Problem
From the figure the points are in order A (house), B (bank), C (center), D (fire station). Write each known distance in meters: A to C = 1 km 480 m = 1480 m, B to C = 670 m, A to D = 3 km 200 m = 3200 m.
Converting km+m into all meters lets me add and subtract distances with plain whole numbers.
4.MD.A.1Draw A DiagramThe bank (B) sits between the house (A) and the center (C). Since A to C is 1480 m and B to C is 670 m, the part from the house to the bank is the difference.
On a line, the near part equals the whole stretch minus the far part.
2.MD.B.5Identify SubproblemsThe whole house-to-fire-station distance (A to D = 3200 m) is the house-to-bank part plus the bank-to-fire-station part. So the bank-to-fire-station distance is the total minus the house-to-bank piece.
Removing the front piece (house to bank) from the full line leaves exactly the bank-to-fire-station stretch.
4.MD.A.2Identify SubproblemsThe bank-to-fire-station distance is the whole house-to-fire-station distance minus the house-to-bank part.
The house-to-fire-station line splits into two touching pieces, house-to-bank and bank-to-fire-station, that add back to the whole.
The bank sits on the line between the house and the fire station, so the two pieces meet at the bank with no gap and no overlap and together cover the whole stretch.
Once the whole equals the house-to-bank part plus the bank-to-fire-station part, taking the house-to-bank part away leaves exactly the bank-to-fire-station part.
Subtracting removes the amount that was just added on, so it undoes the addition and hands back the other part.
Regroup 2390 m using 1000 m = 1 km: 2390 = 2000 + 390, so 2390 m = 2 km 390 m.
Every 1000 m is one kilometer, so trade thousands of meters for km to report the distance.
4.MD.A.1Draw A DiagramLay the places on a line, turn km+m into meters, add and subtract the parts, then turn meters back into km+m!