Transcript Slide 1

Simple Linear Patterns
using diagrams and tables
MTH 2-13a
& MTH 3-13a
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Square Numbers
Triangular Numbers
Simple Linear Patterns
Harder Linear Patterns
Flower Bed Investigation
Starter Questions
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MTH 2-13a
& MTH 3-13a
Q1.
Calculate Area and perimeter
Q2.
30% of 200
Q3.
(25)  (20)
Q4.
If a = 1 , b = 2 and c = 4
Find
c - ab
2
3cm
5cm
4cm
2cm
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MTH 2-13a
& MTH 3-13a
Simple Linear Patterns
using diagrams and tables
Learning Intention
1. We are learning how tables
can help us to come up
with formulae for Simple
Linear Patterns.
Success Criteria
1. Construct tables.
2. Find the difference value
in patterns.
3. Using the difference value
to write down a formula.
Simple Linear Patterns
using diagrams and tables
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MTH 2-13a
& MTH 3-13a
In an internet café 3 surfers can sit round a
triangular table.
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
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MTH 2-13a
& MTH 3-13a
1 Table
Step 1 :
2 Tables
Fill
empty
boxes
3 Tables
Number of Tables
1
2
3
4
5
Number of Surfers
3
6
9
12
15
3
3
3
3
Step 2 : Find difference
Same difference
linear pattern
What is the
formula
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MTH 2-13a
& MTH 3-13a
Simple Linear Patterns
using diagrams and tables
Number of Tables
1
2
3
4
5
Number of Surfers
3
6
9
12
15
3
3
3
3
Can you write down formula connecting
the number of surfers and the number of tables.
HINT : Let the number of surfers be the letter S
and the number of tables be the letter T
Step 3 :
S=3xT
S = 3T
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MTH 2-13a
& MTH 3-13a
Simple Linear Patterns
using diagrams and tables
Key-Points
Write down the 3 main steps
1.
Make a table
2.
Find the difference
3.
Use the difference to write
down the formula
www.mathsrevision.com
MTH 2-13a
& MTH 3-13a
Simple Linear Patterns
using diagrams and tables
Now try Ex 3
Ch11 (Page 135)
Complicated Linear Patterns
using diagrams and tables
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MTH 2-13a
& MTH 3-13a
Q1. Calculate Area and perimeter
6cm
Q2. 32% of 200
10cm
7cm
3cm
Q3.
(25)  (20)
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MTH 2-13a
& MTH 3-13a
Complicated Linear Patterns
using diagrams and tables
Learning Intention
1. We are learning how tables
can help us come up with
formulae for complicated
Linear Patterns.
Success Criteria
1. Construct tables.
2. Find the difference value
in patterns.
3. Calculate correction factor
4. Use the difference value
to write down a formula
connecting the table values.
MTH 2-13a
& MTH 3-13a
Complicated Linear Patterns
using diagrams and tables
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A pattern is made up of pentagons.
Pattern 1
Pattern 2
Pattern 3
Task : Find a formula connecting
the Pattern number and the number of sides.
Complicated Linear Patterns
using diagrams and tables
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MTH 2-13a
& MTH 3-13a
Pattern 1
Step 1 :
Fill empty
boxes
Pattern 3
Pattern 2
Pattern Number (P)
1
2
3
4
5
Number of Sides ( S)
5
9
13
17
21
4
4
4
4
Step 2 : Find difference
Same difference
linear pattern
What is the
formula
Complicated Linear Patterns
using diagrams and tables
www.mathsrevision.com
MTH 2-13a
& MTH 3-13a
Pattern Number (P)
1
2
3
4
Number of Sides (S)
5
9
13
17 21
4
4
4
5
4
Can you write down formula connecting
the Pattern number and the number of Sides.
Find a number
so formula
works
Step 3 :
Part of the Formula
S=4xP
Step 4 :
Correction factor “add on 1” S = 4P +
1
www.mathsrevision.com
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
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
www.mathsrevision.com
MTH 2-13a
& MTH 3-13a
Now try Ex 4
Ch11 (Page 139)
Starter Questions
MTH 2-13a
& MTH 3-13a
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1.
Calculate the area of the following shape.
6 cm
10 cm
Q2. Find the missing angle.
114
o
Q.3 Calculate
(a)
-16 -12 - 6
Monday, 20 July 2015
(b) (-9) x (5)
Created by Mr. Lafferty
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(c) (-22) x (-11)  2
16
Square Numbers
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MTH 2-13a
& MTH 3-13a
Learning Intention
Success Criteria
1. We are learning what a
square number is.
1. To understand what a square
number is.
2. Calculate the first 10 square
numbers.
Monday, 20 July 2015
Created by Mr. Lafferty
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17
Square Numbers
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MTH 2-13a
& MTH 3-13a
Write down
the next
square number
1
12
4
22
9
32
16
42
Write down the first 10 square numbers.
1 4 9 16 25 36 49 64 81 100
20-Jul-15
Created by Mr.Lafferty Math Dept
Square Numbers
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MTH 2-13a
& MTH 3-13a
Now try Ex1
Ch11 (page 131)
Monday, 20 July 2015
Created by Mr. Lafferty
@www.mathsrevision.com
19
Starter Questions
MTH 2-13a
& MTH 3-13a
www.mathsrevision.com
1.
Calculate the area of the following shape.
8 cm
6 cm
Q2. Find the missing angle.
122
o
Q.3 Calculate
(a)
-16 +12  4
Monday, 20 July 2015
(b) (4) x (-2)
Created by Mr. Lafferty
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(c) (4) x (-9)  2
20
Triangular Numbers
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MTH 2-13a
& MTH 3-13a
Learning Intention
Success Criteria
1. We are learning what a
triangular number is.
1. To understand what a
triangular number is.
2. Calculate the first 10
triangular numbers.
Monday, 20 July 2015
Created by Mr. Lafferty
@www.mathsrevision.com
21
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MTH 2-13a
& MTH 3-13a
Which numbers are
square and
Triangular and squareboth
Numbers
triangular number
Write down the
next triangular
number
1
3
2
6
3
15
10
4
5
Write down the first 10 triangular numbers.
1 3 6 10 15 21 28 36 45 55
20-Jul-15
Created by Mr.Lafferty Math Dept
Special Patterns
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MTH 2-13a
& MTH 3-13a
Now try
Ch11 (page 133)
Monday, 20 July 2015
Created by Mr. Lafferty
@www.mathsrevision.com
23
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MTH
3-13a
Flower Bed Investigation
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
This is a slab shape
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MTH
3-13a
Draw this design on the
isometric dot paper provided.
(Ensure that your paper is portrait)
Flower Bed Investigation
Here is the design that has one flower bed surrounded by slabs.
How many slabs
are required to
surround the
flower bed?
1 flower bed
6 slabs
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MTH
3-13a
Flower Bed Investigation
Now draw two flower beds surrounded by slabs.
How many slabs
are required to
surround the
flower bed?
2 flower bed
11 slabs
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MTH
3-13a
Flower Bed Investigation
How many slabs
are required to
Now draw three flower beds surrounded surround
by slabs.the
flower bed?
3 flower bed
16 slabs
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MTH
3-13a
Flower Bed Investigation
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.
As a group you are required to
hand in a single solution for this
task showing all working.
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MTH
3-13a
Flower Bed Investigation
Number Flower Beds (f)
1
2
3
Number of Slabs (s)
6
11
16 21
4
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
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MTH
3-13a
Flower Bed Investigation
Task
What is the maximum number of flower beds
you could surround if you had 83 slabs
16
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MTH
3-13a
Flower Bed Investigation
Homework
Now align the flower beds vertically
and
investigate if the formula is still the same?
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MTH
3-13a
Vertical Flower Bed
Investigation
Number Flower Beds (f)
1
2
Number of Slabs (s)
6
10 14 18
s = 4f + 2
3
4