In the children's book, A Remainder of One (Pinczes, 1995), bug solider Joe is part of a platoon of 25 soldiers. When bugs march in line of 2, 3, or 4, Joe is left out. When they march in lines of , Joe does march. Use concrete objects to explain the following to students in early grades:
A. The above story
B. In how many different ways could 30 bug soldiers march in equal rows?
A. Choose the correct explanation of the story below:
A. The bugs can make 2 lines of 10 with one remainder, 3 lines of 6 with one remainder, or 4 lines of 4 with one remainder. When the bugs make 5 lines of 5 there are no remainders so Joe gets to march.
B. The bugs can make 12 lines of 2 with one remainder, 8 lines of 3 with one remainder, or 6 lines of 4 with one remainder. When the bugs make 5 lines of 5 there are no remainders so Joe gets to march.
C. The bugs can make 2 lines of 12 with one remainder, 3 lines of 8 with one remainder, or 4 lines of 6 with one remainder. When the bugs make 5 lines of 5 there are no remainders so Joe gets to march.
D. The bugs can make 10 lines of 2 with one remainder, 6 lines of 3 with one remainder, or 4 lines of 4 with one remainder. When the bugs make 5 lines of 5 there are no remainders so Joe gets to march.
B. How many ways could 30 bug soldiers march in equal rows?
Select all that apply.
A. 3 rows of 10
B. 5 rows of 6
C. 4 rows of 8
D. 2 rows of 15
