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P6 Number Pattern
In this worksheet, you will learn the 3 basic Number Patterns as follows:
a) Common Difference / Group Common Difference
b) Square Numbers (Sum of Consecutive Odd numbers)
c) Triangular Numbers (Sum of Consecutive numbers)
d) Formula for number pattern 2, 6, 12, 20, …
1)
Date Homework
Name: ___________________________________ Class: ______________
My Learning Notes on Number Pattern!
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 2
Types of Number Patterns
Note: ‘n’ represents Figure Number/Pattern No/Layout No, etc.
Types of Number Patterns
Guiding Formula Examples
Common Difference
n x Common Diff ± A mystery
number
2, 5, 8, 11, 14, …
‘Group’ Common Difference
Applicable to EVEN n ONLY 𝐸𝑣𝑒𝑛 𝑛
2x Group Common Diff ± A
mystery number
2, 5, 9, 12, 16, …
Square numbers (Sum of
consecutive ODD numbers)
n x n
(n+1) x (n+1)
4, 9, 16, 25, 36 …
Triangular numbers
(Sum of consecutive
numbers)
𝑛 𝑥 (𝑛 + 1)
2
(𝑛 + 1) 𝑥 (𝑛 + 2)
2
(𝑛 − 1) 𝑥 𝑛
2
3, 6, 10, 15, 21, …
0, 1, 3, 6, 10, 15, …
0, 2, 6, 12, 20, 30, …
Fig no 1 2 3 4
No.of dots 2 6 12 20
(1x2) (2x3) (3x4) (4x5)
No.of dots 0 2 6 12
(0x1) (1x2) (2x3) (3x4)
Add or subtract
+4 +6 +8
+3 +4 +3 +4
+3 +5 +7 +9
+2 +4 +6
+3 +3 +3 +3
1, 3, 6, 10, 15, …
+2 +3 +4 +5
( 𝐸𝑣𝑒𝑛 𝑛
2 x 7 – 2)
1, 4, 9, 16, 25, …
( n x 3 - 1)
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 3
1. The following figures are made up of heart-shaped stickers. Study the pattern
carefully and answer the following questions.
a) How many heart-shaped stickers are there in Figure 12?
b) How many heart-shaped stickers are there in Figure 25?
c) If each sticker costs $0.25, what is the total cost of the stickers in Figure 32?
d) Which figure has 313 heart-shaped stickers?
Answer: (a) ______________
(b) ______________
(c) ______________
(d) ______________
Figure 1 Figure 2 Figure 3
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 4
2. Study the following pattern and answer the questions.
Pattern 1 Pattern 2 Pattern 3
(a) How many white circles will there be in Pattern 6.
(b) How many grey circles will there be in Pattern 10?
(c) If the total number of circles of a pattern is 339, what will be the pattern number?
Pattern White Grey Total
1 6 3 9
2 10 5 15
3 14 7 21
4 18 9 27
5 22 11 33
6 a) ________
13 39
Answer: (a) __________
(b) __________
(c) __________
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 5
3. Small squares are used to form a series of larger squares as shown below.
(a) Complete the table below.
Length of side
of big square
(units)
Number of
shaded squares
Number of unshaded
squares
Total number of
squares
2 4 0 4
3 8 1 9
4 12 4 16
5
6
(b) How many unshaded squares are there if the length of the side of the big
square is 12 units?
(c) How many shaded squares are there if the length of the side of the big
square is 20 units?
(d) What is the total number of squares if there are 900 unshaded squares?
Answer: (b) ____________
(c) ____________
(d) ____________
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 6
4. Study the given patterns of hexagons-tile carefully.
Pattern 1 Pattern 2 Pattern 3
(a) If the pattern continues, how many shaded hexagon-tiles will there be in
Pattern 6?
(b) Which pattern would need 121 shaded hexagon-tiles?
(c) How many hexagon-tiles are there in Pattern 18?
(d) Which pattern would need 930 white hexagon-tiles?
Answer: (a) ___________
(b) __________
(c) __________
(d) __________
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 7
5. Jane made patterns by drawing shaded and unshaded crosses.
Pattern
1
Pattern
2
Pattern
3
Pattern
4
Pattern Number of
Number of Total number of
crosses
1 1 0 1
2 4 1 5
3 9 4 13
4 16 9 25
…
8 64 i) _______
ii) __________
(a) Complete the table for Pattern 8.
(b) Which pattern will have 196 unshaded crosses?
(c) Which pattern will have 613 crosses in total?
Answer: (b) __________
(c) __________
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 8
6. Linda bought some identical smiley stickers to decorate one of her classroom walls in
the pattern as shown below. Each sticker cost 2 cents.
(a) How many smiley stickers were there in Column 12?
(b) Linda used up all her smiley stickers after she completed Column 19. How much
more will it cost Linda if she wanted to use the same smiley stickers to paste
Column 20?
(c) In which column will there be 378 smiley stickers?
(d) How many rows of smiley stickers will there be if Linda pasted $12.60 to buy the
smiley stickers in that column?
Answer: (a) ___________
(b) __________
(c) __________
(d) __________
Column 1 Column 2 Column 3 Column 4
Row 1
Row 2
Row 3
Row 4
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 9
7. Identical triangles were used to form the figures below. Study the pattern and answer
the questions that follow.
Pattern 1 Pattern 2 Pattern 3
(a) What are the values for A and B in the table?
Answer: _______________
(b) How many white triangles will there be in Pattern 24?
Answer: _______________
Pattern No No. of white triangles No. of grey triangles
1 1 3
2 3 6
3 6 10
4 10 15
5 15 21
6 A B
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 10
7. (c) How many white and grey triangles altogether are there in Pattern 40?
Answer: _______________
(d) In which pattern number will there be 1953 grey triangles?
Answer: _______________
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 11
8. Rita used white and grey squares to form the following 4 patterns. The first
4 patterns are shown below.
Pattern 1 Pattern 2 Pattern 3 Pattern 4
The table below shows the number of grey squares and white squares and the total
number of squares for each pattern.
Pattern Number of grey
squares
Number of white
squares
Total number of
squares
1 1 0 1
2 1 2 3
3 4 2 6
4 4 6 10
5
6
(a) Complete the table for Pattern 5 and Pattern 6.
(b) Find the total number of squares Rita will need to form Pattern 20.
Answer: _______________
(c) In which pattern number will there be a total of 378 squares?
Answer: _______________
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 12
8. (d) How many grey squares will Rita need to form Pattern 35?
Answer: _______________
(e) How many white squares Rita will need to form Pattern 69?
Answer: _______________
(f) How many grey squares will Rita need to form a total of 1326 squares?
Answer: _______________
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 13
9. Study the pattern below carefully. Each figure is formed by identical squares and
circles. The side of each square is 6cm. The circle inside each square touches the
4 sides of the square.
(a) How many squares are there in Figure 14?
Answer: _______________
(b) In which figure will there 529 squares?
Answer: _______________
(c) How many circles are there in Figure 35?
Answer: _______________
(d) In which figure will there be 1035 circles?
Answer: _______________
(e) In which figure will there be 2145 circles?
Answer: _______________
Figure 1 Figure 2 Figure 3
6cm
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 14
(f) *In which figure will there be 153 more squares than circles?
Answer: _______________
(g) *In which figure will there be 406 more squares than circles?
Answer: _______________
(h) **Find the total shaded area in the figure found in (g). (Take 𝜋 = 3.14)
Answer: _______________
9.
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 15
10. Study the figure below and complete the table.
Figure 1 Figure 2 Figure 3 Figure 4
Figure Number of
triangles
Number of
grey squares
Number of
white
squares
Total number
of squares
1 1 1 0 1
2 3 3 1 4
3 5 6 3 9
4 7 10 6 16
5
(a) Complete the table above for Figure 5.
(b) In which figure number will there be 45 triangles?
Answer: __________
(c) Find the number of grey squares in Figure 38?
Answer: __________
(d) Find the number of white squares when there are a total 4624 squares.
Answer: __________
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 16
11. Jasmine uses black and white buttons to form figures that follow a pattern.
The first three figures are shown below.
(a) The table shows the number of black and white buttons used for each figure.
Complete the figure for Figure 4 and 5.
Figure Number 1 2 3 4 5
Number of black buttons 1 3 6
Number of white buttons 4 9 16
Total number of buttons 5 12 22
(b) A figure in the pattern has 961 white buttons. How many black buttons are
there in that figure?
(c) A figure in the pattern has a total of 376 black and white buttons. What is the
Figure Number?
Answer: (b) ______________
(c) ______________
Figure 1 Figure 2 Figure 3
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 17
12. Squares and circles are used to form figures that follow a pattern as shown below
(a) The table shows the number of squares and circles for the first four figures.
Complete the table for Figure 5.
Figure Number Squares Circles Total
1 4 2 6
2 7 8 15
3 10 18 28
4 13 32 45
5 ______ ______ _______
(b) How many squares are there in Figure 10?
(c) How many circles are there in Figure 28?
(d) A figure in the pattern has 3528 circles. What is the Figure Number?
Answer: (b) _____________
(c) ____________
(d) _____________
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 18
13. The diagram shows a sequence of patterns formed by grey and white tiles that are
2 cm by 2 cm.
Figure 1 Figure 2 Figure 3
Figure number Number of grey
tiles
Number of white
tiles
Total number of
tiles
1 6 0 6
2 10 2 12
3 14 6 20
4
(a) Complete the table in Figure 4.
(b) What is the total area for figure 7?
Answer: __________________
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 19
(c) How many white tiles are there in a figure which has 58 grey tiles?
Answer: __________________
(d) Which figure would have 552 grey and white tiles?
Answer: __________________
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 20
14. The pattern shown below is made up of rectangles, grey circles and white circles.
Figure 1 Figure 2 Figure 3 Figure 4
The table below shows the number of rectangles, grey circles and white circles for
each figure.
Figure Number Number of
Rectangles
Number of Grey
circles
Number of white
circles
1 1 3 3
2 2 5 4
3 3 6 6
4 4 8 7
5 5 9 9
… … … …
8
…
13
(a) Complete the table for Figure 8 and Figure 13.
(b) Find the number of white circles in Figure 25.
Answer: ________________
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 21
(c) Find the number of white circles in Figure 43.
Answer: ________________
(d) Find the figure number which has 95 grey circles.
Answer: ________________
(e) Find the number of rectangles when there are 123 grey circles.
Answer: ________________
(f) Find the number of white circles when there are 146 grey circles.
Answer: ________________
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 22
15. Eileen used beads to form figures that follow a pattern.
The first four figures are shown below.
Figure 1 Figure 2 Figure 3 Figure 4
The table below shows the number of beads used for each figure.
(a) Complete the table for Figure 5 and Figure 6.
(b) How many squares will Eileen form in Figure 19?
(c) How many beads were used to form Figure 28?
(d) How many beads were used to form Figure 75?
Answer: (b) __________
(c) __________
(d) __________
Figure Number of squares
formed
Number of beads
1 2 13
2 3 18
3 4 21
4 5 26
5
6
MATHSCLINIX (of KIWI Learning Centre) P6 Number Pattern Page 23
16. Cai Yun followed a pattern to form some figures using sticks. The first four figures
are shown below.
(a) How many sticks did she use for Figure 12?
(b) How many sticks did she use for Figure 23?
(c) Cai Yun used 196 sticks to form a figure. Which figure number did she form?
(d) Cai Yun used 290 sticks to form a figure. Which figure number did she form?
Answer: (a) _______________
(b) _______________
(c) _______________
(d) _______________
