The idea in brief. Build a table from the drawings, read the repeated difference between two rows, and count the gaps between figure numbers. Figure 1 is the starting row, so figure 12 is 11 gaps away. Each new figure adds the same number of pieces, because neighbouring shapes share a join, so the count is the first figure plus the step once for every figure after it. A row of matchstick squares needs 4 + 11 × 3 = 37 sticks for figure 12. In the lesson. Earlier, we found the difference between the numbers in a number pattern. Today, we find how many matchsticks are added each time, and count the gaps between figures. Start with figure 1, then add the same number of matchsticks for each gap after it.
Lesson video, with the working
Growing figures
5 min 32 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
Matchsticks make a row of joined squares. Each new figure adds one square sharing one side. Figures 1, 2 and 3 are shown. How many matchsticks does figure 6 use?
19
Ans: 19
Example 1 of 2
Matchsticks make a row of joined triangles. Each new figure adds one triangle sharing one side. Figures 1, 2 and 3 are shown. How many matchsticks does figure 5 use?
11
Ans: 11
Example 2 of 2
Matchsticks make a row of joined squares. Each new figure adds one square sharing one side. Figures 1, 2 and 3 are shown. Which figure uses 22 matchsticks?
7
Ans: 7
How to solve it
Count the matchsticks in the first figures and find how many are added each time. For 4, 7, 10 it is 3 more.
Figure 1 is where we start, with no gap before it.
Count the gaps from figure 1 to the figure you want. Figure 6 has 5 gaps.
Multiply the gaps by the matchsticks added, then add figure 1's matchsticks: 5 times 3 is 15, and 4 plus 15 is 19.
To find which figure uses 22, work back: 22 minus 4 is 18, and 18 divided by 3 is 6 gaps, so figure 7.
Start with figure 1, then add the same number of matchsticks for each gap after it.
Practice questions with worked solutions
Question 1 is free to try. The other 7 open in the free trial, each with its solution film.
Question 1 of 8 · Basic · free to tryFigures are made with counters. Figures 1, 2 and 3 have 6, 10 and 14…Figures are made with counters…
Figures are made with counters. Figures 1, 2 and 3 have 6, 10 and 14 counters respectively. The same number of counters is added each time. How many counters are in Figure 4?
This page teaches matchstick and shape patterns where each new figure grows by the same amount.
What your child learns here
This page teaches matchstick and shape patterns where each new figure grows by the same amount. The MOE Primary 3 outcome is patterns in number sequences; these questions apply it to pictures, a form children meet in school worksheets.
Count the sticks in the first few figures and write the counts in a table.
Find how many sticks are added from one figure to the next, and check that it stays the same.
See that each new square or triangle shares a side with the one before, so it adds fewer sticks than the first figure has.
Count the increases between two figure numbers: from Figure 1 to Figure 10 there are 9.
Work backwards from a number of sticks to find which figure uses it.
Does the answer make sense?
Every figure here has more counters, tiles, beads or stars than the one before, so a figure's count must be above every earlier figure's count and below any later one shown. Your child can also check that the number added between neighbouring figures stays the same each time.
How to practise these questions
The Basic questions practise finding how many are added each time and counting on to the next figure. The Intermediate questions add figures further along the pattern, so repeated adding must be organised. The Challenge questions work backwards, asking which figure has a given number of counters, or ask about a figure far down the line. If a growing figure question is stuck, watch its solution film, then come back to it later from Revision.
Questions parents ask
Are matchstick patterns in the Primary 3 syllabus? The syllabus names patterns in number sequences, outcome 1.5, rather than matchsticks. Matchstick and shape patterns are a picture form of the same idea: the counts of the figures make a number sequence. This page treats them that way.
Does my P3 child need a formula for growing figures? No. The method on this page is a table of counts, the amount added each time, and the number of increases since Figure 1. Your child adds that many increases to the count for Figure 1.
Why is Figure 10 not 10 times Figure 1? The figures share sides. Each new square uses a side that is already there, so it adds 3 sticks, not 4. Figure 10 of a row of joined squares has 31 sticks, not 40.
