3 mistakes learners make with percentages of an amount, each one named and explained.
A percentage is always a percentage of something, so you work out that amount before you do anything with it.
Asked to order 0.6, 5/8 and 65% you order them by how the digits look rather than by value.
Three different forms in one line is genuinely hard to hold, and the digits are what the eye reaches for.
Question. 0.6, 5/8 and 65%
A common answer. 65%, 0.6, 5/8, ordered by the look of the numbers
The answer. 0.6, 5/8, 65%
Why. As decimals they are 0.6, 0.625 and 0.65, and then the order is obvious.
Convert everything to decimals first. Comparing across forms is guessing.
Asked what you pay after 15% off £200, you answer £30.
You did the hard part correctly and stopped one step early, which is the most frustrating way to lose a mark.
Question. 15% off £200
A common answer. £30, which is the discount
The answer. £170
Why. The question asks what you hand over at the till, so the discount has to come off the price.
Read the last line of the question again before you write anything down.
20% off £60 is answered as £40, with 20 taken off rather than 20 per cent.
The words take off 20 do all the work in your head, and the per cent quietly drops out.
Question. 20% off £60
A common answer. £40, which is £20 taken off
The answer. £48
Why. 20% of £60 is £12, so £12 is what comes off.
A percentage is always a percentage of something. Work out that amount before you take anything away.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.