Find the Error: The Remainder Is Too Big

Every division on this 3rd grade page has already been answered, in orange, and every answer is wrong in the same way: 39 ÷ 5 = 6 R 9, 10 ÷ 4 = 1 R 6, 26 ÷ 4 = 5 R 6, 42 ÷ 5 = 7 R 7, and four more. Under each printed pair sit two empty dashed boxes. The child crosses out the wrong quotient and remainder and writes the right ones beneath — 39 ÷ 5 is 7 R 4, not 6 R 9. The printed answers are not random: six fives and 9 really do make 39. The mistake is that 9 is bigger than 5, so another group of five could still have been taken.

A remainder that is larger than the divisor is the single most common division error at this stage, and this page is built from nothing else. Each wrong answer checks out by multiplication, which is why a child who only tests quotient times divisor plus remainder will find nothing wrong; they have to apply the second rule, that the remainder must be smaller than the divisor. Writing the correction underneath — one more group, a smaller remainder — is the whole lesson in two boxes.

One sheet, eight corrections. This is the checking face of the division-with-remainders family, and it belongs after the practice-rows and exact-or-not pages, when a child can produce answers and needs to learn to doubt them. The divisors stay small — 2 to 5 on this sheet — so the argument is always about the remainder, never about the table.