Upper Elementary:
Question: Mrs. VanFossen is assigning economics project groups to her class of 39 fourth graders. How can Mrs. VanFossen divide the class so that there are at least 10 groups with the same number of students in each group?
Answer: 13 groups of 3 students
Solution: We need to test for divisibility. 39 can’t be divided into groups of 2 because it isn’t even. It can be divided into groups of 3 because the sum of its digits is 3 + 9 = 12 and 12 is divisible by 3. Next, we need to divide the class: 39 ÷ 3 = 13, so there must be 13 equal groups of 3. If we continue testing for divisibility, we’ll find that 1, 3, 13, and 39 are all of the factors of 39, so 3 groups of 13 and 13 groups of 3 are the only ways for the students to be assigned into equal groups.
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