Teacher copy: This page may include teaching prompts or answer keys. Answer keys in this public library can be viewed by anyone. Give learners a clean prompt, use checks as formative evidence, and change a case locally when prior access matters.
Goal: multiply square roots and whole-number coefficients using Card F. Say: “Multiply lengths to get area; the unit changes even when the radical stays.”
0–2: Ask what units follow cm × cm.
2–7: Model sqrt(6)sqrt(15)=sqrt(90) for nonnegative factors, then ask for its square factor.
7–13: Pairs separate coefficients and radicals in (2sqrt(3))(3sqrt(6)).
13–20: Independent exact answers and a reasonableness estimate for the area.
20–25: Exit: check that squaring 3sqrt(10) gives 90; label it cm² in the rectangle case.
Routes: symbolic calculation with units; oral decomposition into coefficient and radical products recorded in notes; arrange factor tiles and caption the exact result. Other domains:Day 6 swaps. Optional/home: create one product of unlike roots that simplifies to a whole number. Move: if sqrt(6)sqrt(15)=sqrt(21), remind students the operation between factors is multiplication and estimate: area is much larger than sqrt(21).