Directed NumbersForm 1 Mathematics

Chapter 1

Reminder Correction of Dictation 2 & Folder checking

Today!! Correction of Closed Book Quiz (Ch. 0) and

Standard Homework 1 8 Oct (Mon)

Extra Tutorial 8 Oct (Mon) – based on Closed Book Quiz result

Sudden Test on Summer Holiday Homework 8 – 12 Oct (the week after Athletics Meet)

Result of Close Book Quiz Result of Open Book Quiz

Highest: 41 (WU SHAN Hao Yi) Lowest: 16 Average: 29.2 Number of students below 30: 17

Result of Close Book Quiz Highest: 48 (LI Sai Kong) Lowest: 18 Average: 31.9 Number of students below 30: 13

Monday Extra Tutorial List Marks in Open Book Quiz < 30

and Marks in Close Book Quiz < 30 9 students Class numbers:

1, 7, 12, 14, 16, 17, 19, 24, 31 If any student wants to join, please talk to me

privately.

Introduction to Directed Numbers Numbers have two parts:

1. Size or Magnitude2. Sign or Direction

The sign of a number has two possibilities (they are always opposites)

Examples of Directed NumbersWhat does the negative mean? Money in bank:

+$1,100 – $950 Students in class (36 students in class)

Mon: – 2; Tue: – 1; Wed: 0; Thu: – 3; Fri:0 World time:

Sydney: +2; Rome: – 6; London: – 8; New York: – 13 Stairs in the building (up is “+”):

Go up 3 steps: +3; Go down 4 steps: – 4

Directed numbers on a number line

How do we write & say this?

-2-6 4 70

+–

-6 4

-2 0

< say “minus six is less than four”

< say “minus two is less than zero”

Directed numbers on a number line

How do we write & say this?

-2-6 4 70

+–

7 -2

4 0

> say “seven is greater than minus two”

> say “four is greater than zero”

Directed numbers on a number line

How do we write & say this?

-2-6 4 70

+–

7 0 -2 -6

-2 0 4 7

> > >

< < <

This called “Descending Order”

This called “Ascending Order”

Why do we learn Directed Numbers? In primary school, you learned: Example 1: 3 + 7 = 10

“3 apples plus 7 apples is 10 apples”

Example 2: 3 – 7 = – 4Are “3 apples minus 7 apples negative 4 apples”?

With Directed Numbers, the “–” now has meaning!

The Four Basic Operations Addition: 3 + 7

Say “3 plus 7” or “The sum of 3 and 7” or “Add 3 to 7”

Subtraction: 3 – 7 Say “3 minus 7” or “The difference of 3 and 7” or “Subtract 7 from 3”

Multiplication: 3 × 7 Say “3 times 7” or “The product of 3 and 7” or “Multiply 3 and 7”

Division: 3 ÷ 7 Say “3 divided by 7” or “The quotient of 3 and 7” or “Divide 3 by 7”

The Four Basic Operations Addition: “+” or “sum” Subtraction: “–” or “difference”

Multiplication: “×” or “product” Division: “÷” or “quotient”

The meaning of “+” and “—” In primary school you learned: Example 1: 3 + 7 = 10

In high school, you learn Directed Numbers: Example 1a: (+3) + (+7) = (+10)

Direction or sign

Magnitude or size

What is this? The OperationWhat sort of operation?

Addition or Sum

The meaning of “+” and “—” “+” has two meanings:

1. Direction of directed number

2. Operation between two directed numbers

The meaning of “+” and “—”Primary school: Example 2: 3 – 7 = –4

Directed Numbers: Example 2a: (+3) – (+7) = (–4)

Direction or sign

What is this? An Operation

What sort of operation? Subtraction or Difference

The meaning of “+” and “—” “–” has two meanings:

1. Direction of directed number

2. Operation between two directed numbers

Rules to Remember (p.50)

( + ) ( + ) = ( + ) ( – ) ( – ) = ( + )

( + ) ( – ) = ( – ) ( – ) ( + ) = ( – )

Rules to Remember (p.50)

( + ) ( + ) = ( + ) ( – ) ( – ) = ( + )

( + ) ( – ) = ( – ) ( – ) ( + ) = ( – )

正正得正 負負得正正負得負 負正得負

Adding directed numbers

+– -2-6 3 70

+–

+–

(+7) + (+3) = (+10)

10

( + ) ( + ) = ( + )

( – ) ( – ) = ( + )

( + ) ( – ) = ( – )

( – ) ( + ) = ( – )

Adding directed numbers

+– -3-6 3 70

+–

+–

(+7) – (+3)

= 4

10

(+7) + (–3)7 – 3

( + ) ( + ) = ( + )

( – ) ( – ) = ( + )

( + ) ( – ) = ( – )

( – ) ( + ) = ( – )

Examples

( + ) ( + ) = ( + )

( – ) ( – ) = ( + )

( + ) ( – ) = ( – )

( – ) ( + ) = ( – )

+3 + (+9)= +3 + 9= +12

–7 + (+12)= –7 + 12= +5

Time for Practice Page 51 of Textbook 1A

Class Practice Page 52 of Textbook 1A

Questions 7 – 13 Page 20 of Workbook 1A

Questions 2 – 7

Mathematics nearby Restaurant problem:

3 students went to a restaurant for a meal of $250. Everyone firstly paid $100. So, totally $300 When the waiter came back with $50, they

decided to get $30 back (everyone gets $10 back) and then left $20 for tips.

So, every student paid $90 only. Now, $90 x 3 + $20 = $290! Where is the last $10?

Ronald HUI

Good Luck!

Enjoy the world of Mathematics!