Author note — to cover

Finding the smallest multiplier, or divisor, that turns a number into a perfect square or cube by making every index even or a multiple of three. Assumes index-form factorisation; counting factors lives on counting-factors; recognising squares and cubes lives on recognising-powers. Both tiers. (N4, N6)

• Fluency — direct questions on squares and cubes from prime factors, limited to this lesson's stated scope (4 questions).
• Application — use the same skill in unfamiliar or contextual questions without introducing a later method (4 questions).
• Check — questions built around the exclusions and likely misconceptions named in the lesson brief (4 questions).