Teaching Long Division Meaningfully CCSS 5.NBT.B.6
By Robert M. van Deusen, PhD
Contents of the packet:
33 pages of Teacher’s Guide including background on quotative and partitive division models. For long division to make sense in context as “repeated subtraction,” the problem context must be quotative. Twenty-four quotative contexts are provided.
Long division is presented as a series of 4 machines, each more complex than the prior. Each has a role to play in the student’s understanding of the meaning of long division.
Machine I (Straight Repeated Subtractions of the Divisor)—171 problems are given at seven different difficulty levels for Machine I so each teacher can choose what is appropriate for her or his students.
Machine II (Repeated Subtractions of Powers of Ten Times the Divisor)—95 problems are given at five different difficulty levels for Machine II. Machine II can be modeled using Base 10 Blocks—an area model. 14 problems and answers are provided that can be modeled using a bag of 6 flats, 25 longs, and 50 units.
Machine III (Repeated Subtractions of Arbitrary Multiples of the Divisor)—95 problems and answers are provided for Machine III at 5 levels of difficulty.
Machine IV (Choosing the Largest Multiple of the Divisor for Each Power of Ten)—118 problems and answers are provided for Machine IV at 7 levels of difficulty.