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Abstract: Students learn the “partial quotients” division strategy (also called “hangman division”). Students may also choose to use the “Repeat Subtraction” division strategy with these larger numbers. *Note: According to the common core state standards, students are NOT necessarily taught the traditional division algorithm in fourth grade. We understand that this is the division strategy that most parents know. However, unless students can demonstrate their understanding of this strategy by explaining each step, we will not accept this strategy for fourth grade math work. Instead, we accept the “make groups,” “repeat subtraction,” or “partial quotients” strategies, or any other student-made strategy that demonstrates understanding of division.
The Partial Quotients Division Strategy (Hangman Division)
125 divided by 3 = ?
Start by setting the problem up like this:
Think, “If you put 125 into 3 groups, how many would be in each group?” A good guess should be a number you can figure out mentally. (Numbers that end in zeroes are great!)
Maybe 60 is close.If I have 3 groups of 60, that would be 180. Too big!
Maybe 30 is close. If I have 3 groups of 30, that would be 90. That would work!
Find out how close you are by subtracting.
You can still put 35 into three groups. Try putting 10 into each group. That would be 30.
Subtract to see how close you are.
You can still put 5 into 3 groups. However, there will be 2 left over. That is the “remainder,” since you can’t put 2 into three groups without making fractions!
The quotient, or answer, is 30 + 10 + 1. Don’t forget the remainder!
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