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