The idea in brief. When things come in a fixed bundle that repeats, the way in is never the price of ONE thing. Build the smallest bundle the rule keeps repeating, price THAT once, and count how many of it the total holds, then come back, because a count of groups is not what the question asked for. Find the value of one whole group first, then divide the total by that group value. In the lesson. In the last lesson, we undid a wrong calculation to find the number. Today, we will count the free item as part of each offer group. Count the free item in each offer group. Find the number of groups first, then the items paid for.
Lesson video, with the working
Groups, gaps and offers
4 min 51 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
A beach stall offers one free shell badge for every 2 shell badges bought. Mei gets 18 shell badges, all from full offers. How many shell badges must Mei pay for?
Badges in one group = 2 + 1 = 3
Groups = 18 ÷ 3 = 6
Badges paid for = 6 × 2 = 12
Ans: 12 shell badges
Example 1 of 2
A beach stall gives 1 free shell badge for every 3 shell badges bought. Kavin gets 20 shell badges, all from full offers. How many shell badges does Kavin pay for?
Badges in one group = 3 + 1 = 4
Groups = 20 ÷ 4 = 5
Badges paid for = 5 × 3 = 15
Ans: 15 shell badges
Example 2 of 2
A beach stall gives 1 free shell badge for every 2 shell badges bought. Each badge bought costs $3. Siti gets 15 shell badges, all from full offers. How much does Siti pay?
Badges in one group = 2 + 1 = 3
Groups = 15 ÷ 3 = 5
Badges paid for = 5 × 2 = 10
Amount paid = $3 × 10 = $30
Ans: $30
How to solve it
Find what one offer group holds: the badges paid for plus the free one. 2 plus 1 is 3.
The free badge is one of the badges she gets, so count it in the group.
Divide the badges she gets by the size of a group to find the groups: 18 divided by 3 is 6.
Multiply the groups by the badges paid for in each group: 6 times 2 is 12.
If each badge costs money, multiply by the price: 10 badges at 3 dollars each is 30 dollars.
Count the free item in each offer group. Find the number of groups first, then the items paid for.
Practice questions with worked solutions
Question 1 is free to try. The other 10 open in the free trial, each with its solution film.
How do you solve P3 groups, gaps and offers word problems?
These word problems hide a repeating group: a deal that adds a free item, posts with gaps between them, or a packet that may be cheaper than singles.
What your child learns here
These word problems hide a repeating group: a deal that adds a free item, posts with gaps between them, or a packet that may be cheaper than singles. The page applies Primary 3 multiplication and division within the tables to them.
Find what one repeating group holds, such as the items paid for plus the free one.
Divide the total by the size of one group to count the groups.
Turn the number of groups back into what the question asks: items paid for, money spent, or posts needed.
Count posts and gaps in a straight row with a post at each end, and around a closed shape.
Compare complete ways of buying, a packet against single items, before choosing the cheapest.
Does the answer make sense?
In a straight row with something at each end, there is always one more marker or clip than gaps, and around a square the shared corner flags make the count less than 4 times one side. With a free-sheet deal, your child can check that the sheets paid for are fewer than the sheets received.
How to practise these questions
The Basic questions practise counting gaps and posts along a line. The Intermediate questions add grouping by value, such as offers where a set number of items costs a set price. The Challenge questions change the layout, such as no post at one end or a closed loop, so the count must be rethought. When a gaps or offers question is stuck, watch its solution film and attempt it again later from Revision.
Questions parents ask
How do I teach buy 2 get 1 free questions to my P3 child? Ask your child to say how many items one offer group holds before any dividing: 2 paid plus 1 free makes 3. Then count the groups, and turn the groups back into items paid for. Real supermarket deals make good practice.
Why is the number of posts one more than the number of gaps? In a straight row with a post at each end, every gap has a post on its right, and the first post has nothing on its left. So there is one extra post. Around a closed shape the ends join, so posts and gaps are equal.
Which P3 topics does this subtopic draw on? Mainly multiplying and dividing within the tables, with adding and subtracting money for the offers. Grouping by a repeating pattern applies those syllabus skills to word problems.
