Discovering Mathematics

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Discovering Mathematics

• Week 3
• Unit 2 Mathematical Models
• Unit 3 Numbers

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Unit 2 Mathematical Models

• Using Formulas
• From words to letters
• Writing formulas concisely
• Constructing your own formulas
• Inequalities
• Notation for working with inequalities
• Illustrating inequalities on a number line

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3. Using Formulas

• In every day life, many things are represented by
  symbols. Give examples.
• Solving a problem in mathematics often involves
  using a formula. For example
• distance (d) average speed (s) x time (t)
• To find the value of d, take the value of s and
  multiply by the value of t, this process is
  called substitution. (give examples)

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Using formula

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Writing formulas concisely

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Substituting negative numbers
 
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Try this examples

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Constructing your own formulas

• You can construct a formula by following the
  three steps
• first, identify the subject of the formula.
• Next, find the relationship between the
  variables.
• Finally, write down all the details of the
  formula.
• Let us solve some examples

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Construct your formula

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4. Inequalities

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Examples

• Put the correct sign (lt or gt )
• 1- 12 __3 2- -2.5 __ -4.5
• Students solve activity 26 and 26

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UNIT 3. Numbers

• Natural numbers
• Rational numbers
• Irrational numbers and real numbers
• Ratios

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1. Natural Numbers

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Multiples

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Common multiples

• A common multiples of two or more numbers is a
  number that is a multiple of all of them.
• Multiple of 6 6, 12,18, 24, 30, 36, 42, 48,..
• Multiple of 8 8, 16, 24, 32, 40, 48, 56,..
• Number 24 appears in both multiples, then 24 is a
  common multiple of 6 and 8. What else?

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Lowest common multiple

• The lowest common multiple (LCM) of two or more
  numbers is the smallest number that is a multiple
  of all of them.
• What is the lowest common multiple for numbers 4
  and 6?
• Multiple of 4 4,8,12,16,..
• Multiple of 6 6,12,18,24,30,..
• Then, LCM 12
• Solve activity 3, page 122.

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Factors

• A natural number that divides exactly into a
  second natural number is called a factor or
  divisor of the second number.
• Find all the factors of 28
• First pair is 1, 28
• Second pair is 2, 14
• Third pair is 4, 7
• Try 5, 5 is not a factor. 6 is not a factor
  either
• Try 7, yes it is 7 and 4 and it is already there,
  so stop here. The factors of 28 is 1,2,4,7,14 and
  28

Find the factors of number 45
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Common factor

• A common factor of two or more numbers is a
  number that is a factor of all of them. The
  highest common factor (HCF) of two or more
  numbers is the largest number that is a factor of
  all of them.
• Find the HCF for numbers 12 and 24
• the factors of 12 1,2,3,4,6,12
• the factors of 24 1,2,3,4,6,8,12,24
• the highest common factors 12

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Powers

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Dividing numbers in index form

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Raising numbers in index form to powers

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Rational numbers

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Multiplying fractions

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Thank you