N2A5TNp12

 

Answer to Problem 12: 

4 pair of socks.

(Note: This is an example of a quotative division problem—How many groups of $3 will fit into $12? Skip counting by 3s to 12 would be another way of solving this problem.)

 

DEFINITIONS:

partitive—distribution division that involves figuring out how many are in the group when the number of groups is known. Example: How would you divide 24 cookies equally among six children? (Think of dividing or partitioning the cookies into six equivalent subsets.)[1]

quotative—measurement division that involves seeing how many groups will fit into a number. Example: If a serving consists of 4 cookies and you have 24 cookies, to how many children can you give a serving of cookies? (Think of making one pile of 4 cookies, then a second pile of 4 cookies, etc.)[2]
Note: The quotative model is also known as the “repeated-subtraction” model.


 

[1] Fosnot, C., & Dolk, M. (2001). Young mathematicians at work: Constructing multiplication and division (pp. 53–57). Portsmouth, NH: Heinemann.

[2] Fosnot, C., & Dolk, M. (2001). Young mathematicians at work: Constructing multiplication and division (pp. 53–57). Portsmouth, NH: Heinemann.