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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 o From words to letters o Writing formulas concisely o 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 ( ): 1- 12 __32- -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
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