4 mistakes learners make with enlargement, each one named and explained.
Lengths multiply by the scale factor and areas multiply by its square.
Translation, reflection or rotation is picked as the transformation that changes the size.
All four are called transformations, and transform sounds like change.
Question. Which transformation does not keep the shape the same size
A common answer. translation
The answer. enlargement
Why. A translation only slides the shape; every length stays exactly as it was.
Three of the four preserve size. Only the one with size in its name does not.
An enlargement makes the shape smaller, because the factor was divided by.
Enlargements with fractional factors do shrink things, so the direction is not automatic.
Question. Area 12 cm squared, scale factor 3
A common answer. 12 / 3 = 4
The answer. 12 x 9 = 108
Why. A scale factor greater than 1 always makes the shape bigger.
Compare the factor with 1. Above it grows, below it shrinks.
An enlargement is carried out by adding the factor to each length.
Adding makes it bigger, which is what enlargement is supposed to do.
Question. Point (6, 2) enlarged by scale factor 2 from the origin
A common answer. (8, 4)
The answer. (12, 4)
Why. Every length has to double, and adding 2 does not double 6.
Enlargement is always a multiplier. Adding would change the shape.
An area is multiplied by the scale factor rather than by its square.
The scale factor is the number the question gives, so it is the number that gets used.
Question. Area 12 cm squared, scale factor 3
A common answer. 12 x 3 = 36
The answer. 12 x 9 = 108
Why. Both the length and the width triple, so the area goes up nine times.
Draw a 1 by 1 square enlarged by 3. Nine of the original fit inside it.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.