The idea in brief. Draw the two bars and make them the same kind of unit. A difference is taken off the longer bar so both bars are whole units; a multiple says how many units each bar is. Then the total or the difference tells you what some number of units is worth, one unit follows, and the question is answered from the bar it asked about, not from the unit.
Lesson video, with the working
Two quantities compared
3 min 43 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
How can I help my child reason through P4 total and difference questions?
Your child finds two unknown quantities from relationships such as a total, a difference or a stated multiple.
What your child learns here
Your child finds two unknown quantities from relationships such as a total, a difference or a stated multiple. This is a problem-solving application of whole-number arithmetic, rather than a separately named Primary 4 content outcome. The important decision is what the given number measures: both amounts together, the gap between them or one amount alone.
Distinguish an additive comparison, such as a stated amount more, from a multiplicative comparison that describes one quantity as several times another.
For a total and a difference, subtract the difference from the total to obtain two equal smaller amounts before dividing by two.
For a times-as-many relationship, express both quantities using the same equal unit and count the units represented by the given total or difference.
Recover the required quantity after finding the smaller amount or one unit, checking which of the two quantities the final sentence asks for.
Test the two recovered amounts against every stated relationship, since fitting the total alone does not establish the correct comparison.
Does the answer make sense?
For a total-and-difference question, add the two recovered amounts and compare their sum with the given total. Then subtract the smaller amount from the larger; the result must also match the stated difference.
How to practise these questions
The Basic question uses a total and a times-as-many comparison. Intermediate questions ask for a difference, recover an amount from a stated gap, combine related item prices or find the smaller quantity from a total and difference. Challenge questions establish two prices before costing a purchase, or use a comparison after some marbles are given away. Your child should say whether the given amount represents all the units or only the difference between them before dividing. Once one unit is known, read the final question again: it may ask for several items rather than either original quantity alone. Check the recovered amounts against both relationships before calculating that final purchase. Use the written solution to review why the known total or difference matches a particular number of equal units.
Questions parents ask
Why is the difference subtracted from the total before halving? The larger quantity includes an extra part equal to the difference. Removing that extra part from the combined total leaves two copies of the smaller quantity. Halving now has a clear meaning, and adding the difference back recovers the larger amount.
How is times as many different from more than? Times as many describes equal copies of an amount, while more than describes an added difference. Ask your child to restate the full comparison using the two quantities' names. That makes it easier to decide whether the relationship needs multiplication or addition.
Does my child need algebra for two unknown amounts? These questions can be solved with equal units and whole-number operations. Your child needs to explain what one unit represents and which given amount corresponds to a known count of units. Formal algebra is not required to make that reasoning clear at this stage.
