4 mistakes learners make with area and perimeter of rectangles, each one named and explained.
Perimeter is the distance round the edge; area is the space inside.
The two lengths are multiplied and given as the distance round the edge.
Multiplying is the move most practised in this topic, so it happens by reflex.
Question. A garden 12 m by 5 m, fenced all round
A common answer. 12 x 5 = 60
The answer. 2 x (12 + 5) = 34
Why. The fence follows the edge, so the four sides are added.
Trace the fence with your finger. You are adding lengths, never multiplying them.
A rectangle is treated as a square, so one of its sides is multiplied by itself.
Area is remembered as a side times a side, and which two sides is not part of the memory.
Question. A rectangle 8 cm by 5 cm
A common answer. 8 x 8 = 64
The answer. 8 x 5 = 40
Why. The two sides of a rectangle are different, and the area uses one of each.
Point at both measurements in the question. Both have to appear in the calculation.
A square with perimeter 36 cm is treated as having sides of 36 cm.
The number given is the only length in the question, so it becomes the length used.
Question. A square of perimeter 36 cm
A common answer. 36 x 36 = 1296 cm squared
The answer. 9 x 9 = 81 cm squared
Why. The 36 is spread across four equal sides, so each one is 9.
Before using a length, ask whether it is one side or all of them.
Area is given as length plus width.
Adding is the first operation you reach for, and it does use both numbers.
Question. A rectangle 8 cm by 5 cm
A common answer. 8 + 5 = 13
The answer. 8 x 5 = 40
Why. Five rows of eight squares is a multiplication.
Picture the squares. Counting them is always a multiplication.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.