The idea in brief. Draw all three bars and make every one of them whole units before you share anything. A piece MORE comes off the total; a piece LESS goes back on to it, drawn dashed on the short bar. Only then does the total price the units, and the answer is read from the bar the question asked about, with its own piece put back. Every bar is made whole first, a piece taken off where a bar has extra and added where a bar is short, and only then is the total shared among the units. In the lesson. In the last lesson, we set the difference aside so the bars made equal units. Today, we will draw three bars with the same unit, and build each bar from the bar it is compared with. Draw every bar with the same unit. Set the extra aside, count all the units, then find one unit.
Lesson video, with the working
Three quantities
5 min 42 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
Kavin, Mei and Siti have 46 shells altogether. Mei has 2 times as many shells as Kavin. Siti has 6 more shells than Mei. How many shells does Siti have?
1 unit + 2 units + 2 units = 5 units
5 units = 46 − 6 = 40
1 unit = 40 ÷ 5 = 8
Mei's shells = 2 × 8 = 16
Siti's shells = 16 + 6 = 22
Ans: 22 shells
Example 1 of 2
Bala, Siti and Ravi have 47 shells altogether. Siti has 3 times as many shells as Bala. Ravi has 5 more shells than Siti. How many shells does Ravi have?
1 unit + 3 units + 3 units = 7 units
7 units = 47 − 5 = 42
1 unit = 42 ÷ 7 = 6
Siti's shells = 3 × 6 = 18
Ravi's shells = 18 + 5 = 23
Ans: 23 shells
Example 2 of 2
Hui Min, Arjun and Dev have 73 shells altogether. Arjun has 4 times as many shells as Hui Min. Dev has 10 more shells than Arjun. How many shells does Arjun have?
1 unit + 4 units + 4 units = 9 units
9 units = 73 − 10 = 63
1 unit = 63 ÷ 9 = 7
Arjun's shells = 4 × 7 = 28
Ans: 28 shells
How to solve it
Draw every bar with the same unit. The smallest quantity, Kavin's shells, is 1 unit.
Build each bar from the bar it is compared with. Mei is 2 units. Siti is as long as Mei, and 6 more.
Set the 6 more aside, so only equal units are left. Count the units in all three bars: 1 plus 2 plus 2 is 5.
Subtract the extra from the total, then divide to find 1 unit: 46 minus 6 is 40, and 40 divided by 5 is 8.
Use 1 unit for the bar asked, adding any extra: 2 times 8 is 16, and 16 plus 6 is 22.
Draw every bar with the same unit. Set the extra aside, count all the units, then find one unit.
Practice questions with worked solutions
Question 1 is free to try. The other 10 open in the free trial, each with its solution film.
Question 1 of 11 · Basic · free to tryBoxes A, B and C contain 82 counters altogether. B contains 2 times as many…Boxes A, B and C contain 82…
Boxes A, B and C contain 82 counters altogether. B contains 2 times as many as A. C contains 10 more than A. First remove the extra counters in C from the total. How many counters are in B?
How do you draw bars for P3 three quantities word problems?
This subtopic extends the two-bar comparison to three people who share one total.
What your child learns here
This subtopic extends the two-bar comparison to three people who share one total. It applies Primary 3 multiplication and division within the tables, with addition and subtraction, to word problems that carry two comparisons at once.
Choose the smallest amount as 1 unit, then build each other bar from the bar it is compared with.
Link every comparison back to the same unit, even when a person is compared with someone other than the smallest.
Take an extra part off the total, or add a missing part on, so every bar is whole units.
Count all the units, find one unit, and answer from the bar the question names.
Does the answer make sense?
When one overall total is given, your child can check that the three amounts add back to it, and where B is twice A, B's amount must be even. When three pair totals are given instead, each pair of crates must add back to its own total.
How to practise these questions
The Basic questions practise drawing three bars from one starting bar and finding the unit. The Intermediate questions add extra or fewer amounts on some bars, which must be removed before dividing. The Challenge questions describe each quantity from a different one, so your child must choose the right bar to draw first. When a three-quantity problem stalls, view its solution film and return to it later from Revision.
Questions parents ask
How do I help my P3 child with three-person bar model questions? Begin with the person everyone is compared with, and draw that bar first. Build each other bar from the bar named in its own sentence. The lesson film on this page shows three questions done this way, with all the bars drawn before any sharing.
What does 'times as many' mean in a P3 word problem? '3 times as many' means 3 equal groups the size of the other amount, so it is drawn as 3 units against 1 unit. It relies on the multiplication tables in the P3 syllabus, which include the tables of 6, 7, 8 and 9.
Which amount should be 1 unit when there are three people? Choose the amount the others are measured against, usually the smallest. If a bar is more than another by a fixed number rather than a multiple, draw it as that bar plus a separate piece, not as a new unit.
