They need to put students into groups so no one is left out. When they divide the class into two groups one student is left out. When they divide by three the same happens. They try 4,5,6 and still one student is left out.
if there are less than 100 students find the number of 5th graders
If there's one student left when the class is divided into groups of 2, that means the number of students must be ONE MORE than a multiple of 2.
If there's one student left when the class is divided into groups of 3, then the number of students must also be ONE MORE than a multiple of 3.
If there's one student left when the class is divided into groups of 4, then the number of students must also be ONE MORE than a multiple of 4.
And if there's one student left when the class is divided into groups of 5, then the number of students must also be ONE MORE than a multiple of 5.
If there's one student left when the class is divided into groups of 6, then the number of students must be ONE MORE than a multiple of 6, too.
Here's how I would suggest a fifth grader approach this problem.
Start by making a list of multiples of 2, another list of multiples of 3, a similar list of multiples of 4, a list of multliples of 5, and finally a list of multiples of 6.
Look for the smallest number that is COMMON to every one of the lists....that number is the "least common multiple" of 2, 3, 4, 5, and 6. You may need to extend your lists in order to find a common number, so don't give up if you don't "see" one right away.
Add ONE to that least common multiple, and you should have your answer as to how many fifth graders there are. Note that this number must be less than 100 (because the problem says there are fewer than 100 fifth graders). You can check to see if the number you got "works" by dividing that number by 2, then by 3, then by 4, and by 5, and finally by 6. You should get a remainder of 1 in each case, meaning that there will be 1 student left over if the students are divided into groups of each of those sizes.
