Maths: Number Plane

Topics: Real number, Negative and non-negative numbers, Integer Pages: 130 (6296 words) Published: October 15, 2013
8
Directed
Numbers and
the Number Plane
This is the last time
I fly El Cheapo Airlines!

Chapter Contents

8:01 Graphing points on the number line
NS4·2
PAS4·2, PAS4·5
PAS4·2, PAS4·5
8:03 The number plane
Mastery test: The number plane
8:04 Directed numbers
NS4·2
NS4·2
Investigation: Directed numbers
8:06 Addition and subtraction of directed
NS4·2
numbers
8:07 Subtracting a negative number
NS4·2
ID Card

Learning Outcomes

8:08 The number plane extended
PAS4·2, PAS4·5
8:09 Multiplication of directed numbers
NS4·2
Investigation: Multiplying directed numbers
Challenge: Using pronumerals
8:10 Division of directed numbers
NS4·2
NS4·2
8:11 Using directed numbers
8:12 Directed numbers and the calculator
NS4·2
Fun Spot: Try this quick quiz!
Maths Terms, Diagnostic Test, Revision
Assignment, Working Mathematically

NS4·2 Compares, orders and calculates with integers.
PAS4·2 Creates, records, analyses and generalises number patterns using words and algebraic symbols in a variety of ways.
PAS4·5 Graphs and interprets linear relationships on the number plane. Working Mathematically Stage 4.
1 Questioning, 2 Applying Strategies, 3 Communicating, 4 Reasoning, 5 Reflecting.

207

8:01 | Graphing Points on the

Outcome NS4·2

Number Line

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quiz
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Write down the number sentence represented by each number line. 1
2
0

8:01

2

4

6

8

0

10

2

4

6

8

10

...+...=9

. . . + . . . = 10
3

4
0

2

4

6

8

10

5

0

2

4

6

8

10

0

2

4

6

8

10

0

2

4

6

8

10

0

2

4

6

8

10

6
0

2

4

6

8

10

0

2

4

6

8

10

7

8

9

10
0

2

4

6

8

10

The number line can be very useful. It can help us to perform additions, subtractions, multiplications and even divisions. The number line can also be used to graph sets of numbers. To graph a number on the number line, place a large dot at the position of that number on the number line.

worked examples
Graph the following sets of points:
1 {2, 4, 5}

0

1

2

3

4

5

6

2 {0, 1, 2, 3, 4}

0

1

2

3

4

5

6

3 {3, 6, 9}

0

2

4

6

8

10

12

--4 {1 1 , 3, 4 1 }

0

1

2

3

4

5

6

5 {0·2, 0·5, 1·1}

0

0·2

0·4

0·6

0·8

1

1·2

2

208

2

NEW SIGNPOST MATHEMATICS 7

We use braces to list
the numbers in a set.

Exercise 8:01
1

Use braces to show the set of numbers graphed
on each number line.
a 0

1

2

3

4

5

6

7

b 0

1

2

3

4

5

6

7

c

9

A set of numbers
is a collection of numbers.

10 11 12 13 14 15 16