Long Division with 2-Digit Divisors

Expect slower going than one-digit divisors. A twelve-problem page takes about twenty minutes at the start. Teach the child to round the divisor to the nearest ten and test the trial digit, then multiply the full divisor to see if it fits. If the product is too big, lower the digit and try again. This is normal. Afterward, use the answer key and check by multiplying quotient and divisor. Remainders is a switch if the class is ready for it.

The skill here is estimating and adjusting. With a divisor in the thirties, a first guess is often one too high or too low, and the child must see this and fix it without panic. Quotients stay at two digits, from 12 to 99, so each problem has just two rounds of divide, multiply, subtract and bring down. Facts for multiples of 10 and good multiplication come before it. After this come three-digit quotients, decimals and word problems.

Start with twelve problems and no Remainders. Encourage writing a small list of multiples of the divisor beside the bracket (1 times, 2 times, up to 9 times) and using it as a lookup. After a few sheets, take away the list and see how the estimation holds up. Twenty problems suits students who have grown comfortable. Missing number mode is a nice change for fast finishers.

Why do divisors stop at 49?

Larger divisors make the first estimate nearly always right, so they teach less. Divisors from 11 to 49 are where students learn to adjust a guess, which is the skill this page is about.

How many digits do the quotients have?

Two, from 12 to 99. That keeps each problem to two rounds of the divide, multiply, subtract, bring down cycle, so it fits the work space and a normal fifth grade textbook pace.

What if my child's first estimate is too big?

That is part of the method. They erase the digit, lower it by one and multiply again. Writing the list of multiples beside the problem shows the right digit quickly and removes the guesswork.