form 1 topics added
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331
components/explorers/identity-inverse-explorer.tsx
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331
components/explorers/identity-inverse-explorer.tsx
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"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 = "identity" | "inverse" | "zero";
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type Op = "add" | "multiply";
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interface Step {
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label: string;
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math: string;
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danger?: boolean;
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}
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function buildIdentitySteps(n: number, op: Op): Step[] {
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if (op === "add") {
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return [
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{ label: "The identity for addition is 0 — it leaves a number unchanged.", math: `${n} + 0` },
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{ label: "Adding 0 changes nothing.", math: `${n} + 0 = ${n}` },
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{ label: "So 0 is the identity element for addition.", math: `n + 0 = n` },
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];
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}
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return [
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{ label: "The identity for multiplication is 1 — it leaves a number unchanged.", math: `${n} \\times 1` },
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{ label: "Multiplying by 1 changes nothing.", math: `${n} \\times 1 = ${n}` },
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{ label: "So 1 is the identity element for multiplication.", math: `n \\times 1 = n` },
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];
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}
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function buildInverseSteps(n: number, op: Op): Step[] {
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if (op === "add") {
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const inv = -n;
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const invText = inv < 0 ? `(${inv})` : `${inv}`;
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return [
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{ label: "The additive inverse is the number that brings you back to the identity, 0.", math: `${n} + \\square = 0` },
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{ label: `Flip the sign of ${n} to get its additive inverse.`, math: `\\text{inverse of } ${n} = ${inv}` },
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{ label: "Check: adding a number and its inverse gives 0.", math: `${n} + ${invText} = 0` },
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];
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}
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// multiplicative inverse (reciprocal)
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const absN = Math.abs(n);
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const recip = n < 0 ? `-\\frac{1}{${absN}}` : `\\frac{1}{${absN}}`;
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const recipParen = n < 0 ? `\\left(-\\frac{1}{${absN}}\\right)` : `\\frac{1}{${absN}}`;
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return [
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{ label: "The multiplicative inverse (reciprocal) brings you back to the identity, 1.", math: `${n} \\times \\square = 1` },
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{ label: `Write ${n} as a fraction and flip it. The sign stays in front.`, math: `\\text{inverse of } ${n} = ${recip}` },
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{ label: "Check: a number times its reciprocal gives 1.", math: `${n} \\times ${recipParen} = 1` },
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];
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}
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function buildZeroSteps(n: number): Step[] {
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return [
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{ label: "Multiplying any number by zero always gives zero.", math: `${n} \\times 0 = 0` },
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{ label: "Zero shared into any number of groups is still zero.", math: `0 \\div ${n === 0 ? 5 : n} = 0` },
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{
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label: "But you can never divide BY zero — there is no answer. It is undefined.",
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math: `${n} \\div 0 = \\text{undefined}`,
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danger: true,
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},
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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() * 5);
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if (roll === 0) {
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const n = randInt(-12, 12) || 3;
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return { prompt: `What is the additive inverse of ${n}?`, answer: -n };
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}
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if (roll === 1) {
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const n = randInt(1, 20);
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return { prompt: `What is ${n} × 0?`, answer: 0 };
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}
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if (roll === 2) {
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return { prompt: `What number is the identity for addition?`, answer: 0 };
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}
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if (roll === 3) {
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return { prompt: `What number is the identity for multiplication?`, answer: 1 };
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}
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const n = randInt(2, 12);
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return { prompt: `The multiplicative inverse of ${n} is 1 over what number?`, answer: n };
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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 IdentityInverseExplorer() {
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const [mode, setMode] = useState<Mode>("identity");
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const [op, setOp] = useState<Op>("add");
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const [input, setInput] = useState("3");
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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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reset();
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}
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function handleGo() {
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setError("");
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const n = parseInt(input, 10);
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if (isNaN(n)) return setError("Enter a valid whole number.");
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if (Math.abs(n) > 100) return setError("Keep the number between -100 and 100.");
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if (mode === "inverse" && op === "multiply" && n === 0) {
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return setError("Zero has no multiplicative inverse — try another number.");
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}
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if (mode === "identity") setSteps(buildIdentitySteps(n, op));
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else if (mode === "inverse") setSteps(buildInverseSteps(n, op));
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else setSteps(buildZeroSteps(n));
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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 showOp = mode !== "zero";
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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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{(["identity", "inverse", "zero"] 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 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 === "identity" ? "Identity" : m === "inverse" ? "Inverse" : "Zero Facts"}
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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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{(["add", "multiply"] as Op[]).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={`rounded-full border-2 px-4 py-2 text-sm font-semibold 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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{o === "add" ? "Addition" : "Multiplication"}
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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 === "identity"
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? "See how the identity leaves a number unchanged"
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: mode === "inverse"
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? "Find the inverse of a number"
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: "Explore what happens with zero"}
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</p>
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<div className="flex flex-wrap items-center gap-3">
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<input
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type="number"
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value={input}
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onChange={(e) => setInput(e.target.value)}
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className="w-24 rounded-lg border-2 border-border bg-surface px-3 py-2 text-center text-lg font-bold outline-none focus:border-unit-8"
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aria-label="Number"
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/>
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<button
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onClick={handleGo}
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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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>
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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 a number 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-3xl ${step.danger ? "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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