3 mistakes learners make with pythagoras' theorem, each one named and explained.
The square on the hypotenuse equals the two smaller squares added, so you square first, combine, and square root at the end.
A missing shorter side is found by adding the squares rather than subtracting them.
Pythagoras is met first as an addition and that is the version that sticks.
Question. Hypotenuse 13, one leg 5
A common answer. the root of 169 + 25
The answer. the root of 169 - 25, which is 12
Why. The answer must be shorter than the hypotenuse, and adding makes it longer.
Identify the hypotenuse first. If you already have it, you are subtracting.
The differences are added and rooted without ever being squared, giving the root of 7.
The formula is remembered as having a root in it and the squares are the part that drops out.
Question. From (1, 2) to (5, 5)
A common answer. the square root of 4 + 3
The answer. the square root of 16 + 9, which is 5
Why. The 4 and the 3 have to be squared before they are added.
Square, add, then root. Three steps, in that order, every time.
The hypotenuse is given as the product of the two shorter sides.
Squaring is a multiplication, so multiplying feels like it is in the right family.
Question. Legs of 6 cm and 8 cm
A common answer. 6 x 8 = 48
The answer. 10
Why. 48 is nearly five times the longest side of the triangle.
Square each side separately. Never multiply the two different sides together.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.