Number patterns

10 questionswork in pencil

name date

G21-A12 marks
Write the missing number in the number pattern below: 7648, 7798, 7948, __________, 8248
answer
G21-A332 marks
A road divider is painted in repeating segments: white 2 m, black 5 m, white 2 m, black 5 m, and so on, beginning and ending with white. If the road divider is 149 m long, how many white segments are there?
```
  [white 2m][ black 5m ][white 2m][ black 5m ][white 2m] ...
  |<----- one repeat = 7 m ----->|

  the whole divider is 149 m
```
answer
G21-A372 marks
Study the pattern of hexagons made from sticks: Pattern 1 is one hexagon (6 sticks), Pattern 2 is two hexagons sharing a side (11 sticks), Pattern 3 is three in a row (16 sticks). In a particular pattern, 206 sticks are used. What is the pattern number?
```
  Pattern 1     Pattern 2       Pattern 3
    / \         / \ / \        / \ / \ / \
   |   |       |   |   |      |   |   |   |
    \ /         \ / \ /        \ / \ / \ /
   6 sticks    11 sticks      16 sticks
```
answer
G21-A402 marks
Bob wrote letters in a repeating pattern: Z E S T Z E S T Z E S T Z E … How many letters ‘Z’ and ‘T’ are there altogether if there is a total of 87 letters in the whole series?
```
  Z  E  S  T   Z  E  S  T   Z  E  S  T   Z  E ...
  |<- one repeat = 4 letters ->|

  87 letters altogether
```
answer
G21-B54 marks
Sally arranges a pattern with sticks and coins. Pattern 1 uses 6 coins and 7 sticks (13 in all), Pattern 2 uses 9 coins and 12 sticks (21 in all), Pattern 3 uses 12 coins and 17 sticks (29 in all). There is a total of 93 coins and sticks in one of the patterns. What is the Pattern Number?
```
  Pattern | coins | sticks | total
  --------+-------+--------+------
     1    |   6   |    7   |  13
     2    |   9   |   12   |  21
     3    |  12   |   17   |  29
     4    |   ?   |    ?   |   ?
```
answer
S23-A132 marks
Study the pattern. What is the missing number in the box? star × star = 49; moon + moon + moon + moon = 100; star × moon = ?
```
   star  ×  star                    =  49
   moon  +  moon  +  moon  +  moon  =  100
   star  ×  moon                    =  ?
```
answer
S23-A202 marks
A length of sticky tape is made up of repeated designs: a 5 cm striped band, then a 3 cm checked band, then a 4 cm grid band, repeating. The sticky tape is 80 cm long. How many checked bands are there altogether?
```
  |  striped  | checked | grid |  striped  | checked | grid | ...
  |<- 5 cm ->|<- 3 cm ->|<-4cm->|
  |<-------- one repeat = 12 cm -------->|

  the whole tape is 80 cm
```
answer
S23-A332 marks
Some circles and triangles are arranged in a repeating pattern: triangle, circle, circle, circle, triangle, circle, circle, circle, triangle, … How many circles are there if there are 122 shapes?
```
  /\  O  O  O   /\  O  O  O   /\  ...
  |<- one repeat = 4 shapes ->|
  (1 triangle and 3 circles)
```
answer
S23-B44 marks
Study the staircase pattern: Figure 1 has 2 squares along the bottom and 1 above the right-hand one (3 squares). Figure 2 has 3 along the bottom, then 2, then 1 (6 squares). Figure 3 has 4, then 3, then 2, then 1 (10 squares). Find the total number of squares needed to form Figure 50.
```
  Figure 1      Figure 2        Figure 3
                                    []
        []          []          [][]
  [][]        [][]          [][][]
              [][][]      [][][][]

    3            6             10   squares
```
answer
S24-B94 marks
Jamie decorated a square classroom of side 6 m 40 cm. She tied balloons in a repeating pattern on a string and hung the string around the classroom once. In every 80 cm of string the pattern holds 4 small balloons (with big balloons between them). How many small balloons did she use to decorate the 4 sides of the classroom?
```
  (BIG) o o (BIG) o o (BIG)
  |<--------- 80 cm --------->|

  o = small balloon · 4 small balloons in every 80 cm
```
answer