1 P4.PA.JM.17092429
Level 3
Mina uses tiles to create patterns as shown.
  1. Find the number of tiles in pattern 6.
  2. Which pattern has 100 tiles?
3 m
Square numbers
2 P4.PA.JM.17092425
Level 3
Ben is building some patterns using square tiles as shown. How many square tiles does he need to build the 21st pattern?
3 m
Square numbers
3 P6.PA.JC.21022201
Level 3
The following is a sequence of numbers.
  1. Find the 39th number.
  2. Find the 40th number.
3 m
Equal intervals Square numbers
4 P6.PA.JM.18011208
Level 3
Tina used stars and sticks to make the following patterns.
  1. How many stars are there in Pattern 5?
  2. If Tina counted 289 stars, which pattern number had she made?
  3. How many stars are there in Pattern 120?
3 m
Square numbers
5 P6.PA.JC.17111315
Level 3
Consider the pattern.
  1. What is the sum of Row 9?
  2. What is the sum of Row 50?
  3. If the sum is 2702, what is the row number?
3 m
Square numbers
6 P6.PA.JC.17111301
Level 2
The first three figures of a sequence are shown. The table records the number of shaded and unshaded rhombuses in each figure.
  1. Find the number of unshaded rhombuses in Figure 10?
  2. Find the number of shaded rhombuses in Figure 40?
  3. Which figure number has 804 shaded rhombuses?
3 m
Equal intervals Square numbers
7 P6.PA.JC.17111306
Level 3
The patterns show a sequence of shapes. Each shape has a number of small right-angled triangles. A dot is placed at each point where there is a vertex of one or more right-angled triangles. The total number of dots and the number of small right-angled triangles of each figure is shown in a table.
  1. Find the total number of dots required to form Pattern 4.
  2. Find the total number of dots required to form Pattern 20.
  3. Find the number of small right-angled triangles in Pattern 50.
3 m
Repeated patterns Square numbers
8 P6.PA.JC.17111305
Level 3
Some patterns of shaded and unshaded small triangles is given. The unshaded triangles are those which have at least one side on the edge of the big triangle. All of the other small triangles are shaded. The table below shows numbers of small triangles.
  1. Find the total number of triangles in Pattern 80.
  2. Find the number of shaded triangles in Pattern 40.
  3. Find the number of unshaded triangles in Pattern 50.
3 m
Repeated patterns Square numbers
9 P6.PA.JC.17111316
Level 3
The figure shows a series of steps built using square cubes. The n number of steps is given by x -step.
  1. How many square cubes were used if n is 5?
  2. How many square cubes were used if n is 40?
  3. Find the number of steps if a total of 144 square cubes are used.
3 m
Square numbers Sum of odd consecutive
10 P6.PA.JC.17111303
Level 3
The diagram shows a sequence of patterns formed by square tiles. By considering the pattern information in the table, answer the questions.
  1. Find the number of tiles at the bottom layer in the 29th pattern
  2. Find the total number of tiles in Pattern 50.
3 m
Equal intervals Square numbers Sum of odd consecutive
11 P6.PA.JC.17111318
Level 3
The diagram shows the pattern for the number of circles.
  1. How many circles will Pattern 4 contain?
  2. How many circles will Pattern 30 contain?
  3. Which pattern contains 421 circles?
3 m
Repeated patterns Square numbers Guess & check
12 P4.PA.JM.17092426
Level 3
Study the table carefully.
  1. How many dots are there in Figure 5?
  2. How many dots are there in Figure 10?
  3. If there are 36 dots, what is the figure number?
4 m
Square numbers Table
13 P4.PA.JM.17092428
Level 3
Darryl was drawing a pyramid-like structure as shown. It consists of shaded and unshaded rectangles. The rest of the structure follows the same pattern.
  1. How many shaded rectangles are there in Row 9?
  2. In which row would there be 37 rectangles?
  3. Darryl had drawn a total of 144 rectangles. How many shaded rectangles were there in the drawing?
4 m
Repeated patterns Square numbers Units method
14 P4.PA.NK.23042605
Level 3
The patterns are made up of identical shaded and identical unshaded squares.

  1. Find the total number of squares in Pattern 4.
  2. Find the number of unshaded squares in Pattern 4.
  3. Which Pattern Number has a total of 100 squares?
4 m
Square numbers
15 P4.PA.JM.17092427
Level 3
Study the pattern. Each figure is made up of identical squares.
  1. What fraction of Figure 1 is shaded? Express your answer in the simplest form.
  2. What is the number of shaded squares in Figure 4?
  3. What is the number of unshaded squares in Figure 8?
4 m
Equal intervals Square numbers Fraction of a whole
16 P5.PA.NK.23010309
Level 3
Find the sum of all the odd numbers that are less than 40.
4 m
Square numbers Odd & even
17 P5.PA.NK.23010307
Level 3
The following pattern is made up of shaded and unshaded squares.
  1. Find the values of (i), (ii) and (iii). Give your answers in the following format. (Eg 1, 2, 3)
  2. Find the number of unshaded squares for Figure 30.
  3. Find the number of shaded squares for Figure 30.
4 m
Repeated patterns Square numbers Odd & even
18 P5.PA.NK.23053003
Level 3
The following is made up of identical triangles. Study the pattern carefully.
  1. Complete the table for Figure 4.
  2. A figure number in the pattern has a total of 144 triangles. What is the figure number?
4 m
Square Numbers Sum of consecutive Triangle
19 P6.PA.JM.18011219
Level 3
Study the number pattern carefully.
  1. What is the missing number in the 5th pattern?
  2. What is the missing number in the 32th pattern?
  3. If this number pattern goes on, which pattern number will give you 445?
4 m
Square numbers
20 P6.PA.JM.18011220
Level 3
May added a certain number of white squares round a grey square and then a certain number of grey squares round the white squares and she continued adding more grey and white squares round the diagram in each pattern as shown.
  1. How many grey squares did she need if the most outer layer had 11 squares on each side?
  2. How many squares are there in the Figure 11?
4 m
Square numbers

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