Discovering Mathematics Week 3 Unit 2: Mathematical Models Unit 3: Numbers.
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Transcript of Discovering Mathematics Week 3 Unit 2: Mathematical Models Unit 3: Numbers.
Discovering Mathematics
Week 3
Unit 2: Mathematical Models
Unit 3: Numbers
Unit 2: Mathematical Models
• Using Formulaso From words to lettersoWriting formulas conciselyo Constructing your own formulas
• Inequalities:
– Notation for working with inequalities
– Illustrating inequalities on a number line
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)
Using formula
Writing formulas concisely
Substituting negative numbers
Try this examples
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:
Construct your formula
4. Inequalities
Examples:
Put the correct sign (< or > ):
1- 12 __3 2- -2.5 __ -4.5
Students: solve activity 26 and 26
UNIT 3. Numbers
• Natural numbers
• Rational numbers
• Irrational numbers and real numbers
• Ratios
1. Natural Numbers
Multiples:
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?
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.
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
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 24the factors of 12 = 1,2,3,4,6,12the factors of 24 = 1,2,3,4,6,8,12,24the highest common factors = 12
Powers
Dividing numbers in index form
Raising numbers in index form to powers
Rational numbers
Multiplying fractions
Thank you