927 24635589.NZL H Directed Numbers NZL

7/27/2019 927 24635589.NZL H Directed Numbers NZL

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P A S S P O R

T P A S S

P O R T

D i r e c t e d N u m b e r s

DIRECTED NUMBERSDIRECTED NUMBERS

www.mathle cs.co.nz


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4HSERIES TOPIC

1Directed NumbersMathletics Passport 3P Learning

Numbers come in all sizes and forms. They can be posi ve or nega ve, whole numbers,frac ons or decimals and ra onal or irra onal.

Posi ve and nega ve numbers:

Whole numbers, frac ons and decimals:

Ra onal and irra onal numbers:

Give t h is a go !

Calculate the value of: ( 2) 2 2 (2 2)[ ]#- - + +{ }3 +Q

Before you start, inves gate these terms and write a brief descrip on about them in the boxes.


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2 Directed NumbersMathletics Passport 3P Learning

4HSERIES TOPIC

Directed NumbersHow does it work ?

Types of numbers

Natural numbers are all the posi ve coun ng numbers , , , ...1 2 3" , .

Integers are all the posi ve ( + ) and nega ve ( - ) whole numbers (including zero).

Circle all the numbers below that belong to the family known as integers.(psst!: some of them need to be simpli ed by calcula ng their value rst)

Your Turn

1-

21

4

5

36

4

45

8-

13

.0 42

0

2-

.5 0-

7

510

-

421

9-

.9 86

30310

1.19284750219...

31

-

83

16-

Place each of these numbers into their correct group below to classify them.

Irra onal numbers cant be wri en as a frac on

Ra onal numbers can be wri en as a frac on

Integers: the posi ve and nega ve whole ra onal numbers including 0 .

Natural numbers: the coun ng ra onal numbers (not including 0 ).

- 1 Put the specialtypes of ra onalnumbers into theircorrect group

0.3-o


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4HSERIES TOPIC

How does it work ? Directed Numbers Your Turn

Measuring instruments and integers

1

2

Shade in each thermometer below to accurately display these temperatures:

(i) C11 c (ii) C5 c- (iii) C6 c (iv) C0 c (v) C8 c above zero

This thermometer shows a reading of C12 c

at the start.Write the new readings that would be displayed a er each of these changes in temperature:

(i) Increases by C3 c

(ii) Becomes C8 c cooler

(iii) Decreases by C13 c

(iv) Warms up by C9c

(v) Rose by C22 c

(vi) Dropped C28 c

(vii) Decrease by C7 c then increase by C12 c

(viii) Warms by C3 c and then a further C9 c

(ix) Cools C15 c before warming by C19 c

(x) Changes to C0 c before dropping 4 Cc

Cc

Cc

Cc

Cc

Cc

Cc

Cc

Cc

Cc

Cc

Cc

12

20 o

15 o

10 o

5o

0 o

- 5o

- 10 o

Cen gradeoC

30 o

25 o

20 o

15 o

10 o

5o

0o

- 5 o

- 10 o

Cen gradeoC

20 o

15 o

10 o

5o

0 o

- 5o

- 10 o

Cen gradeoC

20 o

15 o

10 o

5o

0 o

- 5o

- 10 o

Cen gradeoC

20 o

15 o

10 o

5o

0o

- 5 o

- 10 o

Cen gradeoC

20 o

15 o

10 o

5 o

0 o

- 5o

- 10 o

Cen gradeoC

20 o

15 o

10 o

5o

0 o

- 5o

- 10 o

Cen gradeoC

(vi) C2 c below zero


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4HSERIES TOPIC

7Directed NumbersMathletics Passport 3P Learning


Pip was given $24 and then spent $15 on a dress the same day.

Directed number for the overall change in money that day:

The temperature ini ally increased by 6 degrees and then increased by a further 4 degrees.

Directed number for the overall change in temperature:

Nigel went down 6 rungs on a ladder and then up 2 rungs.Directed number for the overall change in ladder rungs:

Cameron's coolness rose by 4 points when he played guitar, and a further 20 points when hedid maths.

Directed number for the overall change in Cameron's coolness a er doing both ac vi es:

Shiromee hiked 12 km North, 2 km East and then 19 km South. North is the posi ve direc on.

Directed number for the overall change in Shiromee's North-South movement:

Adele's hair grew from 20 cm to 30 cm long at the back. A er a hair cut it was only 17 cm long.

Directed number for the overall change in Adele's hair length from the ini al 20 cm:

Magnitude and direction of integers

For each of these statements, write down:(i) the directed number that matches it and, (ii) the magnitude of the directed number.

1

2

c

Seans bank account balance then changed due to being charged $3 in bank fees.

(iii) Directed number: (iv) Magnitude of the change in Sean's bank balance:

Seans bank account balance earned interest and increased by $4 .

(i) Directed number: (ii) Magnitude of Sean's bank balance increase:

b Aki walked 250 m West from her star ng point.

(i) Directed number: (ii) Magnitude of the distance Aki walked:

Aki then turned around and walked another 600 m East

(iii) Directed number: (iv) Magnitude of this distance walked by Aki:

a The tree in Jamies yard grew 3 metres in one year.

(i) Directed number: (ii) Magnitude of the trees growth:

The same tree was then trimmed which reduced the height of the tree by 4 metres.

(iii) Directed number: (iv) Magnitude of the reduc on in height:

Think carefully for each of these statements and write down the directed number that matchesthe overall change .

a

b

c

d

e

f

+$9

M A

G N I T U D

E A N D

D I R E C T I O N

O F

I N T E G E R S

* ..../ ...../ 20...


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4HSERIES TOPIC

How does it work ? Directed Numbers

Ascending and descending order

When comparing directed numbers, it o en helps to arrange them into numerical order.

Dont be tricked by the magnitude of a number.

Which of these two values is higher?

C2c

C10c

-

C10c

- represents a very cold temperature ( below/less than C0 c ) C2 c is a cold temperature, however it is ( above/greater than C0 c )

C2`c is a higher value than C10 c-

-10 is a bigger number in magnitude than 2 , however the nega ve sign makes it lower in value

Lets look at an ascending and descending order example.

(i) Arrange them into ascending order

(ii) Arrange them into descending order

10 , 6 , 4 , 0 , 3 , 5.2 , 5.4 , 14.5- - -

14.5 , 5.4 , 5.2 , 3 , 0 , 4 , 6 , 10- - -

Lowest nega ve Highest posi ve

Highest posi ve Lowest nega ve

Order is opposite to ascending

For the numbers 4 , 0 , 14.5 , 6 , 5.2 , 3 , 10 , 5.4- - - :

D e s c e n d i n g A s c

e n d i n g

Ascending order = lowest to highest Descending order = highest to lowest

4

3

2

1

0

- 1

- 2

- 3

- 4

- 5

- 6

- 7

- 8

- 9

- 10

- 11

- 12

Cen gradeoC

C2c

C10c-


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4HSERIES TOPIC

9Directed Numbers

Mathletics Passport 3P Learning



1

2

3

Circle the word that represents the order of the values in these statements:

Shortest to Tallest Ascending Descending

Longest to shortest Ascending Descending

Closest to farthest Ascending Descending

Warmest to Coolest Ascending Descending

Heaviest to lightest Ascending Descending

Thinnest to widest Ascending Descending

Arrange the following groups of numbers into ascending order (lowest to highest).

, , ,

, , , ,

, , , ,

, , , ,

, , , , ,

, , ,

, , , ,

, , , ,

, , , ,

, , , , ,

Arrange the following groups of numbers into descending order (highest to lowest).

a

a

a

b

b

b

c

c

c

d

d

d

e

e

e

f

14 , 0 , 17 , 3

21 , 25 , 20 , 19 , 22

10 , 8 , 12 , 4 , 16- - - - -

2.2 , 2.4 , 2.6 , 0 , 2- -

1 , 11 , , 1.5 , 1 ,51

41- -

2 , 16 , 5 , 8

40 , 31 , 32 , 38 , 29

19 , 11 , 16 , 18 , 13- - - - -

1.6 , 1.9 , 1.3 , 1.0 , 1.2- -

0 , , 2 , 2.1 , 1.2 , 3041

21- - - -

A S C E N D

I N G A N D D E S C E N

D I N

G O R D E R

*

..../ ...../ 2 0 ...


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4HSERIES TOPIC



Combo Time!

4 Elevator Riding

A department store elevator operator started work on the 3 rd oor of the 15 storey building.For the rst 15 minutes of work, the operator travelled to the following oors in the order wri en:

12 th oor

8 th oor

Ground oor

2 nd

oorGround oor

15 th oor

4 th oor

10 th oor

5 th oor

If up is posi ve and down is nega ve, write numbers that represent the movement of the

elevator operator during the rst 15 minutes of work.

During the rst 15 minutes, did the operator mostly ascend or descend in the elevator?Explain you answer.

Arrange the directed movements into descending order.

, , , , , , , ,

, , , , , , , ,

13 14 15

10 11 12

7 8 9

4 5 6

1 2 3

G >|< >|

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927 24635589.NZL H Directed Numbers NZL