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. In the lesson. A growing pattern is a first row and the same difference repeated.
Lesson video, with the working
Growing figures
3 min 29 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
Identical matchsticks are laid to make a row of squares, the same way as before: figure 1 uses 4 matchsticks, figure 2 uses 7 and figure 3 uses 10. One figure in this pattern uses 61 matchsticks. Which figure is it?
Figure 20 uses 61 matchsticks.
Ans: 20
Example 1
Figure 1 is a cross made of 5 identical squares and is 12 cm tall. Figure 2 is made by adding one square to the end of each of the four arms of figure 1. Every figure after that is made from the one before it in the same way. Find the area of figure 25.
Area of figure 25 = 101 × 16 = 1616 cm²
Ans: 1616 cm²
How to solve it
Build a table of figure numbers and counts: figure 1 uses 4 matchsticks, figure 2 uses 7 and figure 3 uses 10.
Find the difference between rows: 7 minus 4 is 3, and 10 minus 7 is 3, so the count goes up by 3 each time.
Count the gaps from figure 1. To reach figure 12 there are 11 gaps, because 12 minus 1 is 11.
To go from a count back to a figure, take off the first row's count: 61 minus 4 is 57 matchsticks added after figure 1.
Divide by the difference to count the gaps: 57 divided by 3 is 19 gaps, and 19 gaps after figure 1 lands on figure 20.
A figure number counts the rows. Every gap between them adds the same difference. A growing pattern is a first row and the same difference repeated.
Practice questions with worked solutions
Question 1 is free to try. The other 5 open in the free trial, each with its full working.
Question 1 of 6 · Basic · free to tryIdentical matchsticks are laid to make a row of squares. Figure 1 is one…Identical matchsticks are laid…
Identical matchsticks are laid to make a row of squares. Figure 1 is one square and uses 4 matchsticks. Figure 2 is two squares in a row and uses 7 matchsticks. Figure 3 is three squares in a row and uses 10 matchsticks. The pattern goes on in the same way. How many matchsticks are used in figure 12?
from figure 1 to figure 12 there are 12 − 1 = 11 gaps
figure 12 = 4 + 11 × 3 = 4 + 33 = 37
Answer: 37
For parents
How do you solve growing pattern questions in P6?
In a growing pattern each figure adds the same number of sticks, tiles or squares as the one before.
What your child learns here
In a growing pattern each figure adds the same number of sticks, tiles or squares as the one before. Patterns in number sequences are an earlier-years outcome, and this Primary 6 page applies them to longer figure questions.
Build a table of figure number against count for the first three or four figures.
Find the step: the difference between counts, checked on at least two pairs.
Reach a far figure by counting the gaps from figure 1: figure 10 is 9 steps after figure 1.
Work backwards from a count: take off figure 1's count, divide by the step, and add 1 for figure 1 itself.
Use the count with other measures, such as area or perimeter, when the question asks for them.
Does the answer make sense?
Each figure in a growing pattern has more than the one before, so your child's answer for a far figure must be bigger than the counts shown for the first few. When the question gives a count and asks which figure it is, the answer must be a whole figure number.
How to practise these questions
The Basic questions train building a table, finding the step and reaching a figure far along the pattern. Intermediate questions run the table in reverse, from a count back to the figure number. Challenge questions count copies of a whole figure rather than single pieces, or link edges hidden by joins to areas and perimeters. If a growing pattern loses its rule, read the written step-by-step solution.
Questions parents ask
Is patterns in the P6 syllabus? Patterns in number sequences are listed in the MOE syllabus in earlier years rather than as a separate Primary 6 topic. Growing figure questions apply that idea in longer problem sums, and the syllabus names generalising patterns as part of mathematical reasoning.
Does my child need a formula for the nth figure? No formula is needed. A table of the first few figures, the step between them and a count of the gaps from figure 1 is enough to reach any figure.
Why is the figure number one more than the number of gaps? Figure 1 exists before any step is added. Each gap then adds one figure, so after 20 gaps your child is at figure 21.
