N3B4TNp21

Answer to Problem 21:

The class that has 12 students is the winner because 24 can be divided equally by 12, which means that every student would get 2 cookies each. 24 cannot be evenly divided by 15 or 10.

DEFINITION:

demonstrate fluency—demonstrating the ability for efficient and accurate methods of computing and being able to demonstrate flexibility in computational methods chosen which result in students being able to explain their methods and produce accurate answers.[1]

TEACHER NOTES:

Students should have plenty of experiences working with number combinations that provide opportunities to see or discuss strategies for quickly figuring out multiplication and division “facts.” This does not necessarily involve teaching these strategies in direct instruction, but rather, capitalizing on and labeling the strategies that students will naturally use when presented with the task of finding an answer.

By the end of fourth grade, this grade-level expectation is about having a command of the multiplication and division relationships through 12 ´ 12. This means that students should be able to use the “multiplication and division facts” without counting, tallying, or drawing pictures. Some students might be using known facts to arrive at some of the “facts,” e.g., to compute 4 ´ 8, a student might think to himself, “Two 8s are 16, and 16 + 16 = 32.” This would need to be done as quickly as the student who has memorized the fact 4 ´ 8 = 32.

Having command of these relationships will aid students in their mental arithmetic skills as well as lay the foundation for them to work with fractional number relationships. It is important that students learn these “facts” as relationships rather than in isolation. It is more difficult for students to retrieve or use the “facts” when they are learned in isolation.