Primary 6 · Mathematics

P6 average

An average question almost never wants the average. It wants the total, and the number of things it was shared between has usually just changed. Here is where the marks go.

Level
P6
Usually taught
Term 3
Covers
2 concepts

What changes at P6

At Primary 6, average stops being "add them up and divide". Questions now hand your child an average and ask for something else: a total, one missing value, or how many things there were.

So every question runs through the total, not the average. total = average × how many is the single line the whole topic sits on, and it gets used forwards and backwards in the same question.

The sentence that costs the mark

The average mass of 4 parcels is 18 kg. A fifth parcel is added and the average becomes 19 kg. What is the mass of the fifth parcel?

What the working usually does

19 kg ×4 parcels=76 kg

Uses the new average with the old count, making the fifth parcel 4 kg.

What the question asked

19 kg ×5 parcels=95 kg

The new average belongs to five parcels, making the fifth 23 kg.

Both columns multiply correctly and both give a believable parcel. The slip is one number wide. The count changed the moment the parcel was added, and the working carried on with the old one.

The after bar is one box longer, and that extra box is the fifth parcel. The gap between the two totals is its mass.

The same question, worked properly

  1. Turn the first average into a total

    4 parcels × 18 kg = 72 kg

    An average is only useful once it is a total. This is the rearrangement the topic runs on.

  2. Count what you have now

    4 parcels + 1 = 5 parcels

    This is the step that fails. The line that gets skipped. Adding a parcel changed the count, so the new average is shared between five, not four.

  3. Turn the new average into a total

    5 parcels × 19 kg = 95 kg

    The same rearrangement as step 1, with the count that is true now.

  4. Take the difference

    95 kg − 72 kg = 23 kg

    Whatever the total gained when the parcel arrived is the parcel.

  5. Check it back

    (72 kg + 23 kg) ÷ 5 = 19 kg

    The wrong answer fails here. A 4 kg parcel gives (72 + 4) ÷ 5 = 15.2 kg, which is not the average the question stated.

How can you tell it has clicked?

You do not need to do the maths to check this. When an average turns up, ask one thing: "how many things is that shared between?"

A child who has understood gives you a number and then reaches for the total. A child who repeats the average back has the formula without the idea under it, and that holds up right until a question adds something to the set.

One thing to try tonight

Put four things on the kitchen scale one at a time and work out the average mass together. Then add a fifth and ask what the average does now.

The arithmetic is not the point. Adding one thing changes both numbers in the sum, and noticing that is the entire skill this topic tests.

What your child will meet in this topic

  • Average
  • Average Word Problems

Most Singapore schools introduce this in Term 3, though schools do differ by a term either way. If your child’s school runs a different order, you can set it in the schedule on your dashboard.

What it leads to

Average is the last of the P6 topics that runs on totals and units, after fractions, ratio and percentage. Same habit, different label.

It also shows up as one step inside longer questions, where getting the count right early is what keeps the rest of the working sound.

More in Primary 6

Other topics in the same year, so you can see what sits either side of this one.

Struggling with the working rather than the topic itself? How to help your child with problem sums

See how your child is doing on this topic

StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.

Try it free