form 1 topics added

lib/problems/generators/ratio-problems.ts

@@ -7,6 +7,58 @@ function nextId() {
   return `rp-${++counter}-${Date.now()}`;
 }
 
+export function generateDefineRatio(difficulty: Difficulty): MathProblem {
+  const contexts = [
+    { a: "red", b: "blue", item: "counters in a bag" },
+    { a: "boys", b: "girls", item: "in the class" },
+    { a: "cats", b: "dogs", item: "at the shelter" },
+    { a: "apples", b: "oranges", item: "in the basket" },
+  ];
+  const ctx = randomChoice(contexts);
+  const g = randomChoice(difficulty === 1 ? [1, 2] : difficulty === 2 ? [2, 3, 4] : [3, 4, 5, 6]);
+  const x = randomInt(1, difficulty === 1 ? 6 : 8) * g;
+  const y = randomInt(1, difficulty === 1 ? 6 : 8) * g;
+  const simplified = simplifyRatio([x, y]);
+
+  return {
+    id: nextId(),
+    prompt: `\\begin{array}{l}\\text{There are ${x} ${ctx.a} and ${y} ${ctx.b} ${ctx.item}.}\\\\\\text{Write the ratio of ${ctx.a} to ${ctx.b} in its simplest form.}\\end{array}`,
+    answer: { kind: "ratio", parts: simplified },
+    hints: [
+      `Write it as ${x} : ${y} first.`,
+      "Divide both parts by their highest common factor.",
+    ],
+    steps: [
+      { explanation: `The ratio of ${ctx.a} to ${ctx.b} is ${x} : ${y}.` },
+      { explanation: `In simplest form: ${simplified.join(" : ")}` },
+    ],
+  };
+}
+
+export function generateFractionsAndRatios(difficulty: Difficulty): MathProblem {
+  const a = randomInt(1, difficulty === 1 ? 4 : 7);
+  const b = randomInt(1, difficulty === 1 ? 4 : 7);
+  const whole = a + b;
+  const which = randomChoice([0, 1] as const);
+  const part = which === 0 ? a : b;
+  const [n, d] = simplifyRatio([part, whole]);
+
+  return {
+    id: nextId(),
+    prompt: `\\begin{array}{l}\\text{Two amounts are shared in the ratio } ${a} : ${b}.\\\\\\text{What fraction of the whole is the ${which === 0 ? "first" : "second"} part?}\\end{array}`,
+    answer: { kind: "fraction", numerator: n, denominator: d },
+    hints: [
+      `The whole is ${a} + ${b} = ${whole} parts.`,
+      `The ${which === 0 ? "first" : "second"} part is ${part} out of ${whole}.`,
+      "Simplify the fraction.",
+    ],
+    steps: [
+      { explanation: `Total parts: ${a} + ${b} = ${whole}.` },
+      { explanation: `Fraction = ${part}/${whole}, which simplifies to ${n}/${d}.` },
+    ],
+  };
+}
+
 export function generateSimplifyRatio(difficulty: Difficulty): MathProblem {
   const gcd = randomChoice(difficulty === 1 ? [2, 3, 4, 5] : difficulty === 2 ? [3, 4, 5, 6, 7] : [4, 6, 8, 9, 12]);
   const a = randomInt(1, difficulty === 1 ? 5 : 10) * gcd;