Same pattern as Dot pattern — Figure 6. New numbers, new
story. Try each one on paper, then check the working below — or watch it drawn out, the
same way the problem above is.
Question 1
A path is laid with square tiles, one figure at a time. Figure 1 uses 8 tiles, Figure 2 uses 13 tiles and Figure 3 uses 18 tiles. Each figure is made the same way as the one before. How many tiles does Figure 200 use?
A path is laid with square tiles, one figure at a time. Figure 1 uses 4 tiles, Figure 2 uses 7 tiles and Figure 3 uses 10 tiles. Each figure is made the same way as the one before. Which figure uses 241 tiles?
Mrs Lim gives out stickers on a reward chart, one row at a time. Figure 1 has 9 stickers, Figure 2 has 14 stickers and Figure 3 has 19 stickers. The chart carries on in the same way. How many stickers are on Figure 60?
Wei Jie pastes stamps onto a page of his stamp album. Figure 1 has 6 stamps, Figure 2 has 8 stamps and Figure 3 has 10 stamps. Each page is filled the same way as the one before. How many stamps are on Figure 30?
Tables are pushed together in a row, and chairs are set around them. 1 table seats 7, 2 tables seat 12 and 3 tables seat 17. Every extra table is added in the same way. How many tables are needed to seat 252 people?
Tables are pushed together in a row, and chairs are set around them. 1 table seats 6, 2 tables seat 10 and 3 tables seat 14. Every extra table is added in the same way. How many people can sit at 250 tables?
Tables are pushed together in a row, and chairs are set around them. 1 table seats 5, 2 tables seat 9 and 3 tables seat 13. Every extra table is added in the same way. How many tables are needed to seat 401 people?
After a trip to the beach, Aisha arranges seashells on a shelf. Figure 1 has 4 shells, Figure 2 has 6 shells and Figure 3 has 8 shells. Each row is arranged the same way as the one before. Which figure has 242 shells?
Farhan hangs paper lanterns around the void deck for the Mid-Autumn Festival. Figure 1 has 4 lanterns, Figure 2 has 6 lanterns and Figure 3 has 8 lanterns. Each figure is hung the same way as the one before. How many lanterns are in Figure 25?
A pattern is made of dots. Figure 1 has 8 dots, Figure 2 has 12 dots and Figure 3 has 16 dots. The pattern carries on in the same way. How many dots are in Figure 20?
A pattern is made of dots. Figure 1 has 4 dots, Figure 2 has 6 dots and Figure 3 has 8 dots. The pattern carries on in the same way. How many dots are in Figure 25?
Devi strings fairy lights along the gate of her flat for Deepavali. Figure 1 has 9 lights, Figure 2 has 14 lights and Figure 3 has 19 lights. Each figure is strung the same way as the one before. How many lights are in Figure 30?
In math class, pupils build towers out of unifix cubes. Figure 1 uses 6 cubes, Figure 2 uses 11 cubes and Figure 3 uses 16 cubes. Each tower is built the same way as the one before. How many cubes does Figure 150 use?
Ah Seng lines up coins from his piggy bank on the table. Figure 1 has 3 coins, Figure 2 has 5 coins and Figure 3 has 7 coins. Each row is laid out the same way as the one before. How many coins are in Figure 60?
Count the first few figures and write them in a row.8, 13, 18, 23, 28 …
Each figure has 5 more tiles than the one before, so the pattern goes up by 5 every time.13 − 8 = 5
Going up by 5 each time means 5 × the figure number, and then a fixed amount that never changes.figure 1: 5 × 1 = 5, but it has 8 — so 3 extra
That is the rule, and it can be checked against a figure you have already counted.tiles = 5 × figure number + 3
Put the figure number into the rule.5 × 200 + 3 = 1003
Figure 200 uses 1003 tiles.
The pattern. Every figure is the one before it plus 5 more tiles, with 3 that never change. So the count is 5 × the figure number + 3, and Figure 200 is no harder than Figure 4.
Count the first few figures and write them in a row.4, 7, 10, 13, 16 …
Each figure has 3 more tiles than the one before, so the pattern goes up by 3 every time.7 − 4 = 3
Going up by 3 each time means 3 × the figure number, and then a fixed amount that never changes.figure 1: 3 × 1 = 3, but it has 4 — so 1 extra
That is the rule, and it can be checked against a figure you have already counted.tiles = 3 × figure number + 1
Run the rule backwards: take off the 1 that never change, then share the rest into groups of 3.(241 − 1) ÷ 3 = 80
It is Figure 80.
The pattern. Every figure is the one before it plus 3 more tiles, with 1 that never change. So the count is 3 × the figure number + 1, and Figure 80 is no harder than Figure 4.
Count the first few figures and write them in a row.9, 14, 19, 24, 29 …
Each figure has 5 more stickers than the one before, so the pattern goes up by 5 every time.14 − 9 = 5
Going up by 5 each time means 5 × the figure number, and then a fixed amount that never changes.figure 1: 5 × 1 = 5, but it has 9 — so 4 extra
That is the rule, and it can be checked against a figure you have already counted.stickers = 5 × figure number + 4
Put the figure number into the rule.5 × 60 + 4 = 304
Figure 60 has 304 stickers.
The pattern. Every figure is the one before it plus 5 more stickers, with 4 that never change. So the count is 5 × the figure number + 4, and Figure 60 is no harder than Figure 4.
Count the first few figures and write them in a row.6, 8, 10, 12, 14 …
Each figure has 2 more stamps than the one before, so the pattern goes up by 2 every time.8 − 6 = 2
Going up by 2 each time means 2 × the figure number, and then a fixed amount that never changes.figure 1: 2 × 1 = 2, but it has 6 — so 4 extra
That is the rule, and it can be checked against a figure you have already counted.stamps = 2 × figure number + 4
Put the figure number into the rule.2 × 30 + 4 = 64
Figure 30 has 64 stamps.
The pattern. Every figure is the one before it plus 2 more stamps, with 4 that never change. So the count is 2 × the figure number + 4, and Figure 30 is no harder than Figure 4.
Count the first few figures and write them in a row.7, 12, 17, 22, 27 …
Each figure has 5 more seats than the one before, so the pattern goes up by 5 every time.12 − 7 = 5
Going up by 5 each time means 5 × the figure number, and then a fixed amount that never changes.figure 1: 5 × 1 = 5, but it has 7 — so 2 extra
That is the rule, and it can be checked against a figure you have already counted.seats = 5 × figure number + 2
Run the rule backwards: take off the 2 that never change, then share the rest into groups of 5.(252 − 2) ÷ 5 = 50
50 tables are needed.
The pattern. Every figure is the one before it plus 5 more seats, with 2 that never change. So the count is 5 × the figure number + 2, and Figure 50 is no harder than Figure 4.
Count the first few figures and write them in a row.6, 10, 14, 18, 22 …
Each figure has 4 more seats than the one before, so the pattern goes up by 4 every time.10 − 6 = 4
Going up by 4 each time means 4 × the figure number, and then a fixed amount that never changes.figure 1: 4 × 1 = 4, but it has 6 — so 2 extra
That is the rule, and it can be checked against a figure you have already counted.seats = 4 × figure number + 2
Put the figure number into the rule.4 × 250 + 2 = 1002
250 tables seat 1002 people.
The pattern. Every figure is the one before it plus 4 more seats, with 2 that never change. So the count is 4 × the figure number + 2, and Figure 250 is no harder than Figure 4.
Count the first few figures and write them in a row.5, 9, 13, 17, 21 …
Each figure has 4 more seats than the one before, so the pattern goes up by 4 every time.9 − 5 = 4
Going up by 4 each time means 4 × the figure number, and then a fixed amount that never changes.figure 1: 4 × 1 = 4, but it has 5 — so 1 extra
That is the rule, and it can be checked against a figure you have already counted.seats = 4 × figure number + 1
Run the rule backwards: take off the 1 that never change, then share the rest into groups of 4.(401 − 1) ÷ 4 = 100
100 tables are needed.
The pattern. Every figure is the one before it plus 4 more seats, with 1 that never change. So the count is 4 × the figure number + 1, and Figure 100 is no harder than Figure 4.
Count the first few figures and write them in a row.4, 6, 8, 10, 12 …
Each figure has 2 more shells than the one before, so the pattern goes up by 2 every time.6 − 4 = 2
Going up by 2 each time means 2 × the figure number, and then a fixed amount that never changes.figure 1: 2 × 1 = 2, but it has 4 — so 2 extra
That is the rule, and it can be checked against a figure you have already counted.shells = 2 × figure number + 2
Run the rule backwards: take off the 2 that never change, then share the rest into groups of 2.(242 − 2) ÷ 2 = 120
It is Figure 120.
The pattern. Every figure is the one before it plus 2 more shells, with 2 that never change. So the count is 2 × the figure number + 2, and Figure 120 is no harder than Figure 4.
Count the first few figures and write them in a row.4, 6, 8, 10, 12 …
Each figure has 2 more lanterns than the one before, so the pattern goes up by 2 every time.6 − 4 = 2
Going up by 2 each time means 2 × the figure number, and then a fixed amount that never changes.figure 1: 2 × 1 = 2, but it has 4 — so 2 extra
That is the rule, and it can be checked against a figure you have already counted.lanterns = 2 × figure number + 2
Put the figure number into the rule.2 × 25 + 2 = 52
Figure 25 has 52 lanterns.
The pattern. Every figure is the one before it plus 2 more lanterns, with 2 that never change. So the count is 2 × the figure number + 2, and Figure 25 is no harder than Figure 4.
Count the first few figures and write them in a row.8, 12, 16, 20, 24 …
Each figure has 4 more dots than the one before, so the pattern goes up by 4 every time.12 − 8 = 4
Going up by 4 each time means 4 × the figure number, and then a fixed amount that never changes.figure 1: 4 × 1 = 4, but it has 8 — so 4 extra
That is the rule, and it can be checked against a figure you have already counted.dots = 4 × figure number + 4
Put the figure number into the rule.4 × 20 + 4 = 84
Figure 20 has 84 dots.
The pattern. Every figure is the one before it plus 4 more dots, with 4 that never change. So the count is 4 × the figure number + 4, and Figure 20 is no harder than Figure 4.
Count the first few figures and write them in a row.4, 6, 8, 10, 12 …
Each figure has 2 more dots than the one before, so the pattern goes up by 2 every time.6 − 4 = 2
Going up by 2 each time means 2 × the figure number, and then a fixed amount that never changes.figure 1: 2 × 1 = 2, but it has 4 — so 2 extra
That is the rule, and it can be checked against a figure you have already counted.dots = 2 × figure number + 2
Put the figure number into the rule.2 × 25 + 2 = 52
Figure 25 has 52 dots.
The pattern. Every figure is the one before it plus 2 more dots, with 2 that never change. So the count is 2 × the figure number + 2, and Figure 25 is no harder than Figure 4.
Count the first few figures and write them in a row.9, 14, 19, 24, 29 …
Each figure has 5 more lights than the one before, so the pattern goes up by 5 every time.14 − 9 = 5
Going up by 5 each time means 5 × the figure number, and then a fixed amount that never changes.figure 1: 5 × 1 = 5, but it has 9 — so 4 extra
That is the rule, and it can be checked against a figure you have already counted.lights = 5 × figure number + 4
Put the figure number into the rule.5 × 30 + 4 = 154
Figure 30 has 154 lights.
The pattern. Every figure is the one before it plus 5 more lights, with 4 that never change. So the count is 5 × the figure number + 4, and Figure 30 is no harder than Figure 4.
Count the first few figures and write them in a row.6, 11, 16, 21, 26 …
Each figure has 5 more cubes than the one before, so the pattern goes up by 5 every time.11 − 6 = 5
Going up by 5 each time means 5 × the figure number, and then a fixed amount that never changes.figure 1: 5 × 1 = 5, but it has 6 — so 1 extra
That is the rule, and it can be checked against a figure you have already counted.cubes = 5 × figure number + 1
Put the figure number into the rule.5 × 150 + 1 = 751
Figure 150 uses 751 cubes.
The pattern. Every figure is the one before it plus 5 more cubes, with 1 that never change. So the count is 5 × the figure number + 1, and Figure 150 is no harder than Figure 4.
Count the first few figures and write them in a row.3, 5, 7, 9, 11 …
Each figure has 2 more coins than the one before, so the pattern goes up by 2 every time.5 − 3 = 2
Going up by 2 each time means 2 × the figure number, and then a fixed amount that never changes.figure 1: 2 × 1 = 2, but it has 3 — so 1 extra
That is the rule, and it can be checked against a figure you have already counted.coins = 2 × figure number + 1
Put the figure number into the rule.2 × 60 + 1 = 121
Figure 60 has 121 coins.
The pattern. Every figure is the one before it plus 2 more coins, with 1 that never change. So the count is 2 × the figure number + 1, and Figure 60 is no harder than Figure 4.