12/8/2015 WUPA To find common multiples 1015 25 23 68 812 2530.
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Transcript of 12/8/2015 WUPA To find common multiples 1015 25 23 68 812 2530.
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04/21/23
WUPA
To find common multiples
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10 15
2 5
2 3
6 8
8 12 25 30
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04/21/23
Learning Objective
To know to find and extend number sequences and patterns
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Single machines
• Imagine that we have a robot to help us make patterns.
PROCESSORINPUT OUTPUT
6
7
10+ 5
1
2
5
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2 4 6 8 10 _ _ _1/ 12 14 16
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1 3 5 7 9 _ _ _2/ 11 13 15
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25 50 75 100 125 _ _ _3/ 150 175 200
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1 4 9 16 25 _ _ _4/ 36 49 64
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5 9 13 17 21 _ _ _5/ 25 29 33
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8 14 20 26 32 _ _ _6/ 38 44 50
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1 3 6 10 15 _ _ _7/ 21 28 36
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Square NumbersNumber in sequence Number
1st 1
2nd 4
3rd 9
4th 16
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Square Numbers
Number in sequence Number
5th 25 or 5 x 5
6th 36 or 6 x 6
7th 49 or 7 x 7
8th 64 or 8 x 8
xth x x x or x2
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1
3
6
10
Find the next 5 and describe the patternUse your white boards and/or the squared paper.
Triangular Numbers
15, 21, 28, 36, 45…….x?
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No in sequence
1 2 3 4 5 6
Number 1 3 6 10
15, 21, 28, 36, 45…….x?
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1st/ 1 x 2 = 2
2nd/ 2 x 3 = 6
3rd/ 3 x 4 = 12
4th/ 4 x 5 = 20
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(4 x 5) x ½ = 20 x ½ = 10
4 x 5 = 20
This is the 4th in the sequence
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(4 x 5) x ½ = 20 ½ = 10
So what about the xth number in the sequence?
4 x 5 = 20
This is the 4th in the sequence
x x (x +1) ½
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2 4 6 8 10 ________1/
1 3 5 7 9 ________2/
25 50 75 100 125 ________3/
1 4 9 16 25 x24/
5 9 13 17 21 ________5/
8 14 20 26 32 ________6/
1 3 6 10 15 x x (x +1) x ½ 7/
x x 2
(x x 2) - 1
x x 25
(x x 4) + 1
(x x 6) + 2
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04/21/23
WUPA
To order decimals with a mixture of 1, 2 and 3dp.
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Learning Objective
To represent and interpret information in a pie chart.
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Hmmmmm..Pie!
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L.OCan you read a pie chart?
Success CriteriaBy the end of the lesson can you…..•put a percentage next to a pie chart section?•match the result to the section on a pie chart?•work out the number that each section of a pie chart represents?
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Select the correct answer for each of the shape questions below.
What fraction of the pie chart is coloured red?
1
2
1
4
1
3
1
8
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Select the correct answer for each of the shape questions below.
What fraction of the pie chart is coloured red?
1
2
1
4
1
3
1
8
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Select the correct answer for each of the shape questions below.
What fraction of the pie chart is coloured blue?
1
3
1
6
1
4
1
2
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Select the correct answer for each of the shape questions below.
What fraction of the pie chart is coloured blue?
1
3
1
6
1
4
1
2
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Select the correct answer for each of the shape questions below.
What fraction of the pie chart is coloured Purple?
1
2
1
8
1
4
1
5
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Select the correct answer for each of the shape questions below.
What fraction of the pie chart is coloured Purple?
1
2
1
8
1
4
1
5
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Select the correct answer for each of the shape questions below.
What fraction of the pie chart is coloured orange?
1
5
1
2
1
10
1
8
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Select the correct answer for each of the shape questions below.
What fraction of the pie chart is coloured orange?
1
5
1
2
1
10
1
8
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The method for answering questions such as this is quite simple.
Count the number of
sections that is on the chart.
Write this number on the
bottom of a fraction.
Count the number of sections you are being asked
about.
Write this number on the
top of the fraction.
41
What fraction of the pie chart is coloured red?
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Select the correct answer for each of the shape questions below.
What fraction of the pie chart is coloured blue?
1
4
1
2
1
6
3
6
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Select the correct answer for each of the shape questions below.
What fraction of the pie chart is coloured blue?
1
4
1
2
1
6
3
6
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The method for answering questions such as this is quite simple.
Split up all sections so that they are made up
of the same sized pieces and count them.
Write this number on the
bottom of a fraction.
Count the number of sections you are being asked
about.
Write this number on the
top of the fraction.
63
What fraction of the pie chart is coloured blue?
or21
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Select the correct answer for each of the shape questions below.
What fraction of the pie chart is coloured red?
1
8
1
6
2
8
1
10
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Select the correct answer for each of the shape questions below.
What fraction of the pie chart is coloured red?
1
8
1
6
2
8
1
10
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Select the correct answer for each of the shape questions below.
What fraction of the pie chart is coloured green?
3
10
3
12
3
11
3
15
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Select the correct answer for each of the shape questions below.
What fraction of the pie chart is coloured green?
3
10
3
12
3
11
3
15
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Write down how many letters in your first name on a post it note.
Create a circle by lining up with people who have the same amount of letters as us.
What is the mode?What is the least common?
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Interpreting Pie Charts
This pie chart shows how 20 children got to school.
A)How many children walk to school?
B) How many children catch the bus to school?
C) How many children get a lift to school?
Can you show your answerAs a fraction, decimal and
Percentage?
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Interpreting Pie Charts
Can you show your answerAs a fraction, decimal and
Percentage?
This pie chart shows how 80 children got to school.
A)How many children prefer xbox?
B) How many children prefer Playstation 3?
C) How many children prefer DS?
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Interpreting Pie Charts
Can you show your answerAs a fraction, decimal and
Percentage?
This pie chart shows 40 children’s favourite lessons.
A)How many children ‘s favourite lesson is ICT?
B)How many children ‘s favourite lesson is Games?
C)How many children ‘s favourite lesson is Literacy?
D)How many more children like ICT than Literacy?
E)What fraction of the children prefer Maths?
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Interpreting Pie Charts
Can you show your answerAs a fraction, decimal and
Percentage?
This pie chart shows 120 children’s favourite sport.
A)How many children ‘s favourite sport is Football?
B)How many children ‘s favourite sport is basketball?
C)If there were twice as many children in the survey how many children ‘s favourite sport would be swimming?
D)What fraction of the children liked badminton the most?
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04/21/23
WUPA
To add and subtract negative numbers in
problem solving.
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04/21/23
Learning Objective
To find the mean, median, mode and range from a list of numbers.
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32. The average age of the oldest starting line-ups in a World Cup game:
When Germany played Iran in the 1998 finals in France, the average age was 31 years and 345 days.
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MEAN
The sum of all the values divided by the number of values.
78 1
13
11
7+8+11+3+11= 5
40 = 5
8
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MEDIANThe median is the middle value when they are arranged in size order.
78 1
13
11
3 7 8 11 11
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MODE
The mode is the most common value
78 1
13
11
3 7 8 11 11
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RANGE
The range is difference between the highest and lowest value.
78 1
13
11
11 – 3 = 8
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YOUR TASK!!!FIND THE MEAN, MEDIAN AND MODE AGES OF THE TEAM AND THE RANGE
MEAN
The sum of all the values divided by the number of values.
MEDIAN
The middle value when they are arranged in size order.
MODE
The most common value.
RANGE
The difference between the highest and lowest values.
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WUPA
To reduce fractions to their lowest form.
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Simplified Fractions
To simplify a fraction, we find an equivalent fraction which uses the smallest numbers possible.
We do this by dividing.
We need to know our tables for this!Ask yourself, what can I divide both 24 and 40 by?8 is the biggest number we can divide both by and 3/5 uses the smallest possible numbers as we cannot divide them by anything else.
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Simplified Fractions
9/12
8/10
6/9
12/18
15/40
20/24
18/30
21/28
14/42
36/100
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04/21/23
Learning Objective
To find Prime Factors
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Definition Product – An answer to a multiplication problem.
7 x 8 = 56Product
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Definition Factor – a number that is multiplied by another to give a product.
7 x 8 = 56
Factors
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Definition Factor – a number that divides evenly into another.
56 ÷ 8 = 7
Factor
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What are the factors?6 x 7 = 427 x 9 = 638 x 6 = 484 x 9 = 36
6 & 77 & 98 & 64 & 9
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What are the factors?42 ÷ 7 = 663 ÷ 9 = 748 ÷ 6 = 836 ÷ 9 = 4
7969
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Definition Prime Number – a number that has only two factors, itself and 1.
77 is prime because the only numbers
that will divide into it evenly are 1 and 7.
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Examples of Prime Numbers
2, 3, 5, 7, 11, 13, 17, 19
Special Note:One is not a prime number.
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Definition Composite number – a number that has more than two factors.
8The factors of 8 are 1, 2, 4, 8
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Examples of Composite Numbers
4, 6, 8, 9, 10, 12, 14, 15
Special Note:Every whole number from 2 on is
either composite or prime.
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Our Lonely 1
Special Note:One is not a prime nor a composite number.
It is not primebecause it doesnot have exactly
two differentfactors.
It is not composite
because it doesnot have morethan 2 factors.
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Definition
Prime Factorization – A way to write a composite number as the product of prime factors.
2 x 2 x 3 = 12or
2 x 3 = 122
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How to Do Prime Factorization Using a Factor Tree
48Step 1 – Start with a composite number.
Step 2 – Write down a multiplication problem that equals this number orany pair of factors of this number.
6 x 8 = 48
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How to Do Prime Factorization Using a Factor Tree
Step 3 – Find factors of these factors.
6 x 8 = 48
2 x 3 x 2 x 4 = 48
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How to Do Prime Factorization Using a Factor Tree
Step 4 – Find factors of these numbersuntil all factors are prime numbers.
6 x 8 = 482 x 3 x 2 x 4 = 48
2 x 3 x 2 x 2 x 2 = 48
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How to Do Prime Factorization Using a Factor Tree
Step 5 – Write the numbers from leastto greatest.
6 x 8 = 482 x 3 x 2 x 2 x 2 = 482 x 2 x 2 x 2 x 3 = 48
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How to Do Prime Factorization Using a Factor Tree
Step 6 – Count how many numbers arethe same and write exponents for them.
6 x 8 = 482 x 3 x 2 x 2 x 2 = 482 x 2 x 2 x 2 x 3 = 48 2 x 3 = 484
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Prime factor this number
42 x 2
2 = 42
= 4
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Prime factor this number
62 x 3 = 6
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Prime factor this number
82 x 4
2 = 83
= 82 x 2 x 2 = 8
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Prime factor this number
93 x 3 = 9
3 = 92
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Prime factor this number
102 x 5 = 10
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Prime factor this number
123 x 4
2 x 3 = 122
= 123 x 2 x 2 = 122 x 2 x 3 = 12
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Prime factor this number
142 x 7 = 14
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Prime factor this number
153 x 5 = 15
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Prime factor this number
164 x 4
2 = 164
= 162 x 2 x 2 x 2 = 16
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Prime factor this number
183 x 6
2 x 3 = 182
= 183 x 2 x 3 = 182 x 3 x 3 = 18
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Prime factor this number
204 x 5
2 x 5 = 202
= 202 x 2 x 5 = 20
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Prime factor this number
213 x 7 = 21
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Prime factor this number
222 x 11= 22