1. Discovering Mathematics Week 3 Unit 2: Mathematical Models Unit 3: Numbers

2. 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

3. 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)

4. Using formula

6. Writing formulas concisely

7. Substituting negative numbers

8. Try this examples

9. 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:

10. Construct your formula

11. 4. Inequalities

12. Examples: Put the correct sign ( ): 1- 12 __32- -2.5 __ -4.5 Students: solve activity 26 and 26

13. UNIT 3. Numbers Natural numbers Rational numbers Irrational numbers and real numbers Ratios

14. 1. Natural Numbers

15. Multiples:

16. 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?

17. 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.

18. 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

19. 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

20. Powers

21. Dividing numbers in index form

22. Raising numbers in index form to powers

23. Rational numbers

24. Multiplying fractions

25. Thank you