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MTH 3-13a
Linear PatternsLinear Patternsww
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Simple Linear Patterns
Complicated Linear PatternsSimple Linear Graphs
Linear Graphs
Sequences & Patterns
Flower Beds
MTH 3-13a
Starter QuestionsStarter Questions
Sunday 14 May 2023Sunday 14 May 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected] 22
Q2. Find the missing angle.
Q.3 Calculate -16 -12- 6
1. Calculate the area of the following shape.
10 cm
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6 cm
114o
MTH 3-13a
Sunday 14 May 2023Sunday 14 May 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected] 33
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To understand what square To understand what square and triangular numbers are.and triangular numbers are.
1. We are revising square and triangular number.
2.2. Calculate the first 10 Calculate the first 10 square and triangular square and triangular numbers.numbers.
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mSquare and Triangular NumbersSquare and Triangular Numbers
MTH 3-13a
Square NumbersSquare Numbers
May 14, 2023May 14, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Deptwww.
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Write down the first 10 square numbers.
12 22 32
1 4 9 16 25 36 49 64 81 100
Write down the next square number
1 4 9 1642
MTH 3-13a
Triangular and square NumbersTriangular and square Numbers
May 14, 2023May 14, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Deptwww.
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1 3 6 102 3 4
Write down the first 10 triangular numbers.
Write down the next triangular
number
1 3 6 10 15 21 28 36 45 55
5
Which numbers are both square and triangular
number
15
MTH 3-13a
14 May 202314 May 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ3b
Ex 1Ch4 (page 36)
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mLinear PatternsLinear Patterns
MTH 3-13a
Starter QuestionsStarter Questionsww
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aths
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sion.
com Q1. Calculate Area and perimeter
Q4. If a = 1 , b = 2 and c = 4
Find
Q3.
Q2. 30% of 200
( 25) ( 20)
5cm
2cm
3cm
4cm
2c - ab
MTH 3-13a
Simple Linear Patterns using Simple Linear Patterns using diagrams and tablesdiagrams and tables
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m Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. Find the difference in a Find the difference in a pattern.pattern.
1. We are learning to use tables to help us come up with formulae for Simple Linear Patterns. 2.2. Write down formulaWrite down formula
MTH 3-13a
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mSimple Linear Patterns Simple Linear Patterns
using diagrams and using diagrams and tablestables
In an internet café 3 surfers can sit round a triangular table.
1 Table 3 Tables2 Tables
Task :Find a formula connecting
the number of tables and the number of surfers.
MTH 3-13a
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mSimple Linear Patterns Simple Linear Patterns
using diagrams and using diagrams and tablestables
1 Table 3 Tables2 Tables
3For Linear Patterns the difference is the same
each time
Find the difference
9 12 15
MTH 3-13a
9 12 15
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mSimple Linear Patterns Simple Linear Patterns
using diagrams and using diagrams and tablestables
Can you write down the formula connectingthe number of surfers and the number of tables.
S = 3 x TS = 3T
HINT : Let the number of surfers be the letter S and the number of tables be the letter T
MTH 3-13a
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mSimple Linear Patterns Simple Linear Patterns
using diagrams and using diagrams and tablestables
Key-PointsKey-Points1. Fill in the table2. Find the difference3. Use the difference to write
down the formula
MTH 3-13a
14 May 202314 May 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ3b
Ex 2 Q1 to Q5Ch4 (page 38)
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mLinear PatternsLinear Patterns
MTH 3-13a
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mSimple Linear Patterns Simple Linear Patterns
using diagrams and using diagrams and tablestables
310 2
3
1
4
2
6
5xx 00 11 22 33yy 00 22 44 66
(0,0)(1,2) (3,6)
(2,4)
Simple linear patterns always give a straight line through the origin
y
x
y = 2x
MTH 3-13a
14 May 202314 May 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ3b
Ex 2 Q6 to Q7Ch4 (page 40)
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mLinear PatternsLinear Patterns
MTH 3-13a
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mComplicated Linear Complicated Linear
Patterns using diagrams Patterns using diagrams and tablesand tables
Q1. Calculate Area and perimeter
Q3.
Q2. 32% of 200
( 25) ( 20)
10cm
3cm
6cm7cm
MTH 3-13a
Complicated Linear Patterns using Complicated Linear Patterns using diagrams and tablesdiagrams and tables
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m Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1. We are learning to use tables to help us come up with formulae for complicated Linear Patterns using diagrams and tables.
1.1. Find the difference Find the difference value in patterns.value in patterns.
2.2. Calculate correction factorCalculate correction factor
3.3. Write down formula Write down formula using steps 1 & 2 aboveusing steps 1 & 2 above
MTH 3-13a
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m A pattern is made up of pentagons.
Pattern 1 Pattern 3Pattern 2
Task :Find a formula connecting
the Pattern number and the number of Sides.
Complicated Linear Patterns Complicated Linear Patterns using diagrams and tablesusing diagrams and tables
MTH 3-13a
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4
Pattern 1 Pattern 3Pattern 2
Complicated Linear Patterns Complicated Linear Patterns using diagrams and tablesusing diagrams and tables
Find differenceFor Linear Patterns the difference is the same
each time
13 17 21
Find a formula connecting the Pattern Number (P)
and the Number of Slides (S)
MTH 3-13a
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S = 4P + 1
Complicated Linear Patterns using Complicated Linear Patterns using diagrams and tablesdiagrams and tables
Correction factor “add on 1”
MTH 2-13a & MTH 3-13a
13 17 21
S = 4PPart of the formula
MTH 3-13a
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m Key-PointsKey-Points1. Fill in the table2. Find the difference3. Write down part of formula
Complicated Linear Patterns Complicated Linear Patterns using diagrams and tablesusing diagrams and tables
4. Find the correction factor and then write down the full formula
MTH 3-13a
14 May 202314 May 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ3b
Ex 3 Q1 to Q6Ch4 (page 41)
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mLinear PatternsLinear Patterns
MTH 3-13a
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mSimple Linear Patterns Simple Linear Patterns
using diagrams and using diagrams and tablestables
xx 00 11 22 33yy 11 44 77 11
00(0,1)
(1,4) (3,10)(2,7)
Complicated linear patterns always give a straight line NOT through the origin310 2
3
1
4
2
65
y
x
78
109
y = 3x + 1
MTH 3-13a
14 May 202314 May 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ3b
Ex 3 Q7 Q8Ch4 (page 44)
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mLinear PatternsLinear Patterns
Have you updated your Learning Log ?
Are you on Target ?I can ?
MTH 3-13a
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mFlower Bed Flower Bed
InvestigationInvestigation
This is the flower bed shape
This is a slab shape
David is designing a flower bed pattern for the local garden show. He wants to use regular hexagonal shapes for the bed and slabs.
MTH 3-13a
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mFlower Bed Flower Bed
InvestigationInvestigation
Here is the design that has one flower bed surrounded by slabs.
1 flower bed6 slabs
How many slabs are
required to surround the flower bed?
Draw this design on the isometric dot paper
provided.(Ensure that your paper is
portrait)
MTH 3-13a
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mFlower Bed Flower Bed
InvestigationInvestigation
Now draw two flower beds surrounded by slabs.
2 flower bed11 slabs
How many slabs are
required to surround the flower bed?
MTH 3-13a
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mFlower Bed Flower Bed
InvestigationInvestigation
3 flower bed 16 slabsNow draw three flower beds surrounded by slabs.
How many slabs are
required to surround the flower bed?
MTH 3-13a
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mFlower Bed Flower Bed
InvestigationInvestigation
TaskIn 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.
MTH 3-13a
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mFlower Bed Flower Bed
InvestigationInvestigation
s = 5f + 1 How many hexagonal slabs are needed for 25 flower beds.
126
15If we had 76 available slabs how many flower beds could we surround
11 216 16
MTH 3-13a
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mFlower Bed Flower Bed
InvestigationInvestigation
TaskWhat is the maximum number of flower beds
you could surround if you had 83 slabs
16
MTH 3-13a
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mFlower Bed Flower Bed
InvestigationInvestigation
Homework
Now align the flower beds vertically and
investigate if the formula is still the same?
MTH 3-13a
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mVertical Flower Bed Vertical Flower Bed
InvestigationInvestigation
10 186 14
s = 4f + 2