Problem-solving method

The grouping method, explained for parents

For every problem sum where things are only sold in fixed sets. Here is how to spot one, and why working out the price of a single item is usually the wrong first move.

Used from
P4
Taught at
P4–P6

What this method is

Some questions only let you buy things in fixed sets. A packet of 8. A box of 4. One of each. A price table that charges by the block. The method is to work out what one whole group is worth, then find how many groups fit.

It needs teaching because the instinct runs the other way. Most children reach for the price of one item, and here that gives a number that won't divide cleanly. Nobody sells a quarter of a packet.

When to reach for it

These are the words in a question that point at this method. You do not need to be able to solve it to spot them.

  • “sold in packets of 8”

    The question has already fixed the group for you. You cannot buy part of a packet, so whatever else happens, the answer has to come out in whole packets.

  • “an equal number of pencils and pens”

    One of each is the group. Add the two prices together to get what a single set is worth, then divide the total by that.

  • “the least amount of money”

    The last group will usually be a part group, and that is the whole question. Read carefully whether she has to buy it or can leave it behind.

  • “for every 4 pens bought, 1 free”

    A deal, not a package. The group is five pens at the price of four, so you count in fives and pay in fours.

  • “the table shows the parking charges”

    Tiered pricing. The first block nearly always costs something different from the rest, so the group is each extra half hour, not each hour.

Watch it work

Lina bought an equal number of pencils and pens. Each pencil costs $0.40 and each pen costs $0.30 more than a pencil. She spent $16.50 in all. How many pens did she buy?

  1. Price one pen

    1 pen = $0.40 + $0.30 = $0.70

    The question gives the pen by comparison rather than outright. Settle it first, or the group gets built on a number nobody has worked out yet.

  2. Decide what one group is

    1 set = $0.40 + $0.70 = $1.10

    She bought the same number of each, so one pencil and one pen travel together. This is the step children skip, and everything after it depends on naming it.

  3. Find how many groups

    $16.50 ÷ $1.10 = 15 sets

    One division, because the set now has a price of its own. Notice how little arithmetic is left once that is true.

  4. Go back to what was asked

    15 sets → 15 pens

    The question wanted pens, not sets. The two match here only because the group holds one of each, and this is exactly where a mark gets dropped.

The one it gets confused with

All three of these show up in the same P5 and P6 papers and look alike on the page. What separates them is one question you can ask before any arithmetic starts.

  • Units and Parts

    Do you know what things are actually worth, or only how they compare? Grouping works in real prices. Units and parts counts equal units when nothing has a value yet.

  • Guess and Check

    Can you work out what one group is worth directly? If you can, grouping gets there in a single division. Guessing is the fallback for when no group has a price you can find.

  • The assumption method

    Are the two things bought in a fixed pairing, or in numbers nobody has told you? An equal number of each is a group. Chickens and rabbits sharing 94 legs is not.

How can you tell it has clicked?

Ask one question before they start: what is one group here? If they can answer that in a sentence, the rest is arithmetic they can already do. If they cannot, more practice questions will not help until that part is fixed.

Watch what happens when the division does not come out even. A child who has understood stops and asks whether the leftover means one more packet or one fewer. A child who has memorised writes down the decimal and carries on.

One thing to try tonight

Do it in the supermarket aisle, on anything sold in a multipack. These come in packs of 6 and we need 20. How many packs?

Then ask the part that is actually the skill: we will have some left over, so do we round up or down? That is the same decision the exam question is testing, with the shopping still in your hands.

Where your child will meet it

Want the bigger picture on how these methods fit together? Maths heuristics, explained for parents

See which methods your child reaches for

StudyLah names the method in every worked solution, so you can see whether the problem was the method or the arithmetic.

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