Divisibility and Remainder Reasoning
A remainder is what is left after exact grouping, and it must stay smaller than the divisor. Problems range from finding common multiples and numbers meeting divisibility clues, to recovering a dividend from quotient-and-remainder, adjusting a total to leave no remainder, rounding bundles up, and maximizing a remainder. The controlling fact is the division algorithm: dividend = divisor x quotient + remainder.
grade 3–4 MDNBTOA Eliminate PossibilitiesMake a Systematic List
Progression (8)
3-1 1. Numbers divisible by several are common multiples 3.OA.B.63.OA.C.7
3-1 2. Narrow candidates by divisibility conditions 3.OA.B.63.OA.C.7
3-2 3. Adjust the total to leave no remainder 3.OA.A.33.OA.C.7
3-2 4. Exact division means remainder zero 3.OA.C.73.OA.B.6
3-2 5. Recover the dividend from quotient and remainder 3.OA.B.63.OA.A.4
3-2 6. Remainder must be less than the divisor 3.OA.B.63.OA.C.7
3-2 7. Round the quotient up to carry the remainder 3.OA.A.33.MD.A.2
4-1 8. The remainder is always less than the divisor 4.NBT.B.6