Why "think multiplication" is the foundation of division fluency

Asking 42 ÷ 6 is really asking 6 times what makes 42, and Think Multiplication builds that connection visually instead of treating division as a separate fact to memorize from scratch. The array's row count (the divisor) is fixed and known from the start. Columns of that same size get added one at a time, and the running total climbs until it reaches the dividend: the number of columns added is the quotient, the missing factor the whole strategy was hunting for. Every other strategy in this suite (equal sharing, repeated subtraction, break apart, halving, using known facts) ultimately points back to this same relationship, which is why it comes first.

Fluency here means multiplying and dividing within 100 using that same relationship, not drilling two operations as if they're unrelated. The Fact Family toggle makes 42 ÷ 6 = 7, so 42 ÷ 7 = 6 visible instead of just stated: flip it on and the other division fact hiding in the same family shows up, built from the identical 6 × 7 = 42 multiplication fact underneath both.