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 starts at the first figure and adds the same difference for every gap.
Lesson video, with the working
Growing figures
3 min 34 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 hexagons. Figure 1 uses 6 matchsticks, figure 2 uses 11 and figure 3 uses 16. One figure in this pattern uses 96 matchsticks. Which figure is it?
difference = 11 − 6 = 5
difference = 16 − 11 = 5
added after figure 1 = 96 − 6 = 90
number of gaps = 90 ÷ 5 = 18
figure number = 18 + 1 = 19
Figure 19 uses 96 matchsticks.
Ans: Figure 19 uses 96 matchsticks.
Example 2
Figure 1 is a T-shape made of 4 identical squares and is 12 cm tall. Figure 2 is made by adding one square to the end of each of the three arms of figure 1. Every figure after that is made from the one before it in the same way. Find the area of figure 20.
one square's side = 12 ÷ 2 = 6 cm
area of one square = side × side
area of one square = 6 × 6 = 36 cm²
difference = 7 − 4 = 3 squares
gaps to figure 20 = 20 − 1 = 19
squares added = 19 × 3 = 57
figure 20 = 4 + 57 = 61 squares
area of figure 20 = 61 × 36 = 2196 cm²
The area of figure 20 is 2196 cm².
Ans: The area of figure 20 is 2196 cm².
Practice questions with worked solutions
Question 1 is free to try. The other 6 open in the free trial, each with its full working.
Question 1 of 7 · 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 can I help my child reason about P4 growing patterns?
Your child connects a sequence of pictures with a sequence of numbers.
What your child learns here
Your child connects a sequence of pictures with a sequence of numbers. This applies the MOE Primary 4 outcome on patterns in number sequences to growing figures. Counting what each figure contains and recording its position gives your child two different pieces of information to use when explaining the growth.
Distinguish the figure number, which tells where a picture comes in the sequence, from the number of objects contained in that picture.
Record the counts of the figures shown and compare successive totals to identify how the next figure is built from the previous one.
For constant growth, count the increases between the starting figure and the target before multiplying by the amount added each time.
Recognise that shared pieces belong to the completed figure only once, even when they help form more than one adjoining shape.
Work back from an object count to a figure number when the growth rule allows an exact whole number of steps.
Does the answer make sense?
For a pattern that adds a fixed positive number of objects each time, subtract the starting count from the proposed later count. Dividing this difference by the increase per figure should give the number of steps between the two figure positions, not the target figure number itself.
How to practise these questions
Basic questions use growing rows of joined shapes or tables, where the next addition changes the count by a steady amount. The Intermediate question distinguishes the total number of squares in a rectangular arrangement from the squares in its border. Challenge practice connects growing figures with perimeter or area, including finding a component count or size from a completed figure. Your child should identify what is being counted or measured before extending a pattern. A rule for the number of pieces does not automatically give the perimeter. Use the supplied figures to check the first few counts, and keep length units separate from square units in the final answer. When the repeated arrangement is hard to follow, members can review its solution film and check how each added piece changes the required count.
Questions parents ask
Are growing figures a separate Primary 4 syllabus topic? The syllabus names patterns in number sequences. Growing figures provide a picture-based application of that outcome: the object counts form the sequence. Your child can move between the pictures and the counts without needing an algebraic formula for the figure number.
Why does the first figure need special attention? A later figure contains the starting collection as well as everything added afterwards. Multiplying the increase by the target figure number can overlook that starting collection. Ask your child to identify the first count and the number of increases separately before combining them.
Should my child draw every figure up to the answer? Drawing a few figures can help establish the rule, but a distant figure is easier to handle with organised counts. Ask your child to check the growth on the supplied figures, then calculate from a known count. A small drawing can still help explain a shared piece.
