Problem
If 8 buses are needed, then 7 buses must NOT be enough. Seven full buses hold 7 times 36 people.
Rounding the bus count UP to 8 means the students spilled past what 7 buses can hold, so the count must be more than 252.
5.NBT.A.4Work BackwardsSince 252 students would fit in exactly 7 buses, we need one more person to force an 8th bus. So the smallest count is 252 + 1.
Just one student over a full 7 buses tips us up to 8 buses, the same way 1 over a ten tips you up when rounding up.
3.NBT.A.1Guess And CheckThe smallest possible number of fifth graders is 253.
Seven buses carry seven equal loads of 36, which comes to 252, so 252 students would still fit without an eighth bus.
One student beyond a full seven buses forces the eighth, because that person has nowhere left to sit.
Each seat takes exactly one student, so once the last seat is filled the next student needs a new bus.
Eight full buses hold 8 times 36 people. The count cannot be more than this, or a 9th bus would be needed.
Keeping the units straight (people inside buses), 8 buses cap out at exactly 288 seats.
5.NBT.A.4Analyze The Units289 students would need a 9th bus, so the largest count still fitting 8 is 288.
The very last person who can ride without opening a 9th bus is the 288th seat, so 288 is the top of the range.
3.NBT.A.1Guess And CheckWhen you have to round UP to fill whole buses, the smallest crowd is just one past the last full bus, and the largest is exactly the new buses filled to the top.