4 mistakes learners make with turning a problem into an equation, each one named and explained.
The equation has to say what the situation says, so name what you do not know, write the sentence in symbols, and check it against the words before solving.
A quadratic modelling a garden gives two roots and the negative one is offered as the answer.
Both roots solve the equation, and rejecting one feels like throwing away correct work.
Question. A garden of length x + 2 and width x has area 35
A common answer. x = -7
The answer. x = 5
Why. A garden cannot have a width of minus seven metres.
When a quadratic models something physical, check both roots against the situation before answering.
Perimeter is given as length plus width, with the opposite pair never added.
A rectangle is described by two numbers, so it feels as though two lengths is the whole of it.
Question. A garden 12 m by 5 m
A common answer. 12 + 5 = 17
The answer. 12 + 5 + 12 + 5 = 34
Why. A rectangle has four sides, and the opposite ones are equal but still there.
Walk round the shape and count what you walk along. You cross four sides, not two.
The distance round the edge is calculated and offered as the area.
Both are worked out from the same two lengths, and both are called the size of the shape.
Question. A rectangle 8 cm by 5 cm
A common answer. 2 x (8 + 5) = 26
The answer. 8 x 5 = 40
Why. Area counts the squares inside; perimeter measures the fence around.
The unit tells you which. If the answer has a squared unit, it must be an area.
For a rectangle of length x + 4 and width x with perimeter 36 you write x + 4 + x = 36.
The numbers in the question all get used, which feels like the job is done, and the situation itself never gets checked.
Question. perimeter of a rectangle x + 4 long and x wide
A common answer. x + 4 + x = 36, which is two sides
The answer. 2(x + 4) + 2x = 36
Why. A rectangle has four sides, so each length and each width is counted twice.
Read your equation back as a sentence. If it does not describe the picture, solving it will not help.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.