Lesson 1 - Whole Numbers (Grade 9 Mathematics)

Please find the below slides, which talk about the Grade 9 content of whole numbers.

1. Numbers, Operations and Relationships

2. Lesson Outcomes

3. KAHOOT TIME (Baseline TEST) https://create.kahoot.it/details/6c9ed82d-fada-4f58-bd9f-b5da05957a84 Instructions: Please search Kahoot.it online. Wait for the code. Work in pairs and use one phone.

4. Properties of Whole numbers

5. Whole numbers Whole numbers are the set of positive integers or natural numbers along with the zero .

6. The Properties of Whole Numbers Closure Property Commutative Property of Addition and Multiplication Associative Property of Addition and Multiplication Distributive Property of Multiplication over addition Identity Property

7. 1. Closure Property According to the Closure Property “Whole numbers are closed under addition and multiplication”. 5 + 9 = 14 5 x 9 = 45 Note Closure Property is not applicable for subtraction and division of whole numbers. Division of a whole number by zero is undefined.

8. Commutative Property of Addition and Multiplication According to the commutative property of whole numbers, if two whole numbers are added or multiplied together, then the change in the order of the numbers does not change the result. We can add or multiply two whole numbers in any order. 3 + 6 = 6 + 3 3 x 6 = 6 x 3 Note Commutative Property is not applicable for subtraction and division.

9. Associative Property of Addition and Multiplication The associative property of addition and multiplication states that the regrouping of three whole numbers does not change the result of their sum and product. 6 + (3 + 2) = (6 + 3) + 2 (6 x 3) x 2 = 6 x (3 x 2) Note The Associative Property does not exist for subtraction and division.

10. Distributive Property of Multiplication over addition In this property, the multiplication is distributive over addition. 2 x (7 + 4) = 2 x 7 + 2 x 4 Identity Property (for Addition and Multiplication) W + 0 = W W x 1 = W

11. CALCULATING USING WHOLE NUMBERS

12. CALCULATING USING WHOLE NUMBERS 1. Addition and subtraction of whole numbers to at least 6-digit numbers 2. Multiplication of at least whole 4-digit by 2-digit numbers 3. Division of at least whole 4-digit by 2-digit numbers 4. Perform calculations using all four operations on whole numbers, estimating and using calculators where appropriate

13. estimation To try to get close to an answer without actually doing the required calculations with the given numbers. Is 8 x 117 more than 2000 or less than 2000 ? The difference between the estimate and the actual answer is called an error. Example : Actual answer : 764+ 829 = 1593 Estimate : 800 + 800 = 1600 Therefore the error = 1600 – 1593 = 7

14. Addition and subtraction of whole numbers to at least 6-digit numbers Review of Basic Math Operations – ADDITION AND SUBTRACTION ADDITION : The result is called the sum. We can add numbers in any order. 44 + 41 = 85 41+44=85 SUBTRACTION : The result is called the difference. Follow the given order to get the correct answer. 55 - 15 = 40 MULTIPLICATION and DIVISION MULTIPLICATION: The result is called the product. Numbers can be multiplied in any order. 5 × 10 = 50 10 x 5 = 50 DIVISION : The result is called the quotient. Follow the given order to get the correct answer 30 ÷ 5 = 6

15. Addition and subtraction of whole numbers to at least 6-digit numbers Addition Methods - Working with Number Parts Break down numbers into parts based on their place value (units, tens, hundreds, thousands, etc.). Add the corresponding parts separately for easier calculation. Example: Adding 31 837 + 4 994 31 837 + 4 994 = 36 831 Subtraction Techniques - Breaking Down Numbers by Place Value Simplify subtraction by separating numbers into their place value components (thousands, hundreds, tens, units, etc.). Subtract each place value component individually for a more straightforward approach. Example: Subtracting 8 764 - 2 352 8 764 - 2 352 6 412

16. Multiplication of at least whole 4-digit by 2-digit numbers Multiplication Techniques - Breaking Down Numbers into Parts Simplify multiplication by separating numbers into parts based on place value. Multiply each part separately and then add the results to find the final answer. Example: Multiplying 7 × 4 598 7 x 4000 = 28000 7 x 500 = 3500 7 x 90 = 630 7 x 8 = 56 Add the four partial answers for a final result of 32186. To keep it neat, arrange the numbers in columns by units, tens, hundreds

17. Long division(using “car method”)

18. Steps to follow when doing long division D D ivide M M ultiply S S ubtract B B ring down R R epeat or Remainder

19. Multiple and factors of whole numbers

20. Multiple and factors of whole numbers Exploring whole numbers . Working in pairs to investigate relationships between multiple and factors of whole numbers
Each pair should have 2 cards The task is to find as many numbers as you can that can be divided by their chosen numbers without leaving a remainder. Record your answer

21. Factors of whole numbers A factor is a whole number that divides evenly into another whole number without leaving a remainder.
For example,
the factors of 12 are 1, 2, 3, 4, 6, and 12 because all these numbers divide evenly into 12.

22. Multiple of whole numbers A multiple is a whole number obtained by multiplying a given whole number by another whole number.
For instance, the multiples of 3 include 3, 6, 9, 12, and so on, as they are the products of multiplying 3 by other whole numbers.

23. The relationship between multiple and factors of whole numbers A whole number is a multiple of its factors. For example, 12 is a multiple of its factors, such as 1, 2, 3, 4, and 6. Conversely, a whole number is a factor of its multiples. For instance, 3 is a factor of its multiples, such as 9, 12, and 15.
Examples of Factors:
Factors of 8: 1, 2, 4, and 8
Factors of 10: 1, 2, 5, and 10
Examples of Multiples:
Multiples of 4: 4, 8, 12, 16, 20, …
Multiples of 5: 5, 10, 15, 20, 25, …

24. Any Question?