SAMPLE - mightyminds.com.aumightyminds.com.au/assets/Uploads/term-3-resources/year-8/27052…107 55...

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Colour numbers in this sequence RED: 448, 224 ,112, ___ ,___ ,___ ,___

Colour numbers in this sequence YELLOW: 8, 15, 22, ___ ,___ ,___ ,___ ,___

Colour numbers in this sequence BLUE: 107, 96, 85, ___ ,___ ,___ ,___ ,___ ,___

Colour numbers in this sequence BLACK: 1, 3, 9, ___ ,___ ,_____ ,_____

Colour numbers in this sequence GREEN: 55, 64, 73, ___ ,___ ,____ ,____ ,____ ,____ ,____ ,____ ,____ ,____

Xiang-Wen Pan’s bad luck will occur in the Year of the _________

52 19 41 30 96 52 30 107 96 74 52 107 30 74 41 52

96 30 52 63 85 19 96 85 30 163 91 73 64 163 30 107

107 55 73 91 109 43 163 74 52 64 22 127 100 118 96 74

52 64 136 36 136 145 73 63 19 127 73 19 36 109 52 30

63 50 100 91 19 50 100 96 74 8 91 107 73 118 74 96

96 55 145 73 41 91 109 30 96 100 145 96 91 50 19 63

63 243 109 729 41 136 50 52 63 118 36 41 163 73 30 74

52 100 82 127 96 82 163 63 19 82 73 52 43 127 96 52

96 74 56 96 74 36 145 136 163 50 109 30 118 100 30 41

19 14 112 7 85 91 73 43 91 73 163 96 100 43 63 19

19 56 52 448 52 63 52 96 107 52 74 63 64 136 73 15

74 41 19 30 96 74 19 41 19 30 96 52 29 82 163 91

The Chinese Zodiac is a 12-year cycle where each year is assigned a different

animal. Xiang-Wen Pan is doing very well in the tea trade but is very upset when a fortune

teller predicts that a year of heavy storms and government taxes will render him bankrupt.

Complete each of the number sequences below, then colour in the grid below according

to the following instructions to reveal in which year of the zodiac Mr Pan thinks his

business will suffer. Q1

SAMPLE

During the 19th Century, the British Empire and China engaged in trading of tea,

porcelain and silk. Xiang-Wen Pan, who is a tea merchant in 1826, gets a very good price

for his quality tea when he trades with Captain Marsh, a British trader. They must organise

their meetings in secret, for fear of their valuable cargo being intercepted and stolen, so

they create a code to send messages to each other. Height = 1.1cm

A: 5, 10, 15, 20, 25, __

B: 6, 12, 24, __

C: 62, 54, 46, __

D: 464, 232, 116, 58, __

E: 9, 26, 43, 60, __

G: 1, 8, 64, __

H: 128, 102, 76, __

I: 12, 36, 108, ___

M: 5500, 1100, 220, __

N: 7, 21, 63, ___

O: 435, 374, 313, 252, ___

P: 71, 74, 77, 80, __

R: 26, 111, 196, ___

S: 23328, 3888, 648, 108, __

T: 7, 28, 112, ___

U: 9, 18, 36, 72, ___

W: 2058, 294, 42, __

Y: 856, 733, 610, 487, ___

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

__ __ __ __ __ __ __ __ __ __ __ __

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ .

__ __ __ __ __ __ , __ __ __ __ __ __ __

__ __ __ __ __ !

44 77 77 448 30 448 38 30 189 448 191 189

38 324 448 364 44 191 189 29 30 364 189 324 512 50 448

48 77 6 30 281 77 83 324 281 30 448 77 18

30 48 191 144 448

In the code at the bottom of the page, each number represents a letter. Decipher the code

by completing each number pattern below to reveal Mr Pan’s message to Captain Marsh.

The first pattern has been completed for you. Q1

SAMPLE

1 2 3 4 Bricks used in 5th

arrangement

Lee

Ch

en

Hu

ang

Tsan

g W

on

g D

ang

The Great Wall of China, still standing today, was constructed in the 5th Century

BC, then reinforced and rebuilt many times up until the 16th Century AD. Xiang-Wen

Pan’s great-great-grandfather, Lee Pan and his friends, helped rebuild some of the Great

Wall during the Ming Dynasty along China’s northern border in order to protect the

country from invasion by outside tribes. Whilst previous workers had used packed earth

as building material, Lee Pan’s generation used bricks to make the wall stronger. Height = 1.1cm

Each man adds bricks to the wall according to a pattern. By looking at the brickwork of each

man, determine the pattern and draw the 4th arrangement. Using your knowledge of

number sequences, determine how many bricks each man will use in the fifth arrangement.

Q1

SAMPLE

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SAMPLE

Firstly, thank you for your support of Mighty Minds and our resources. We endeavour to create high-

quality resources that are both educational and engaging, and results have shown that this approach

works.

To assist you in using this resource, we have compiled some brief tips and reminders below.

About this resource

This Mighty Minds ‘Fundamentals’ Lesson focusses on one subtopic from the NAPLAN Tests and

presents this skill through a theme from the Australian Curriculum (History, Science or Geography).

This lesson is also targeted at a certain skill level, to ensure that your students are completing work

that is suited to them.

How to use this resource

Our ‘Fundamentals’ Lessons are split into two main sections, each of which contain different types of

resources.

The student workbook contains

• The main title page; and

• The blank student worksheets for students to complete.

The teacher resources section contains

• This set of instructions;

• The Teacher’s Guide, which offers information that may be needed to teach the lesson;

• The Item Description, which gives a brief overview of the lesson and its aims, as well as extension

ideas;

• The student answer sheets, which show model responses on the student worksheets to ensure

that answers to the questions are clear;

• The teacher’s answer sheets, which provide a more detailed explanation of the model responses

or answers; and

• Finally, the ‘end of lesson’ marker.

We suggest that you print the student workbook (the first set of pages) for the students. If students

are completing this lesson for homework, you may also like to provide them with the student answer

pages.

Feedback and contacting us

We love feedback. Our policy is that if you email us with suggested changes to any lesson, we will

complete those changes and send you the revised lesson – free of charge.

Just send your feedback to [email protected] and we’ll get back to you as soon as we

can.

SAMPLE

mailto:[email protected]

Number Patterns Number patterns involve a sequence of numbers, in either ascending or descending order, where

each number follows the same rule. Students will often be asked to identify the next number in a

sequence, which involves them first working out the rule that underlies the sequence.

Addition and Subtraction Sequences These are the most simple type of sequence, where each number in the sequence is calculated by

adding or subtracting a value from the previous number. When encountering a number sequence, the

first step should always be to check the difference between each number. If the difference is the

same between each number, then the rule is either addition or subtraction. For example:

3, 10, 17, 24, 31

This pattern is ascending and each number is calculated by adding 7 to the previous number in the

sequence. The next number in the sequence is 38, as 31 + 7 = 38. Another example:

85, 71, 57, 43

This pattern is descending and each number is calculated by subtracting 14 from the previous

number in the sequence. The next number in the sequence is 29, as 43 – 14 = 29.

Multiplication and Division Sequences These sequences are slightly more difficult to identify, as each number is calculated by multiplying or

dividing the previous number in the sequence by a value. For example:

2, 6, 18, 54

This pattern is ascending and each number is calculated by multiplying the previous number by 3.

The next number in the sequence is 162, as 54 x 3 = 162.

112, 56, 28, 14

This pattern is descending and each number is calculated by dividing the previous number by 2.

The next number in the sequence is 7, as 14 ÷ 2 = 7.

Special Sequences These sequences are often encountered by students, but do not abide by addition, subtraction,

multiplication or subtraction rules, thus it is important to familiarise students with them.

Square Numbers

1, 4, 9, 16, 25, 36, 49, 64

Numbers in this sequence are calculated by squaring each consecutive integer. The numbers in this

series are calculated thus: 12 (1x1) = 1, 22 (2x2) = 4, 32 (3x3) = 9...

This teaching guide is continued on the next page...

SAMPLE

Cube Numbers

1, 8, 27, 64, 125, 216, 343, 512

Numbers in this sequence are calculated by cubing each consecutive integer starting with 1. The

numbers in this series are calculated thus: 13 (1x1x1) = 1, 23 (2x2x2) = 8, 33 (3x3x3) = 27…

...This teaching guide is continued from the previous page.

Complex Sequences Complex sequences involve a rule that requires two or more steps in order to calculate a number in

the sequence from the previous. For example:

3, 5, 9, 17, 33

Each number in this sequence is calculated by multiplying the previous number by 2 then subtracting

1. Complex sequences are often very difficult to determine. A good strategy for working out a

complex sequence is to list the ways in which the second number can be calculated from the first

number, then seeing if any of these methods work to calculate the third number. For example, in the

sequence above, 5 can be calculated from 3 by:

• 3 + 2 = 5

• 3 + 3 – 1= 5

• 3 / 3 + 5 = 5

• 32 – 4 = 5

• 3 x 2 – 1 = 5

When applying these rules to the third and fourth numbers in the sequence, only the last rule

produces the right third and fourth numbers in the sequence.

Diagram Patterns A diagrammatic pattern is one where, in a series of diagrams, each diagram changes (often by

increasing or decreasing its complexity) by a certain rule. Consider the following sequence of

diagrams:

In this sequence, each diagram is increasing its size by increasing the length of each side by one

square. Additionally, this diagram increases the number of boxes according to a square number

numerical pattern (see previous page). A strategy for solving diagrammatic patterns is to use a

highlighter or coloured pencil to colour the part of the diagram that has changed from the previous

picture in the series. Additionally, often diagrammatic patterns are related to numerical patterns, so

counting the diagram’s constituents (in this cases the number of small squares), can help determine

the number required for the next diagram in the series.

SAMPLE

Please note: any activity that is not completed during class time may be set for homework or

undertaken at a later date.

‘Pan’s Plight’, ‘Pan’s Patterns’ and ‘Brick Barricades’

• Activity Description: • This lesson contains three worksheets of increasing complexity, which require students to

use their knowledge of numerical and diagrammatic patterns to complete sequences and

solve problems. The first and second worksheets require students to continue simple

addition, subtraction, multiplication or division number sequences by determining the

pattern rule, then applying it. The completed number sequences are needed to solve a

code in ‘Pan’s Patterns’, then uncover a hidden picture in ‘Pan’s Plight’. In the final

worksheet, students are required to analyse a set of diagrams, which increase in

complexity according to a rule. Students need to determine the rule, then apply it to

complete the sequence.

• Purpose of Activity: • Students will reinforce their ability to determine and continue numerical and

diagrammatic patterns.

• KLAs: • Mathematics, History

• CCEs: • Recognising letters, words and other symbols (α1)

• Interpreting the meaning of pictures/ illustrations (α5)

• Identifying shapes in two and three dimensions (α51)

• Visualising (β50)

• Calculating with or without calculators (Ф16)

• Applying a progression of steps to achieve the required answer (Ф37)

• Sketching/ drawing (π60)

• Extrapolating (θ35)

• Perceiving patterns (β49)

• Suggested Time Allocation: • This lesson is designed to take approximately an hour to complete – 20 minutes per

activity.

This Item Description is continued on the next page...

Item Description

SAMPLE

…This Item Description is continued from the previous page.

‘Pan’s Plight’, ‘Pan’s Patterns’ and ‘Brick Barricades’

• Teaching Notes: • These lessons have been designed so that all students will be busy for the complete hour.

However, as all students work at different rates, some will take longer than others.

Furthermore, these activities contain a fair amount of colouring, which some students tend

to spend too much time on. If students are spending too long on the drawing and colouring,

ask them to move on to the next part of the activity.

• Before commencing the worksheets, go through strategies for solving numerical sequences

and examples, such as those discussed on the Teacher’s Guide accompanying this item.

• As an additional activity, have students create their own patterns and write them on the

board to see if their peers can work out the rule.

• Once students have finished each activity, go through the answers as a class. Ask students

to volunteer their own answers and discuss the model answers and how to reach them.

Item Description – continued

SAMPLE

56 28 14 7 Colour numbers in this sequence RED:

448, 224 ,112, ___ ,___ ,___ ,___

Colour numbers in this sequence YELLOW:

8, 15, 22, ___ ,___ ,___ ,___ ,___

Colour numbers in this sequence BLUE:

107, 96, 85, ___ ,___ ,___ ,___ ,___ ,___

Colour numbers in this sequence BLACK:

1, 3, 9, ___ ,___ ,_____ ,_____

Colour numbers in this sequence GREEN:

55, 64, 73, ___ ,___ ,____ ,____ ,____ ,____ ,____ ,____ ,____ ,____

Xiang-Wen Pan’s bad luck will occur in the Year of the _________

52 19 41 30 96 52 30 107 96 74 52 107 30 74 41 52

96 30 52 63 85 19 96 85 30 163 91 73 64 163 30 107

107 55 73 91 109 43 163 74 52 64 22 127 100 118 96 74

52 64 136 36 136 145 73 63 19 127 73 19 36 109 52 30

63 50 100 91 19 50 100 96 74 8 91 107 73 118 74 96

96 55 145 73 41 91 109 30 96 100 145 96 91 50 19 63

63 243 109 729 41 136 50 52 63 118 36 41 163 73 30 74

52 100 82 127 96 82 163 63 19 82 73 52 43 127 96 52

96 74 56 96 74 36 145 136 163 50 109 30 118 100 30 41

19 14 112 7 85 91 73 43 91 73 163 96 100 43 63 19

19 56 52 448 52 63 52 96 107 52 74 63 64 136 73 15

74 41 19 30 96 74 19 41 19 30 96 52 29 82 163 91

The Chinese Zodiac is a 12-year cycle where each year is assigned a different

animal. Xiang-Wen Pan is doing very well in the tea trade but is very upset when a fortune

teller predicts that a year of heavy storms and government taxes will render him bankrupt.

Snake

29 36 43 50 57

74 63 52 41 30 19

27 81 243 729

82 91 100 109 118 127 136 145 154 163

Complete each of the number sequences below, then colour in the grid below according

to the following instructions to reveal in which year of the zodiac Mr Pan thinks his

business will suffer.

Q1

SAMPLE

This answer guide is continued on the next page...

Pan’s Plight

Question One:

Students are required to complete each number sequence by determining the rule that the first three

numbers obey, then using this rule to calculate the subsequent numbers in the sequence. Once the

sequences have been correctly completed, students are required to colour the grid. Each square of

the grid contains a number, which corresponds to a number in one of the sequences. Students are

required to colour each box of the grid the specified colour for each sequence (as instructed). The

coloured grid will reveal a picture of a snake, which answers the question of which year of the zodiac

Mr Pan thinks he will lose his fortune.

The completed sequences are as follows:

a) 448, 224, 112, 56, 28, 14, 7

The difference between each number is not the same in this sequence, therefore the sequence

does not follow an addition or subtraction rule. The sequence is decreasing, therefore it is likely to

be a division sequence. 448 / 2 = 224 and 224 / 2 = 112, therefore this sequence follows the rule:

divide by 2. The next four numbers are calculated by dividing the previous number by two as

follows: 112 / 2 = 56, 56 / 2 = 28, 28 / 2 = 14, 14 / 2 = 7. The numbers in this sequence are to be

coloured in red.

b) 8, 15, 22, 29, 36, 43, 50, 57

The difference between each number is 7 and the sequence in increasing, therefore the

sequence follows the rule: add 7. The next five numbers in the series are calculated by adding 7

to the previous as follows: 22 + 7 = 29, 29 + 7 = 36, 36 + 7 = 43, 43 + 7 = 50, 50 + 7 = 57. The

numbers in this sequence are to be coloured in yellow.

c) 107, 96, 85, 74, 63, 52, 41, 30, 19

The difference between each number is 11 and the sequence is decreasing, therefore the

sequence follows the rule: subtract 11. The next six numbers in the series are calculated as

follows: 85 – 11 = 74, 74 – 11 = 63, 63 – 11 = 52, 52 = 11 = 41, 41 – 11 = 30, 30 – 11 = 19. The

numbers in this sequence are to coloured in blue.

d) 1, 3, 9, 27, 81, 243, 729

The difference between each number is not the same in this sequence, therefore the sequence

does not follow an addition or subtraction rule. The sequence is increasing, therefore it is likely to

be a multiplication sequence. 1 x 3 = 3 and 3 x 3 = 9, therefore the sequence follows the rule:

multiply by 3. The next four numbers are calculated by multiplying the previous by 3 as follows: 9

x 3 = 27, 27 x 3 = 81, 81 x 3 = 243, 243 x 3 = 729. The numbers in this sequence are to be

coloured in black.

e) 55, 64, 73, 82, 91, 100, 109, 118, 127, 136, 145, 154, 163

The difference between each number in the sequence is 9 and the sequence is increasing.

Therefore the sequences follows the rule: add 9. The next ten numbers are calculated by adding

9 to the previous as follows. 73 + 9 = 82, 82 + 9 = 91, 91 + 9 = 100, 100+ 9 = 109, 109 + 9 = 118,

118 + 9 = 127, 127 + 9 = 136, 136 + 9 = 145, 145 + 9 = 154, 154 + 9 = 163.

SAMPLE

...This answer guide is continued from the previous page.

52 19 41 30 96 52 30 107 96 74 52 107 30 74 41 52

96 30 52 63 85 19 96 85 30 163 91 73 64 163 30 107

107 55 73 91 109 43 163 74 52 64 22 127 100 118 96 74

52 64 136 36 136 145 73 63 19 127 73 19 36 109 52 30

63 50 100 91 19 50 100 96 74 8 91 107 73 118 74 96

96 55 145 73 41 91 109 30 96 100 145 96 91 50 19 63

63 243 109 729 41 136 50 52 63 118 36 41 163 73 30 74

52 100 82 127 96 82 163 63 19 82 73 52 43 127 96 52

96 74 56 96 74 36 145 136 163 50 109 30 118 100 30 41

19 14 112 7 85 91 73 43 91 73 163 96 100 43 63 19

19 56 52 448 52 63 52 96 107 52 74 63 64 136 73 15

74 41 19 30 96 74 19 41 19 30 96 52 29 82 163 91

When each square in the grid is coloured correctly according to the instructions provided, the

following picture is revealed. SAMPLE

__ __ __ __ __ __ __ __ __ __ __ __

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ .

__ __ __ __ __ __ , __ __ __ __ __ __ __

__ __ __ __ __ !

44 77 77 448 30 448 38 30 189 448 191 189

38 324 448 364 44 191 189 29 30 364 189 324 512 50 448

48 77 6 30 281 77 83 324 281 30 448 77 18

30 48 191 144 448

Multiply by 2

Subtract 8

Divide by 2

Add 17

Multiple by 8

Subtract 26

Multiply by 3

Divide by 5

Multiply by 3

Subtract 61

Add 3

Add 85

Divide by 6

Multiply by 4

Multiply by 2

Divide by 7

Subtract 123

During the 19th Century, the British Empire and China engaged in trading of tea,

porcelain and silk. Xiang-Wen Pan, who is a tea merchant in 1826, gets a very good price

for his quality tea when he trades with Captain Marsh, a British trader. They must organise

their meetings in secret, for fear of their valuable cargo being intercepted and stolen, so

they create a code to send messages to each other. Height = 1.1cm

A: 5, 10, 15, 20, 25, 30

B: 6, 12, 24, 48

C: 62, 54, 46, 38

D: 464, 232, 116, 58, 29

E: 9, 26, 43, 60, 77

G: 1, 8, 64, 512

H: 128, 102, 76, 50

I: 12, 36, 108, 324

M: 5500, 1100, 220, 44

N: 7, 21, 63, 189

O: 435, 374, 313, 252, 191

P: 71, 74, 77, 80, 83

R: 26, 111, 196, 281

S: 23328, 3888, 648, 108, 18

T: 7, 28, 112, 448

U: 9, 18, 36, 72, 144

W: 2058, 294, 42, 6

Y: 856, 733, 610, 487, 364

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

The Rule is _____________________

????????

M E E T A T C A N T O N

C I T Y M O N D A Y N I G H T .

B E W A R E , P I R A T E S

A B O U T . .

Add 5

In the code at the bottom of the page, each number represents a letter. Decipher the code

by completing each number pattern below to reveal Mr Pan’s message to Captain Marsh.

The first pattern has been completed for you. Q1

SAMPLE

Pan’s Patterns

Question One:

Students are required to determine the rule that each number pattern is obeying, then use the rule to

calculate the next number in the sequence. Once the number is determined, students are required to

replace the number with the letter preceding that sequence in order to decipher a hidden message.

A: 30. The difference between each number is five and the sequencing is increasing. Therefore, the

rule is Add 5. By adding 5 to the last number in the series, 25, the next number is calculated as 30.

Therefore, 30 represents ‘A’ in the code.

B: 48. The difference between each number is not the same in this sequence, therefore the sequence

does not follow an addition or subtraction rule. The sequence is increasing, therefore it is likely to be

a multiplication sequence. 6 x 2 =12 and 12 x 2 =24, therefore the rule is multiply by 2. By

multiplying 24 by 2, the next number is calculated as 48. Therefore, 48 represents ‘B’ in the code.

C: 38. The difference between each number is 8 and the sequence is descending. Therefore, the rule

is Subtract 8. By subtracting 8 from the last number in the series, 46, the next number is calculated

as 38. Therefore, 38 represents ‘C’ in the code.

D: 29. The difference between each number is not the same in this sequence, therefore the sequence

does not follow an addition or subtraction rule. The sequence is decreasing, therefore it is likely to be

a division sequence. 464 / 2 = 232, 232 / 2 = 116 and 116 / 2 = 58, therefore the rule is divide by 2.

By dividing 58 by 2, the next number is calculated as 29. Therefore, 29 represents ‘D’ in the code.

E: 77. The difference between each number is 17 and the sequence is increasing. Therefore, the rule

is Add 17. By adding 17 to the last number in the series, 60, the next number is calculated as 77.

Therefore, 77 represents ‘E’ in the code.

G. 512. The difference between each number is not the same in this sequence, therefore the

sequence does not follow an addition or subtraction rule. The sequence is increasing, therefore it is

likely to be a multiplication sequence. 1 x 8 = 8 and 8 x 8 = 64, therefore the rule is multiply by 8. By

multiplying 64 by 8, the next number is calculated as 512. Therefore, 512 represents ‘G’ in the code.

H: 50. The difference between each number is 26 and the sequence is descending. Therefore, the

rule is subtract 26. By subtracting 26 from the last number in the sequence, 76, the next number is

calculated as 50. Therefore, 50 represents ‘H’ in the code.

I: 324. The difference between each number is not the same in this sequence, therefore the


likely to be a multiplication sequence. 12 x 3 = 36 and 36 x 3 = 108, therefore, the rule is multiply by

3. By multiplying the last number, 108, by 3, the next number in the sequence is calculated as 324.

Therefore, 324 represents ‘I’ in the code.


SAMPLE



M: 44. The difference between each number is not the same in this sequence, therefore the

sequence does not follow an addition or subtraction rule. The sequence is decreasing, therefore it is

likely to be a division sequence. 5500 / 5 = 1100 and 1100 / 5 = 220, therefore the rule is divide by 5.

By dividing the last number, 220, by 5, the next number in the sequence is calculated as 44.

Therefore, 44 represents ‘M’ in the code.

N: 189. The difference between each number is not the same in this sequence, therefore the


likely to be a multiplication sequence. 7 x 3 = 21 and 21 x 3 = 63, therefore the rule is multiply by 3.

By multiplying the last number in the series, 63, by 3, the next number is calculated as 189.

Therefore, 189 represents ‘N’ in the code.

O: 191. The difference between each number is 61 and the sequence is descending. Therefore, the

rule is Subtract 61. By subtracting 61 from the last number in the series, 252, the next number is

calculated as 191. Therefore, 191 represents ‘O’ in the code.

P: 83. The difference between each number is three and the sequence is increasing. Therefore, the

rule is Add 3. By adding 3 to the last number in the series, 80, the next number is calculated as 83.

Therefore, 83 represents ‘P’ in the code.

R: 281. The difference between each number is 85 and the sequence is increasing. Therefore, the

rule is Add 85. By adding 85 to the last number in the series, 196, the next number is calculated as

281. Therefore, 281 represents ‘R’ in the code.

S: 18. The difference between each number is not the same in this sequence, therefore the sequence


a division sequence. 23328 / 6 = 3888, 3888 / 6 = 648 and 648 / 6 = 108, therefore the rule is divide

by 6. By dividing the last number, 108, by 6, the next number in the sequence is calculated as 18.

Therefore, 18 represents ‘S’ in the code.

T: 448. The difference between each number is not the same in this sequence, therefore the


likely to be a multiplication sequence. 7 x 4 = 28 and 28 x 4 = 112, therefore the rule is multiply by 4.

By multiplying the last number in the series, 112, by 4, the next number is calculated as 448.

Therefore, 448 represents ‘N’ in the code.

U: 144. The difference between each number is not the same in this sequence, therefore the


likely to be a multiplication sequence. 9 x 2 = 18, 18 x 2 = 36 and 36 x 2 = 72, therefore the rule is

multiply by 2. By multiplying the last number in the series, 72, by 2, the next number is calculated as

144. Therefore, 144 represents ‘U’ in the code.

W: 6. The difference between each number is not the same in this sequence, therefore the sequence


a division sequence. 2058 / 7 = 294 and 294 / 7 = 42, therefore the rule is divide by 7. By dividing the

last number, 42, by 7, the next number in the sequence is calculated as 6. Therefore, 6 represents ‘M’

in the code.

SAMPLE


Y: 364. The difference between each number is 123 and the sequence is descending. Therefore, the

rule is Subtract 123. By subtracting 123 from the last number in the series, 487, the next number is

calculated as 364. Therefore, 364 represents ‘Y’ in the code.

By substituting in each letter for its corresponding number, the code is deciphered as:

__ __ __ __ __ __ __ __ __ __ __ __

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ .

__ __ __ __ __ __ , __ __ __ __ __ __ __

__ __ __ __ __ !

44 77 77 448 30 448 38 30 189 448 191 189

38 324 448 364 44 191 189 29 30 364 189 324 512 50 448

48 77 6 30 281 77 83 324 281 30 448 77 18

30 48 191 144 448

M E E T A T C A N T O N

C I T Y M O N D A Y N I G H T .

B E W A R E , P I R A T E S

A B O U T . .

SAMPLE

1 2 3 4 Bricks used in 5th

arrangement

Lee

21

Ch

en

25

Hu

ang

25

Tsan

g

25

Wo

ng

25

Dan

g

21

The Great Wall of China, still standing today, was constructed in the 5th Century

BC, then reinforced and rebuilt many times up until the 16th Century AD. Xiang-Wen

Pan’s great-great-grandfather, Lee Pan and his friends, helped rebuild some of the Great

Wall during the Ming Dynasty along China’s northern border in order to protect the

country from invasion by outside tribes. Whilst previous workers had used packed earth

as building material, Lee Pan’s generation used bricks to make the wall stronger. Height = 1.1cm

Each man adds bricks to the wall according to a pattern. By looking at the brickwork of each

man, determine the pattern and draw the 4th arrangement. Using your knowledge of

number sequences, determine how many bricks each man will use in the fifth arrangement.

Q1

SAMPLE

Brick Barricades

Question One:

Students were required to analyse a set of diagrams of ‘bricks’ whereby each subsequent

arrangement increases in size. Then students determined and drew the next diagram by following the

same pattern. Additionally, students were required to calculate the number of bricks used in the fifth

diagram in the series by applying their knowledge of number sequences.

The fourth diagram for each sequence is as follows:

Lee Chen Huang

Tsang Wong Dang

The number of bricks in the fifth arrangement are calculated by first counting the number of bricks in

the first four diagrams and organising a number sequence.

Lee: 3, 6, 10, 15, 21

The difference between each number is increasing, i.e. the difference between 3 and 6 is 3, the

difference between 6 and 10 is 4 and the difference between 10 and 15 is 5. Thus, to complete the

sequence, the next number is calculated by adding 6 to the previous, 15; therefore, the fifth number in

the sequence is 21.

Chen: 1, 4, 9, 16, 25

This is a special sequence of square numbers. Each number in the series is calculated by squaring

each consecutive integer i.e. 12 (1x1) = 1, 22 (2x2) = 4, 32 (3x3) = 9, 42 (4x4) = 16. Therefore, the fifth

number in the series is calculated by squaring 5: 52 (5x5) = 25.

Huang, Tsang and Wong’s sequence of bricks follow the same numerical pattern as that of Lee’s.

Dang’s sequence of bricks follows the same numerical pattern as that of Chen’s.

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