input card */}
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<Card>
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<p className="mb-3 text-xs font-bold uppercase tracking-wider text-unit-8">
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{mode === "distributive" ? "Enter a, b and c for a × (b + c)" : showThree ? "Enter three numbers" : "Enter two numbers"}
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</p>
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<div className="flex flex-wrap items-center gap-3">
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<input type="number" value={a} onChange={(e) => setA(e.target.value)} className="w-20 rounded-lg border-2 border-border bg-surface px-3 py-2 text-center text-lg font-bold outline-none focus:border-unit-8" aria-label="a" />
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<input type="number" value={b} onChange={(e) => setB(e.target.value)} className="w-20 rounded-lg border-2 border-border bg-surface px-3 py-2 text-center text-lg font-bold outline-none focus:border-unit-8" aria-label="b" />
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{showThree && (
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<input type="number" value={c} onChange={(e) => setC(e.target.value)} className="w-20 rounded-lg border-2 border-border bg-surface px-3 py-2 text-center text-lg font-bold outline-none focus:border-unit-8" aria-label="c" />
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)}
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<button onClick={handleGo} className="rounded-lg bg-unit-8 px-6 py-2.5 text-sm font-bold text-white transition-colors hover:bg-unit-8-dark">
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Go →
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</button>
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</div>
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{error && <p className="mt-2 text-sm text-incorrect">{error}</p>}
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</Card>
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{/* Display card */}
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<Card className="flex min-h-[220px] flex-col items-center justify-center gap-4 p-6">
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{!step ? (
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<p className="text-muted/50">
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Enter numbers above and click <strong>Go</strong>
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</p>
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) : (
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<>
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<p className="text-center text-sm font-medium text-muted">{step.label}</p>
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<MathDisplay
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math={step.math}
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className={`text-2xl ${step.match === true ? "text-correct" : step.match === false ? "text-incorrect" : ""}`}
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/>
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</>
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)}
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</Card>
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{/* Controls */}
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<Card className="p-4">
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<StepControls
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currentStep={currentStep + 1}
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totalSteps={steps?.length ?? 0}
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isPlaying={isPlaying}
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onStepForward={stepForward}
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onStepBack={stepBack}
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onTogglePlay={togglePlay}
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onReset={reset}
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canStepForward={!!steps && !done}
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canStepBack={!!steps && currentStep > 0}
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/>
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</Card>
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{/* Quick practice */}
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<ClientOnly fallback={<Card className="min-h-[220px]" />}>
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<QuickPractice />
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</ClientOnly>
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</div>
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);
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}
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