Anderson's Pumpkin Patch Name _____________________
Ms. Juncos is the lead teacher for the fourth grade team at Newton Elementary School. One week before Halloween, the team teachers assigned all of the fourth graders a new project. They thought that the students might enjoy making geometric jack-o-lanterns, so they planned a field trip to Anderson's Pumpkin Patch to hunt, clean, and create the jack-o-lanterns.
Looking at the class lists the night before the trip, Ms. Juncos decided to put the students into groups so no one would have to work in the pumpkin patch alone. Her first attempt using pairs did not work - one person was left out. Next she tried groups of five, but that didn't work either. Then she tried groups of three and again had someone left over. Still no luck when she tried groups of four. Each attempt ended with one person left out.
If each grade at Ms. Juncos's school has fewer than 80 students, how many pupils are on her team?
Bonus: What number of group members should Ms. Juncos use to make this work?
All 2 3 4 5 6 8 9 10 12 14 15 16 18 20 21 22 24 25 26 27 28 30 32 33 34 35 36 38 39 40 42 44 45 46 48 50 51 52 54 55 56 57 58 60 62 63 64 65 66 68 69 70 72 74 75 76 78 80
Two’s 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80
Three’s 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78
Four’s 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80
Five’s 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Unused: 1 7 11 13 17 19 23 29 31 37 41 43 47 49 53 59 61 67 71 73 77 79
Divides into all with 1 left over: 61