Simple Linear Patterns

1
Simple Linear Patterns using diagrams and tables
MTH 2-13a MTH 3-13a
Square Numbers
Triangular Numbers
Simple Linear Patterns
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Harder Linear Patterns
Flower Bed Investigation
2
Starter Questions
MTH 2-13a MTH 3-13a
Q1. Calculate Area and perimeter
Q2. 30 of 200
Q3.
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Q4. If a 1 , b 2 and c 4 Find
3
Simple Linear Patterns using diagrams and tables
MTH 2-13a MTH 3-13a
Learning Intention
Success Criteria

1. Construct tables.

1. We are learning how tables can help us to come up
   with formulae for Simple Linear Patterns.

1. Find the difference value in patterns.

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• Using the difference value
• to write down a formula.

4
Simple Linear Patterns using diagrams and tables
MTH 2-13a MTH 3-13a
In an internet café 3 surfers can sit round a
triangular table.
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5
Simple Linear Patterns using diagrams and tables
MTH 2-13a MTH 3-13a
Fill empty boxes
Number of Tables
Step 1
12
15
Number of Surfers
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Step 2 Find difference
What is the formula
Same difference linear pattern
6
Simple Linear Patterns using diagrams and tables
MTH 2-13a MTH 3-13a
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S 3 x T
S 3T
7
Simple Linear Patterns using diagrams and tables
MTH 2-13a MTH 3-13a
Key-Points
Write down the 3 main steps
1. Make a table
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2. Find the difference
3. Use the difference to write down the formula
8
Simple Linear Patterns using diagrams and tables
MTH 2-13a MTH 3-13a
Now try Ex 3 Ch11 (Page 135)
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9
Complicated Linear Patterns using diagrams and
tables
MTH 2-13a MTH 3-13a
Q1. Calculate Area and perimeter
Q2. 32 of 200
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Q3.
10
Complicated Linear Patterns using diagrams and
tables
MTH 2-13a MTH 3-13a
Learning Intention
Success Criteria

1. Construct tables.

1. We are learning how tables can help us come up
   with formulae for complicated Linear Patterns.

1. Find the difference value in patterns.

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1. Calculate correction factor

4. Use the difference value to write down a
formula connecting the table values.
11
Complicated Linear Patterns using diagrams and
tables
MTH 2-13a MTH 3-13a
A pattern is made up of pentagons.
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Task Find a formula connecting the Pattern
number and the number of sides.
12
Complicated Linear Patterns using diagrams and
tables
MTH 2-13a MTH 3-13a
Fill empty boxes
Pattern Number (P)
Step 1
17
21
Number of Sides ( S)
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Step 2 Find difference
What is the formula
Same difference linear pattern
13
Complicated Linear Patterns using diagrams and
tables
MTH 2-13a MTH 3-13a
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Find a number so formula works
Step 3
Step 4
S 4P 1
Correction factor add on 1
14
Complicated Linear Patterns using diagrams and
tables
MTH 2-13a MTH 3-13a
Key-Points
Write down the 4 main steps
1. Make a table
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2. Find the difference
3. Write down part of formula
4. Find the correction factor and then write
down the full formula
15
Complicated Linear Patterns using diagrams and
tables
MTH 2-13a MTH 3-13a
Now try Ex 4 Ch11 (Page 139)
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16
Starter Questions
MTH 2-13a MTH 3-13a
6 cm
10 cm
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17
Square Numbers
MTH 2-13a MTH 3-13a
Learning Intention
Success Criteria

1. To understand what a square number is.

1. We are learning what a square number is.

1. Calculate the first 10 square numbers.

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18
Square Numbers
Write down the next square number
MTH 2-13a MTH 3-13a
42
12 22 32
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Write down the first 10 square numbers.
1 4 9 16 25 36 49 64 81 100
19
Square Numbers
MTH 2-13a MTH 3-13a
Now try Ex1 Ch11 (page 131)
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20
Starter Questions
MTH 2-13a MTH 3-13a
8 cm
6 cm
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21
Triangular Numbers
MTH 2-13a MTH 3-13a
Learning Intention
Success Criteria

• To understand what a
• triangular number is.

1. We are learning what a triangular number is.

1. Calculate the first 10 triangular numbers.

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22
Triangular and square Numbers
Which numbers are both square and triangular
number
Write down the next triangular number
MTH 2-13a MTH 3-13a
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2 3 4
5
Write down the first 10 triangular numbers.
1 3 6 10 15 21 28 36 45 55
23
Special Patterns
MTH 2-13a MTH 3-13a
Now try Ch11 (page 133)
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24
Flower Bed Investigation
MTH 3-13a
David is designing a flower bed pattern for the
local garden show. He wants to use regular
hexagonal shapes for the bed and slabs.
This is the flower bed shape
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This is a slab shape
25
Draw this design on the isometric dot paper
provided. (Ensure that your paper is portrait)
Flower Bed Investigation
MTH 3-13a
Here is the design that has one flower bed
surrounded by slabs.
How many slabs are required to surround the
flower bed?
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1 flower bed
6 slabs
26
Flower Bed Investigation
MTH 3-13a
Now draw two flower beds surrounded by slabs.
How many slabs are required to surround the
flower bed?
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2 flower bed
11 slabs
27
Flower Bed Investigation
MTH 3-13a
How many slabs are required to surround the
flower bed?
Now draw three flower beds surrounded by slabs.
3 flower bed
16 slabs
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28
Flower Bed Investigation
MTH 3-13a
Task
In your group discuss how best to record these
results and work out a formula to calculate the
number of slabs for given number of flower beds.
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As a group you are required to hand in a single
solution for this task showing all working.
29
Flower Bed Investigation
MTH 3-13a
Number Flower Beds (f)
2
4
1
3
Number of Slabs (s)
11
21
6
16
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s 5f 1
126
How many hexagonal slabs are needed for 25 flower
beds.
If we had 76 available slabs how many flower beds
could we surround
15
30
Flower Bed Investigation
MTH 3-13a
Task
What is the maximum number of flower beds you
could surround if you had 83 slabs
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16
31
Flower Bed Investigation
MTH 3-13a
Homework
Now align the flower beds vertically and
investigate if the formula is still the same?
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32
Vertical Flower Bed Investigation
MTH 3-13a
Number Flower Beds (f)
2
4
1
3
Number of Slabs (s)
10
18
6
14
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s 4f 2