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. With two bars drawn, the difference comes off before the halving, and the question is read again to see which bar it asks about before the answer is written. In the lesson (Two quantities). In Primary 2, you learned that 3 times 4 means 3 groups of 4. 3 groups of 4 make 12. Today, we will draw bars of equal units and find the value of one unit. Count the units under the number you know. Then find one unit, and use it to answer the question. In the lesson (Sum and difference). In the last lesson, we drew bars of equal units and found one unit. Then we used one unit to answer the question. Today, we will set the difference aside, so the two bars make equal units. Set the difference aside, and the two bars make equal units. Find one unit, then add the difference back for the bigger bar.
Lesson videos, with the working
Lesson 1
Two quantities
4 min 40 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
How do you solve P3 word problems total and difference with bar models?
This is the first bar model subtopic in the chapter.
What your child learns here
This is the first bar model subtopic in the chapter. Two amounts are compared, by a difference or by 'times as many', and either their total or their difference is given. It applies Primary 3 multiplication, division, addition and subtraction to two-bar word problems.
Draw two bars made of equal units when one amount is a number of times the other.
Set the difference aside so the two bars become equal, then halve what is left.
Find one unit from the total or the difference, using division within the tables.
Answer for the bar the question names, adding the difference back for the bigger one.
Does the answer make sense?
When two clubs, trays or boxes share a total, the bigger amount is more than half of it and the smaller one is less than half. When one box has several times as many as the other, your child can check that the gap between them is an exact number of the smaller box's amount.
How to practise these questions
The Basic questions practise drawing two bars from a total or a difference and finding one unit. The Intermediate questions add stories that give both a times relationship and a difference. The Challenge questions ask for an amount the bars do not give directly, so your child needs a final step. If a two-quantity question is stuck, watch its solution film together and attempt it again later from Revision.
Questions parents ask
Is total and difference in the Primary 3 syllabus? The P3 syllabus lists multiplying and dividing within the multiplication tables, and addition and subtraction up to 4 digits. Total and difference questions apply those skills to a story with two amounts. The lesson on this page starts from the Primary 2 idea that 3 times 4 means 3 groups of 4.
Does my P3 child need to draw a bar model for these questions? The MOE syllabus does not require one particular method. The lesson on this page draws two bars because they show the total, the difference and the units in one picture, so each line of working follows from what is drawn. A child who solves it another way can still use the bars to check.
What is the fastest way to teach my P3 child total and difference questions? Start with 'times as many' and a total, where the bars split into equal units. Then bring in a difference, and practise covering it before sharing. Watch the lesson film on this page together and pause before each step to ask what comes next.
