number theory grade 7, 8 and 9

Number TheoryMr. Khanyile

Content

▪ History▪ Natural and Whole Counting Numbers▪ Products, Factors and Multiples▪ Rules Of Divisibility▪ HCF, LCM▪ Prime And Composite Numbers▪ Prime Factors▪ Square Numbers/Roots, Cubic Numbers/Roots

History

▪ The system of writing numerals was developed some 10,000 years ago. India was the main centre for the development of the number system which we use today. It took about 5000 years for the complete development of the number system. The Whole numbers are fountain head of all Mathematics. The present system of writing numerals is known as Hindu-Arabic numeral system. In this system, we use the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. It is also called the decimal system with base 10. The word ‘decimal’ comes from Latin word ‘Decem’ which means ‘Ten’.

Natural and Whole Counting Numbers (Gather and Organise) 3 minutes

Natural Numbers Whole Counting Number

▪ Natural Numbers all positive whole Numbers starting from 1. N={1,2,3,….,∞}

▪ Whole or Counting Numbers are set of numbers starting from zero to infinite. N0={0,1,2,3,…….∞}

Identify: What is the task?

Task 1 in Keys BookTask 2 in Keys BookTask 3 in Classwork Book

Everyone can do maths! Growth Mind-set

Evaluate: How Well Did I Do?

Learn From Experience: What Have I Learned? 5 Minutes

Number TheoryProducts, Factors, and Multiples

Gather 5 minutes

A Product is the answer to the multiplication of numbers.

Gather 3 minutes

Multiples (Time-tables)

Gather 5 minutes

Factors

Identify: What is the task?

Task 4 number 1- 5 in Classwork book

Generate: How many Ideas can I think of?

Factors

▪ T-Chart▪ Ladder method

Multiples

▪ Times-table▪ Calculator

Decide: Which is the best idea/method?

Factors Multiples

Evaluate: How well did I do?

Answer the evaluate questions.

Learn from experience: What have I learned? (Feedback)

Factors

▪ Numbers you multiply together to get a number. E.g. 2 and 3 are factors of 6

▪ T-chart and Ladder Method

▪ Perfect Number▪ Mathematical Notation

Multiples

▪ Numbers you multiply with natural numbers. Time-tables

▪ Calculator▪ Grid▪ Mathematical Notation

Number TheoryRules of Divisibility

Gather and organise

▪ What are rules of divisibility?▪ What do I really know about this?

Rules of Divisibility

Highest/Greatest Common Factor

▪ What is a HCF (Explain)?▪ Give an example.▪ Explain in your own words how to find HCF of any two

numbers and give an example

Highest/Greatest Common Factor

Biggest same factor between two or more numbers.

How to find the HCF

▪ List all factor of given numbers (use ladder method).

▪ Highlight/circle common(same) factors.

▪ The biggest same factor is the HCF.

Lowest Common Multiple (LCM)

▪ What is a LCM (Explain)?▪ Give an example.▪ Explain in words how to find a LCM and give an

example.

Lowest Common Multiple

The smallest same multiple between two or more numbers.

How to find the LCM

▪ List the multiples of the given numbers (Use a calculator or a 100 chart grid).

▪ Highlight/circle the common(same) multiples.

▪ The smallest same multiple is the LCM.

Classwork

▪ Task 6 and Task 7 in exercise book

Prime and Composite Numbers

Prime Numbers

▪ What are prime numbers (explain)?

▪ Give an example▪ Explain in words how to

find any prime number and give an example.

Composite Numbers

▪ What are Composite Numbers (explain)?

▪ Give an example▪ Explain in words how to

find any composite number and give an example.

Prime numbers

Prime numbers are numbers with only two factors i.e. 1 and the number How to find Prime Numbers

▪ List the factors(Ladder Method) of the given number.

▪ If the number has only two factors which are one and itself then it is a Prime number

▪ E.g. F2= 1,2 ▪ NB! 1 is not a prime number!

Classwork on Prime and Composite Numbers

▪ Task 8 and Task 9 ( In keys Book)

Exponential Notation

▪ What is a power (explain) ?▪ Give an example.▪ Explain in words what an exponential notation is and

give an example

Exponential Notation

A power is a number that is made up of a base and an exponent. The Exponent tells us how many times the base is being multiplied by itself.

Exponential Notation is a short way of writing an expanded notation.

Exponential Notation Classwork

▪ Task 10 in exercise book

Prime Factors

▪ What are prime factors (explain)?▪ Give an example of a Prime Factor.▪ Explain in words how to find a Prime Factor and give an

example.

Prime Factors

The product of prime numbers of a given number.How to find Prime Factors• Divide the given

number with prime numbers until you get 1 using Ladder method.

• Divide the given number with prime numbers using the method.

• Note you can repeat prime numbers.

• Use a calculator!

Prime Factors Classwork

▪ Task 11 No 1-3 only in exercise book.

Square Numbers and Square Roots

▪ What is a square number (explain)?▪ What is a square root (explain)?▪ Give an example of a square number and a square root▪ Explain in words how to find a Square number and a

Square root.

Square Number and Square Root

Square number is a number multiplied by itself. A number to the power of 2.

Square roots is the inverse of squaring a number.

Cubic Number and Cubic Root

Cubic number is a number to that is multiplied by itself three times. A number with an exponent 3 Cubic

root is the inverse operation for a cubic number

Square Numbers, Square Roots, Cubic Numbers and Cubic Roots classwork.

▪ Task 12, 13, 14, 15 and 18

Number Patterns

▪ Number patterns▪ Triangular and Square numbers▪ Pascal’s Triangle

Number Patterns

▪ What are number patterns?▪ Give an example

Number Pattern

A list of numbers that follow a certain sequence or pattern.

Number Patterns classwork

▪ Task 1

Triangular And Square Numbers

▪ What are triangular and Square numbers?▪ Give an example

Triangular and Square Number

any of the series of numbers (1, 3, 6, 10, 15, etc.) obtained by continued summation of the natural numbers 1, 2, 3, 4, 5

Square Numbers

Triangular and Square numbers classwork

▪ Task 2

Pascal’s Tiangle

▪ What is it?▪ One of the most interesting Number Patterns

is Pascal's Triangle (named after Blaise Pascal, a famous French Mathematician and Philosopher). To build the triangle, start with "1" at the top, then continue placing numbers below it in a triangular pattern. Each number is the numbers directly above it added together.

Pascal’s Number Pattern

Pascal’s Triangle

▪ Task 3

Revision

▪ Number system and Number Pattern