Reasoning · Grade 3-1 Speed and Distance
Problem
With the station at centre, the school sits 600 west.
West means straight left on the compass, so the school is on the same horizontal line as the fire station, just to the left.
4.MD.A.2Draw A DiagramThe school is north of the station, so it sits 400 south of the school.
If the school is north of the police station, then going the opposite way, the police station is south of the school, the same 400 feet.
4.MD.A.2Work BackwardsThe city hall moves 400 east of the police station.
East is straight right, so the city hall is level with the police station but 400 feet to the right.
4.MD.A.2Draw A DiagramThe hall is south of the hospital, so the hospital is 400 north of it.
City hall being south of the hospital means the hospital is north of city hall by the same 400 feet.
4.MD.A.2Work BackwardsThe north-south moves cancel, leaving 200 west.
By handling east-west moves and north-south moves separately, the leftover east-west distance (200 ft west) is the only difference, and there is no north-south difference.
4.NBT.B.4Identify SubproblemsHandling the east-west moves apart from the north-south moves shows the hospital ends up 200 feet west with no north-south difference at all.
Walking east or west never changes how far north you are, so the two directions can be totalled separately and combined at the end.
Gathering all the east-west steps into one pile and all the north-south steps into another cannot change where you end up, because reordering a sum never changes it.
Turn 'north, south, east, west' clues into a little map, hop from place to place, and the answer appears!