Problem
Find what 'round up' gives
The ones digit 8 keeps the number off a whole hundred, so rounding up always lands on 3600.
Rounding up means 'go to the next hundred unless you are already on one.' Since 35□8 sits strictly between 3500 and 3600, it climbs to 3600 every time.
3.NBT.A.1Make A Systematic ListSee when 'round half up' also gives 3600
Round half up looks at the tens digit instead: 5 or more goes to 3600, 4 or less to 3500.
Nearest-hundred rounding is decided by the tens digit: halfway (50) and above leans to the bigger hundred, below 50 leans to the smaller one.
5.NBT.A.4Make A Systematic ListMatch the two results
The two roundings agree only when the box holds 5, 6, 7, 8 or 9.
The cut-off is the same '5 or more rounds up' idea — the pattern in the list is exactly the rounding rule for the tens place.
3.NBT.A.1Look For A PatternThe two ways of rounding agree exactly when the boxed digit is 5 or more.
Why?
Rounding up always lands on 3600, because the ones digit 8 leaves the number short of a whole hundred no matter what the box holds.
Why?
Round half up lands on 3600 only once the tens digit reaches 5, because that is when the number has passed the middle of the hundred it sits in.
Why?
A hundred is ten tens bundled together, so the tens digit says which half of that hundred the number falls in.
Since the ones digit is 8, rounding up always reaches 3600 — so plain rounding matches only when the tens digit is big enough (5 or more) to round up too.
- Find what 'round up' gives
- See when 'round half up' also gives 3600
- Match the two results