4 mistakes learners make with compound shapes, each one named and explained.
Split it, work out each piece, then add or subtract as the picture requires.
A path round a garden is worked out from the four side strips, with the four corner squares missed.
The strips along the sides are the visible parts of the path; the corners look like nothing.
Question. A 12 by 7 garden with a 1 m path around it
A common answer. 2 x 12 + 2 x 7 = 38
The answer. 14 x 9 - 12 x 7 = 42
Why. The four corner squares are part of the path too, and here they add 4.
Never build a border out of strips. Take the inner rectangle from the outer one instead.
The removed square is added to the rectangle rather than taken away.
Compound shapes are usually made by joining pieces, so adding is the practised move.
Question. A 6 by 4 rectangle with a 2 by 2 square removed
A common answer. 24 + 4 = 28
The answer. 24 - 4 = 20
Why. The answer has to be smaller than the rectangle it was cut from.
Look at the picture and ask whether the shape got bigger or smaller. Then choose the sign.
The area of the part that was removed, or of the original rectangle, is given as the answer.
It is one of the numbers the working produced, and it is a real area of something.
Question. A 6 by 4 rectangle with a 2 by 2 square removed
A common answer. 4, the square
The answer. 20, what is left
Why. The question asked for the remaining area, not the piece that went.
Reread the question after finishing. It names which region it wants.
The whole rectangle is calculated and the missing square is never subtracted.
Finding the big rectangle is the main work, and it looks like a finished answer.
Question. A 6 by 4 rectangle with a 2 by 2 square removed
A common answer. 24
The answer. 24 - 4 = 20
Why. The square was taken away, so its area is not part of the shape.
Shade the shape in. Anything you did not shade should not be in the answer.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.