Simple Linear Patterns

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# Simple Linear Patterns - PowerPoint PPT Presentation

Simple Linear Patterns using diagrams and tables. MTH 2-13a & MTH 3-13a. Square Numbers. Triangular Numbers. Simple Linear Patterns. www.mathsrevision.com. Harder Linear Patterns. Flower Bed Investigation. 3cm. 5cm. 4cm. 2cm. MTH 2-13a & MTH 3-13a. Starter Questions.

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Simple Linear Patterns using diagrams and tables

MTH 2-13a

& MTH 3-13a

Square Numbers

Triangular Numbers

Simple Linear Patterns

www.mathsrevision.com

Harder Linear Patterns

Flower Bed Investigation

3cm

5cm

4cm

2cm

MTH 2-13a

& MTH 3-13a

### Starter Questions

Q1. Calculate Area and perimeter

Q2. 30% of 200

Q3.

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Q4. If a = 1 , b = 2 and c = 4

Find

MTH 2-13a

& MTH 3-13a

### Simple Linear Patterns using diagrams and tables

Learning Intention

Success Criteria

• Construct tables.
• We are learning how tables can help us to come up with formulae for Simple Linear Patterns.
• Find the difference value in patterns.

www.mathsrevision.com

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

1 Table

2 Tables

3 Tables

Task : Find a formula connecting

the number of tables and the number of surfers.

Simple Linear Patterns using diagrams and tables

MTH 2-13a

& MTH 3-13a

In an internet café 3surfers can sit round a triangular table.

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2

4

5

1

3

6

3

9

1 Table

2 Tables

3 Tables

3

3

3

3

Simple Linear Patterns using diagrams and tables

MTH 2-13a

& MTH 3-13a

Fill empty boxes

Number of Tables

Step 1 :

Number of Surfers

12

15

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Step 2 : Find difference

What is the formula

Same difference

linear pattern

Number of Tables

Number of Surfers

12

15

2

4

5

3

3

6

9

1

3

3

3

3

HINT : Let the number of surfers be the letter S

and the number of tables be the letter T

Step 3 :

Can you write down formula connecting

the number of surfers and the number of tables.

Simple Linear Patterns using diagrams and tables

MTH 2-13a

& MTH 3-13a

www.mathsrevision.com

S = 3 x T

S = 3T

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

www.mathsrevision.com

2. Find the difference

3. Use the difference to write

down the formula

Simple Linear Patterns using diagrams and tables

MTH 2-13a

& MTH 3-13a

Now try Ex 3

Ch11 (Page 135)

www.mathsrevision.com

6cm

10cm

7cm

3cm

Complicated Linear Patterns using diagrams and tables

MTH 2-13a

& MTH 3-13a

Q1. Calculate Area and perimeter

Q2. 32% of 200

www.mathsrevision.com

Q3.

MTH 2-13a

& MTH 3-13a

### Complicated Linear Patterns using diagrams and tables

Learning Intention

Success Criteria

• Construct tables.
• We are learning how tables can help us come up with formulae for complicated Linear Patterns.
• Find the difference value in patterns.

www.mathsrevision.com

• Calculate correction factor

4. Use the difference value

to write down a formula

connecting the table values.

3 Tables

1 Table

2 Tables

Task : Find a formula connecting

the number of tables and the number of surfers.

MTH 2-13a

& MTH 3-13a

A internet café decides to change it’s table design to.

### Complicated Linear Patterns using diagrams and tables

www.mathsrevision.com

3 Tables

1 Table

2 Tables

2

4

5

1

3

6

4

8

2

2

2

2

MTH 2-13a

& MTH 3-13a

### Complicated Linear Patterns using diagrams and tables

Fill empty boxes

Number of Tables

Step 1 :

Number of Surfers

10

12

www.mathsrevision.com

Step 2 : Find difference

What is the formula

Same difference

linear pattern

Number of Tables

Number of Surfers

10

12

6

4

8

2

4

5

1

3

2

2

2

2

S = 2 x T

Part of the Formula

Can you write down formula connecting

the number of surfers and the number of tables.

MTH 2-13a

& MTH 3-13a

### Complicated Linear Patterns using diagrams and tables

www.mathsrevision.com

Find a number

so formula works

Step 3 :

Step 4 :

S = 2T + 2

MTH 2-13a

& MTH 3-13a

### Complicated Linear Patterns using diagrams and tables

Key-Points

Write down the 4 main steps

1. Make a table

www.mathsrevision.com

2. Find the difference

3. Write down part of formula

4. Find the correction factor and

then write down the full formula

Complicated Linear Patterns using diagrams and tables

MTH 2-13a

& MTH 3-13a

Now try Ex 4

Ch11 (Page 137)

www.mathsrevision.com

114o

MTH 2-13a

& MTH 3-13a

### Starter Questions

6 cm

10 cm

www.mathsrevision.com

Created by Mr. Lafferty @www.mathsrevision.com

Square Numbers

MTH 2-13a

& MTH 3-13a

Learning Intention

Success Criteria

• To understand what a square number is.
• We are learning what a square number is.
• Calculate the first 10 square numbers.

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Created by Mr. Lafferty @www.mathsrevision.com

Write down the next square number

MTH 2-13a

& MTH 3-13a

### Square Numbers

1 4 9

16

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

Created by Mr.Lafferty Math Dept

Square Numbers

MTH 2-13a

& MTH 3-13a

Now try Ex1

Ch11 (page 131)

www.mathsrevision.com

Created by Mr. Lafferty @www.mathsrevision.com

122o

MTH 2-13a

& MTH 3-13a

### Starter Questions

8 cm

6 cm

www.mathsrevision.com

Created by Mr. Lafferty @www.mathsrevision.com

Triangular Numbers

MTH 2-13a

& MTH 3-13a

Learning Intention

Success Criteria

• To understand what a
• triangular number is.
• We are learning what a triangular number is.
• Calculate the first 10 triangular numbers.

www.mathsrevision.com

Created by Mr. Lafferty @www.mathsrevision.com

Which numbers are both square and triangular number

Write down the next square number

MTH 2-13a

& MTH 3-13a

### Triangular and square Numbers

15

1 3 6 10

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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

Created by Mr.Lafferty Math Dept

Special Patterns

MTH 2-13a

& MTH 3-13a

Now try

Ch11 (page 133)

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Created by Mr. Lafferty @www.mathsrevision.com

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

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

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

Flower Bed Investigation

MTH

3-13a

How many slabs are required to surround the flower bed?

Now draw three flower beds surrounded by slabs.

16 slabs

3 flower bed

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Flower Bed Investigation

MTH

3-13a

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.

Flower Bed Investigation

MTH

3-13a

Number Flower Beds (f)

1

2

3

4

Number of Slabs (s)

6

11

16

21

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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

Flower Bed Investigation

MTH

3-13a

What is the maximum number of flower beds

you could surround if you had 83 slabs

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16

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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Vertical Flower Bed Investigation

MTH

3-13a

Number Flower Beds (f)

1

2

3

4

Number of Slabs (s)

6

10

14

18

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s = 4f + 2