MathBrush

Practice

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?

Work it out on paper, then check below. ▶ See the working

Question 2

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?

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Question 3

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?

Work it out on paper, then check below. ▶ See the working

Question 4

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?

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Question 5

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?

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Question 6

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?

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Question 7

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?

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Question 8

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?

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Question 9

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?

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Question 10

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?

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Question 11

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?

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Question 12

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?

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Question 13

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?

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Question 14

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?

Work it out on paper, then check below. ▶ See the working

The working

Question 1

  1. Count the first few figures and write them in a row.8, 13, 18, 23, 28 …
  2. Each figure has 5 more tiles than the one before, so the pattern goes up by 5 every time.13 − 8 = 5
  3. 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
  4. That is the rule, and it can be checked against a figure you have already counted.tiles = 5 × figure number + 3
  5. 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.

Question 2

  1. Count the first few figures and write them in a row.4, 7, 10, 13, 16 …
  2. Each figure has 3 more tiles than the one before, so the pattern goes up by 3 every time.7 − 4 = 3
  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
  4. That is the rule, and it can be checked against a figure you have already counted.tiles = 3 × figure number + 1
  5. 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.

Question 3

  1. Count the first few figures and write them in a row.9, 14, 19, 24, 29 …
  2. Each figure has 5 more stickers than the one before, so the pattern goes up by 5 every time.14 − 9 = 5
  3. 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
  4. That is the rule, and it can be checked against a figure you have already counted.stickers = 5 × figure number + 4
  5. 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.

Question 4

  1. Count the first few figures and write them in a row.6, 8, 10, 12, 14 …
  2. Each figure has 2 more stamps than the one before, so the pattern goes up by 2 every time.8 − 6 = 2
  3. 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
  4. That is the rule, and it can be checked against a figure you have already counted.stamps = 2 × figure number + 4
  5. 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.

Question 5

  1. Count the first few figures and write them in a row.7, 12, 17, 22, 27 …
  2. Each figure has 5 more seats than the one before, so the pattern goes up by 5 every time.12 − 7 = 5
  3. 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
  4. That is the rule, and it can be checked against a figure you have already counted.seats = 5 × figure number + 2
  5. 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.

Question 6

  1. Count the first few figures and write them in a row.6, 10, 14, 18, 22 …
  2. Each figure has 4 more seats than the one before, so the pattern goes up by 4 every time.10 − 6 = 4
  3. 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
  4. That is the rule, and it can be checked against a figure you have already counted.seats = 4 × figure number + 2
  5. 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.

Question 7

  1. Count the first few figures and write them in a row.5, 9, 13, 17, 21 …
  2. Each figure has 4 more seats than the one before, so the pattern goes up by 4 every time.9 − 5 = 4
  3. 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
  4. That is the rule, and it can be checked against a figure you have already counted.seats = 4 × figure number + 1
  5. 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.

Question 8

  1. Count the first few figures and write them in a row.4, 6, 8, 10, 12 …
  2. Each figure has 2 more shells than the one before, so the pattern goes up by 2 every time.6 − 4 = 2
  3. 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
  4. That is the rule, and it can be checked against a figure you have already counted.shells = 2 × figure number + 2
  5. 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.

Question 9

  1. Count the first few figures and write them in a row.4, 6, 8, 10, 12 …
  2. Each figure has 2 more lanterns than the one before, so the pattern goes up by 2 every time.6 − 4 = 2
  3. 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
  4. That is the rule, and it can be checked against a figure you have already counted.lanterns = 2 × figure number + 2
  5. 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.

Question 10

  1. Count the first few figures and write them in a row.8, 12, 16, 20, 24 …
  2. Each figure has 4 more dots than the one before, so the pattern goes up by 4 every time.12 − 8 = 4
  3. 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
  4. That is the rule, and it can be checked against a figure you have already counted.dots = 4 × figure number + 4
  5. 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.

Question 11

  1. Count the first few figures and write them in a row.4, 6, 8, 10, 12 …
  2. Each figure has 2 more dots than the one before, so the pattern goes up by 2 every time.6 − 4 = 2
  3. 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
  4. That is the rule, and it can be checked against a figure you have already counted.dots = 2 × figure number + 2
  5. 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.

Question 12

  1. Count the first few figures and write them in a row.9, 14, 19, 24, 29 …
  2. Each figure has 5 more lights than the one before, so the pattern goes up by 5 every time.14 − 9 = 5
  3. 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
  4. That is the rule, and it can be checked against a figure you have already counted.lights = 5 × figure number + 4
  5. 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.

Question 13

  1. Count the first few figures and write them in a row.6, 11, 16, 21, 26 …
  2. Each figure has 5 more cubes than the one before, so the pattern goes up by 5 every time.11 − 6 = 5
  3. 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
  4. That is the rule, and it can be checked against a figure you have already counted.cubes = 5 × figure number + 1
  5. 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.

Question 14

  1. Count the first few figures and write them in a row.3, 5, 7, 9, 11 …
  2. Each figure has 2 more coins than the one before, so the pattern goes up by 2 every time.5 − 3 = 2
  3. 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
  4. That is the rule, and it can be checked against a figure you have already counted.coins = 2 × figure number + 1
  5. 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.