VA ClassesWhat Are Percentages?
Percent means per hundred. A child who hears the word that way stops treating percentages as a new topic and starts treating them as fractions they already know, which is most of the battle.
Percent means per hundred
A percentage is a fraction with 100 on the bottom.
The word does most of the explaining, if anyone bothers to unpack it. "Per cent" means "per hundred", from the same root that gives us century and cent, so 35 percent is 35 out of every 100 and nothing more mysterious than that.
Which is why 35100, 35% and 0.35 are the same amount written three ways. Nothing is being converted between them in any real sense, it is only being renamed.
The hundred square
A grid of 100 small squares makes the definition literal rather than abstract. Shade some of them and you have shaded a percentage, with no calculation involved at any point.
Use the heavier grid lines and count in blocks of five. Counting one square at a time is slow, error-prone and exactly where children start to dislike this topic.
The percentage bar
Grids are good for showing what a percentage is. Bars are better once you want to compare two of them, because the eye judges lengths far more reliably than areas.
Worth knowing by heart
These few turn up again and again, in tests and in shops. A child who simply knows them has their attention free for the actual question instead of spending it on the conversion.
- 50% is a half
- 25% is a quarter, and 75% is three quarters
- 10% is a tenth, which is the most useful one of all
- 20% is a fifth
- 1% is a hundredth
- 100% is all of it, and 0% is none of it
Above one hundred
Almost every child assumes 100% is a ceiling, and nobody corrects it, so the assumption survives quietly until a question about a price rising by 150% brings it down.
100% means all of one thing, so something that doubles has become 200% of what it was. Prices rise by 150%, a business grows 300%, and none of those is a typo.
When 100% really is the limit
It depends on what is being measured. You cannot eat 120% of a cake, because the cake runs out. You can absolutely earn 120% of last year's salary. The percentage is not the limit, the thing it describes is.
Common mistakes
1. Forgetting what the whole is
20% of a small class gets compared with 20% of a large one as though the two were the same number of children. A percentage is always a percentage OF something, and until the something is settled the number on its own means very little. Getting a child into the habit of asking "of what?" before anything else prevents a great deal of trouble later.
2. Reading the percent sign as a decimal point
5% gets written as 5.0 or as 0.5. Five percent is five out of a hundred, which puts the 5 in the hundredths column and makes the decimal 0.05. Saying "five per hundred" out loud produces the right decimal almost automatically, which is a good reason to keep using the long version of the word for a while.
3. Adding percentages of different wholes
A child scores 80% on a short test and 60% on a long one and calls the average 70%. That is only right if both tests were worth the same number of marks, which they were not. Percentages taken from different wholes cannot be averaged, and questions in later years lean on this deliberately.
Practice questions
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For parents
For one week, say "per hundred" instead of "percent" every time it comes up, out loud, including in shops. "Thirty per hundred off." It sounds odd for the first couple of days and then something shifts, because your child is now hearing the definition of the word every single time it is used, rather than a label they have to remember the meaning of separately.
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