Problem
A smaller divisor makes a bigger quotient. The two smallest digits, 1 and 2, build the smallest 2-digit number: 12.
Splitting something into fewer, smaller-size groups means each share is bigger, so a small divisor lifts the quotient.
4.NBT.B.6Guess And CheckTo make the quotient as large as possible, the divisor must be the smallest 2-digit number you can build from the cards, which is 12.
For a fixed dividend, a smaller divisor gives a larger quotient, so the best divisor is the smallest one you can make.
Division asks how many groups of the divisor's size fit inside the dividend, and smaller-size groups fit more times into the same amount.
The quotient times the divisor rebuilds the dividend, so with the dividend held fixed a smaller divisor has to be paired with a larger quotient.
A product is that many equal groups of that size, so covering the same total with smaller groups needs more of them.
The smallest 2-digit number uses the two smallest leftover cards, 1 and 2, with the smaller digit in the tens place, giving 12.
A 2-digit number's size is set first by its tens place, because each ten there counts for ten ones, so keeping the tens digit small keeps the whole number small.
The remaining cards are 8, 5, 4. The largest 3-digit number puts the biggest digit first: 854.
Place the biggest digit in the hundreds spot to make the number as large as it can be.
4.NBT.A.2Guess And CheckCompute 854 divided by 12. Since 12 × 71 = 852, the quotient is 71 with a remainder of 2.
Find how many 12s fit in 854; 71 of them reach 852, leaving 2 left over.
4.NBT.B.6Guess And CheckBiggest top number over smallest bottom number makes the biggest answer - then just divide, which is Grade 4 work you know!