Order and Position Word Problems

Positions counted from the front and from the back are the clues for finding a place or a number of people. After Switching Front and Back and Position in Line come the people in between, found for Same Direction and Opposite Direction, and then the size of the line as a whole.

When someone is fifth from the front and third from the back, taking the whole line as 5 + 3 = 8 and counting that person twice is the classic error. An answer one larger than the true count identifies it. With the people in between, the opposite happens, as 1 is subtracted once too often and the count that excludes both ends is used by mistake.

The ability to count what place someone holds from the front or the back, settled by Order and Position, is broadened here to finding the number of people in between or in the whole line. This way of counting carries straight through into Tree-Planting Problems in grade 3, which finds the number of gaps between trees or people lined up.