Primary 6 · Patterns · Question type 11.1

P6 Patterns: Growing Figure Patterns

Build a table of figure number against count, find the repeated step from two differences, then count the gaps from figure 1.

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Primary 6, on the MOE Primary Mathematics syllabus.

In the Patterns chapter2 question types · see the chapter

The lesson · 2 minutes 55 seconds

How do you find a rule for growing figure patterns in P6?

Watch: a row of matchstick squares, and which figure uses 61 of them

Another worked example

A worked example

Figure 1 is made of 4 identical squares and is 10 cm tall. Figure 2 is made of 3 copies of figure 1, figure 3 is made of 5 copies of figure 1 and figure 4 is made of 7 copies. The pattern goes on in the same way. Find the area of figure 20.

The working · Ten lines

The step-by-step working

Written out in full, the way it should appear on paper.

figure 1 is 2 squares tall, so one square's side = 10 ÷ 2 = 5
area of one square = 5 × 5 = 25
area of figure 1 = 4 × 25 = 100
copies of figure 1 in figure 1 = 1
copies of figure 1 in figure 2 = 3
copies of figure 1 in figure 3 = 5
difference = 3 - 1 = 2
from figure 1 to figure 20 there are 20 - 1 = 19 gaps
copies in figure 20 = 1 + 19 × 2 = 1 + 38 = 39
area of figure 20 = 39 × 100 = 3900

The answer is 3900 cm².

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Count the seats

Find the rule before calculating the number of seats.

Identical square tables are pushed together in a straight row for a party. One table seats 6 people. Two tables joined seat 10 people. Three tables joined seat 14 people. The pattern goes on in the same way. How many people can sit at 20 joined tables?

Show the step-by-step solution

figure 1 = 6 chairs
figure 2 = 10 chairs
figure 3 = 14 chairs
difference = 10 - 6 = 4
difference = 14 - 10 = 4
the count goes up by 4 each time
from 1 table to 20 tables there are 20 - 1 = 19 gaps
figure 20 = 6 + 19 × 4 = 6 + 76 = 82

Ans: 82

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Next, find the repeating unit and any leftover. Repeating Patterns and Leftovers →

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