Fraction of the remainder: why your child keeps getting it wrong
On your child's script it looks like neat working with one wrong number: "2/3 of the remainder" has been worked out as 2/3 of the whole amount. Every step after that is correct, and the answer is still wrong. In a 3 to 5 mark question this one slip can cost most of the marks.
What it looks like
Mei had $360. She spent 1/4 of her money on a bag and 2/3 of the remainder on a pair of shoes. How much money did she have left?
- Bag: 1/4 × $360 = $90
- Remainder: $360 − $90 = $270
- Shoes: 2/3 × $270 = $180
- Left: $270 − $180 = $90
Why $30 is wrong: The shoes were taken as 2/3 of $360 ($240) instead of 2/3 of the $270 remainder, so $360 − $90 − $240 = $30.
Why children do it
- The question names the whole amount first, so that number is the one sitting in your child's head when the next fraction appears.
- Most fraction questions in earlier years are "a fraction of the whole", so the habit of reaching for the whole feels safe.
- Under time pressure the word "remainder" gets read but not acted on.
How to fix it at home
- Before every fraction, ask your child: "of what?" and have them write the answer above the fraction.
- Draw the bar model in two stages: one bar for the whole, then a second bar for the remainder only, cut into the new fraction.
- Have your child underline "remainder", "the rest" and "what was left" in every question before starting.
- After the answer, check that each amount spent is smaller than what was there at that moment.
Questions parents ask
Is this a careless mistake or a concept gap?
Usually it is a habit, not a gap. Your child can find 2/3 of a number; the slip is choosing which number. Habits like this one fade once your child gets the same type of question right several times in a row.
Does the bar model really help with remainder questions?
Yes. Redrawing the remainder as its own bar makes it hard to take the fraction of the wrong amount, because the whole is no longer on that line.
How can I tell if this is the reason my child loses marks?
In Knowbotic every wrong answer is traced to the habit behind it, so the weekly report shows you whether "fraction of the remainder" is the one costing marks.
Where it shows up
Other careless mistakes
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