Fourth and fifth graders are all immersed now in numbers less than one. Fourth graders have just begun a fraction unit, while fifth graders are investigating decimal multiplication and division.
In fourth grade, students are investigating a fair sharing situation in which different groups are sharing sub sandwiches. A group of 4 shared 3 sandwiches, a group of 5 shared 4 sandwiches, a group of 7 shared 8 sandwiches, and a group of 5 shared 3 sandwiches. Students used reasoning to immediately realize that it was not fair between the groups. If one group of 5 shared 3 sandwiches and one group of 5 shared 4 sandwiches, it is apparent that the second group ate more food. They are now trying to figure out how to rank the groups in order of how much of a sandwich they received. Stay tuned to see what strategies they use to figure this out!
Fifth graders had some mind-boggling realizations in the last week. As we were exploring decimal multiplication, they discovered that when we multiply by a number less than 1, our product actually is smaller than the other factor. This is a complete shift in thinking from whole number multiplication. In their previous experiences, when we multiply, the product generally gets larger (except when multiplying by 0 or 1). While logically they could reason that if they are multiplying a number (for example 3) by a number between 0 and 1, the product should be between 0 and 3 since 3×1=3 and 3×0=0. However, seeing that 3 x 0.1 = 0.3 still caused a disconnect. This is a huge shift in thinking that occurs in fifth grade.
As we were discussing these ideas, the following question came up: “If when we multiply by a factor less than one, our product decreases, will our quotient increase when we divide by a divisor less than one since multiplication and division are inverse operations?” This is an idea we will be continuing to grapple with.
Have a great weekend!