Kirri Algebra

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Patterns And Algebra Made Easy With Tom and
Jerry!!

• By Kira-Leigh Rule

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Whats a pattern?

• Definition of Pattern
• A pattern is made up of a set of numbers or
  objects in which they are all linked with each
  other by a specific rule.
• More about Pattern
• Pattern is also known as a sequence. A pattern
  can be made up of just about anything you want
  It just has to be able to be repeated over and
  over.
• Example of Pattern
• The pattern above contains three ,shapes, a
  hexagon, pentagon and a rectangle. This pattern
  can be repeated over and over again and still be
  the same

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Questions

• Circle which ones of these are patterns
• 1)
• 2)
• 3)

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Questions Answers
I thought Id get these right

• These should have being your answers
• 1)
• 2)
• 3)
• Now if you got both of them correct great job. If
  you didnt and are confused lets try some more!

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One more question!
This is easy I am sure I have it this time!!

• Solve the example the next three terms of
  the following pattern.?81, 79, 77, ___, ___,
  ___,...?Choices?A. 79, 81, and 83?B. 83, 81, and
  79?C. 75, 73, and 71?D. 79, 77, and 75?

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Lets break it down!

• Answer

• Solution

• Correct Answer Was C?

• ?Step 1 The rule for the pattern is to count
  down by 2 repeatedly and continue the sequence to
  find the next 3 terms. ?Step 2 So, the next
  three terms in the sequence are 75, 73, and 71.

I did get it right!! YAY!!
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Finding Rules From Patterns
It is as easy as licking a ice cream!

• Each pattern to be a pattern has to have a rule.
  For example this pattern
• 3,6,9,12,15,18
• The rule in this pattern is 3. Another example
  is
• 2,6,18
• The rule is x 3. To find a rule sometimes you
  just have to look at the pattern to find it.
  Sometimes it is harder. There can be more than
  one rule that works. When in doubt choose the
  simplest rule that makes sense, but also mention
  that there are other rules that work as well.
• The rule between each figure (number or objects)
  should stay the same. For example you cant go x2
  then 2 then -6. It has to be x2 then x2 etc.
• It can help sometimes to find the differences
  between each number. This can often help you find
  a rule.

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Questions

• Lets try find the rule of these two examples

10 3 30 50
20 6 60 100
15 12 18 24
5 4 6 8
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Question Answers

• These are the answers
• Answer Times 2
• Answer Divided by 3

10 3 30 50
20 6 60 100
15 12 18 24
5 4 6 8
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The Language of Algebra

• Algebraic Expressions
  
  An Algebraic Expression is one or
  more terms put together. It can include
  variables, constants, and operating symbols, such
  as plus and minus signs. It's only a phrase, not
  the whole sentence, so it doesn't include an
  equal sign. Here is an example 3x2 2y 7xy
  5.
• Variables
  
  Variables are the letters in a
  algebraic expression. They are numbers hiding as
  letters. 3x2 2y 7xy 5. In this for example
  the variables are x and y. But a variable can be
  any letters in the alphabet. They can even be put
  together to make a group. Like this 5yxy 6zba
  10 yxy.
• Coefficients
  
  Coefficients are the number
  part of a term. For example in this 3x2 2y
  7xy 5 the first Coefficient is 3, the second is
  2 and the third is 7. If a term consists of only
  variables, its coefficient is 1.

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The Language of Algebra

• Term
• It is a single number or a variable. It can also
  be both together. For example 2t or 2 or t.
• Equation
• An Algebraic Expression is one or more terms put
  together. It can include variables, constants,
  and operating symbols, such as plus and minus
  signs. This is just like a sentence so it has an
  sign.
• Constants
• They are the terms that only have numbers in
  them. This means that they dont have any
  variables. They are called constants because
  there value can never change. For example 7x2
  3xy 8 the constant is 8.

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Lets test you!

• Circle which ones that are a variable. Put a
  square around the ones that are a equations.
• 1) 5x 3c 7x 36
• 2) xyc
• 3) 2xyc
• 4) 2h8j 40
• 5) 8, 26 , 1093

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Answers

• Circle which ones that are a variable. Put a
  square around the ones that are equations.
• 1) 5x 3c 7x 36
• 2) xyc
• 3) 2xyc
• 4) 2h8j 40
• 5) 8, 26 , 1093

AHH!! I got them right!! YAY
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Function Machine

• I would like to introduce you to the function
  machine

Input
This is going to make things easy!
It can have or or x or inside it.
Output
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Function Machine
Why didnt I think of this before!

• The rule happens inside the function machine.
• For example if the rule is x3 and the input
  number was 3 it would look like this

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Input
x3
3 9
Output
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Questions

• Answer in the following question what the output
  number should be. Remember to use the function
  machine. If it helps you draw it on a sheet of
  paper and work it out on there.
• What is the output number when the input number
  is 4 and the rule is x2
• What is the output number when the input number
  is 12 and the rule is -7
• What is the output number when the input number
  is 2 and the rule is x12
• What is the output number when the input number
  is 6 and the rule is 3

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Answers

• Here are the answers
• What is the output number when the input number
  is 4 and the rule is x2 8
• What is the output number when the input number
  is 12 and the rule is -7 5
• What is the output number when the input number
  is 2 and the rule is x12 24
• What is the output number when the input number
  is 6 and the rule is 3 9

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Another way!

• There is another way to do this. You can use a
  table. Like this
• In these types of tables you have to find the
  rule. The rule for this table is 6

Input 12 18 24 30 36 42 48 54
Output 2 3 4 5 6 7 8 9
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Creating an Equation from a Rule

• In a table diagram like you saw before, there is
  always a rule. If there is a rule there has to be
  an equation. For example the one we had before
• In this table the rule is6. So to get to the
  input number to the output number you have to 6.
  This is your equation, now you just have to put
  it into shorter terms.

Input 12 18 24 30 36 42 48 54
Output 2 3 4 5 6 7 8 9
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Creating an Equation

• Remembering that the rule was 6 we have to now
  make the equation. So the equation always starts
  with the letter or letters at the bottom of the
  table. For example
• Now that you know this the rest is easy. So if we
  were using the example before it would be
  Output. so far. Next you have to put what was
  the letter or letters above it. So now it would
  look like this OutputInput. Lastly you put
  what the rule is. So it would look like this
  OutputInput6.

Input
Output
A
B
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Lets help Jerry!

• Jerry has a problem. Jerry wants to have a party
  with 16 people but Jerry doesnt know how many
  tables to put out. Lets help Jerry! These are the
  kind of tables Jerry wants but each table can
  only fit three people

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Jerry's Problem
T P
1 3
2 4
3 5
4 6
8
12
13
16

• So far we have started working out Jerrys
  problem. In this table p stands for people and
  t stands for tables. So far we know that with
  one table it 3 people, 24, 35.
• Can you see a pattern? Try fill in the rest
  yourself if you can find the pattern. I will
  start you off. Can you now see what the rule is?
  If not the rule is PT2. So this means the
  number of tables 2 gives you the answer of
  people that can fit. Fill in the rest of the
  table now that you know the rule.

T P
1 3
2 4
3 5
4 6
8 10
12 14
11 13
14 16
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What you have learnt
I learnt so much without even knowing!

• It is a good time now to revise what you have
  learnt.
• First you learnt what a pattern is. Do you
  remember what that was? If not go back and
  revise.
• Secondly you learnt about Finding Rules From
  Patterns. Try remember this if you cant go back
  and read through again.
• Next you learned about the Language of Algebra.
  Do you remember what that was? If not go back and
  revise.
• Lastly you learnt about the Function Machine and
  Creating an Equation from a Rule. Try remember
  this if you cant go back and read through again.

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THANK YOU!

• Tom, Jerry and myself hope you have learnt heaps
  of stuff about maths and algebra through this
  power point.

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Bibliography

• Algebra, http//www.mathsisfun.com/algebra/index.h
  tml (1/9/12)
• Definitions, http//www.math.com/school/subject2/l
  essons/S2U1L1GL.htmlsm1 (1/9/12)
• Math is fun, http//www.mathsisfun.com/index.htm
  (1/9/12)
• Patterns, http//www.mathsisfun.com/algebra/patter
  ns.html (1/9/12)