Preparation for

Commercial / ATP Pilots

Your instructor for this Ground School…

Brand WesselsCell: 073-591 3907

Email: brandwessels@yahoo.com

Agenda:

• Personal Introductions – name, background, qualifications

• What is our expectations from this course

• Course Rules – be on time, be prepared and participate constructively

• Be Professional• Course Schedule• Have FUN!

MathematicsWhat do we need to know?

We need to have basic understanding of:

• Basic Algebra - cross-multiplication, cross-addition and -subtraction, averaging, powers and roots, bracketing, percentages, inverse calculation and vectors.

• Basic Trigonometry – Triangles, Ratio’s, Pythagoras.

• Basic Interpolation.• How to operate the Navigation Computer and

Scientific Calculator.

The Myth – “this is difficult…”

• If you passed Mathematics up to Grade 10 standard grade, you have covered everything you will need.

• There is NOTHING in the CAA theory syllabus, that is as difficult as passing a current Grade 12 Higher Grade Mathematics' exam – go try one….

SA Grade 12 formulas in 2008……

That Being Said….

• You have to know the basics WELL.• You have to know your calculators WELL.• You have to stay CURRENT.• You have to show enough RESPECT for the

basics required.• The CPL/ATPL exam is quite a lot of work –

about the same volume as the first 3 month’s of Engineering studies at University. If you are not on top of the required mathematics, you will waste time.

The ABC of this course….

•APPLY your

•BACKSIDE to the

•CHAIR….

Push this button just before you choose a 2nd

function buttonInverse Button

Square Root

Force of 2

Force of 3

10 to the force …

Degree, minutes, seconds – also hours, minutes, seconds

% ButtonBrackets

Trig Example: You are taking off from a runway, with a hill 300’ high, 6000’ from the threshold. What angle of climb must you maintain to clear the hill?

tan c = b/a

And y=300’ and x=6000’

Tan x = 0.05

Divide by tan same as inverse (or cot, or tanˉ¹)

Thus c = 2,86º

Functions

A fraction is an ordered pair of whole numbers, the 1st one is usually written on top of the other, such as ½ or ¾ .

The denominator tells us how many pieces the whole is divided into, thus this number cannot be 0.

The numerator tells us how many such pieces are being considered.

numerator

denominatorba

• Variable – A variable is a letter or symbol that represents a number (unknown quantity).

• 8 + n = 12

• A variable can use any letter of the alphabet.

• n + 5

• x – 7

• w - 25

An Equation is like a balance scale. Everything must be

equal on both sides.

10 5 + 5=

When an amount is unknown on one side of the equation it is

an open equation.

7 n + 2=

When you find a number for n you change the open equation to a true equation. You solve

the equation.

7 n + 2=

5

Simple Algebra• Remember Rules:

• The sum of two positive numbers is always positive.

• The sum of two negative numbers is always negative.

• Multiplication/Division of two positive numbers is always positive.

• Multiplication/Division of two negative numbers is always positive.

• Multiplication/Division of a positive and a negative number is always negative.

Addition and Subtraction

26+(-38)-(-55)+(-61)-(23) =

-41

On the calculator – type it all without the brackets….

Powers and Roots

2 x 2, same as 2², same as 2 to the power of 2, same as 4.

The root of 4, same as √4, same as 2.

On the calculator:

2x², enter = 4

√4, enter = 2

Inverse operation the opposite operation used to

undo the first. • 4 + 3 = 7 7 – 4 = 3• 6 x 6 = 36 36 / 6 = 6• Use “xˉ¹” on you calculator.

Parentheses and Brackets)

Use brackets when you want to do certain calculation before the rest:

b² = 60² - (35000÷6080)²

b² = 3566,8. Now press √ and

b = 59,72

C = 2 x ((9÷3) + (4+3)²)

C = 2 x (3 + 49)

C = 104

Order of Algebraic Operation:

“PEMDAS”Solve in the following sequence:

• P for solving Parentheses(or brackets)

• E for solving Exponents next

• MD for Multiplication and Division next

• AS for Adding and Subtracting next.

Example:

• y = ((4³ + √((3+27) – (25÷5))) ÷ 3) + 273

• P is y = ((4³ + √(30 – 5)) ÷ 3) +273 And y = ((4³ + √25) ÷ 3) +273• E is y = ((64 + 5) ÷ 3) +273• MD is y = (69 ÷ 3) + 273• AS is y = 23 + 273 = 296

Prove it by typing the whole equation into your calculator at once….

Solving Addition and Subtraction Equations

Procedure

• Isolate the variable by performing the inverse operation on that variable.

• The inverse of subtraction is adding. The inverse of adding is subtracting.

• Perform the same operation on the side of the equal sign that does not have a variable.

Example

y + 13 = 25

We want to get the y by itself. Perform the inverse operation. The inverse of adding is subtracting.

- 13 Do the same operation on the other side of the equal sign.

- 13

y = 12

Check the answer in the original equation.

y + 13 = 2512 + 13 = 25

25 = 25

Example 2

k – 12 = 4To get k by itself, we perform the inverse operation. The opposite of “minus 12” is “plus 12.”

+ 12 + 12

k = 16

Check

k – 12 = 4

16 – 12 = 4

4 = 4

Solving Multiplication and Division Equations

Procedure

• Isolate the variable by performing the inverse operation on the number that is attached to the variable.

• The inverse of multiplication is division. The inverse of division is multiplication.

• Use the “Golden Rule.” Perform the same operation on the other side of the equal sign.

Example

m ÷ 3 = 10The inverse of division is multiplication. x 3Repeat the operation on the other side.

x 3

m = 30

Check. Use the original equation.

m ÷ 3 = 1030 ÷ 3 = 10

10 = 10

Example 2

7b = 105The inverse of multiplying is dividing.

÷ 7 ÷ 7

b =10571

735

5

350

15

Check

7b = 1057(15) = 105

105 = 105

Cross MultiplicationMoving the variable around in a function, until the

unknown variable is isolated.

Example: In a² = b² + c², if we have to

solve for c we have to isolate it on one side of the equal sign.

Important: What you do on one side of the equation has to be done on the other side.

Thus: a² = b² + c² - b² leaves c² isolated,

but then we have to subtract b² on the left side of the equation as well:

a² - b² = c²

SIN B =

And solving for B in the following function:

b x x b Something divided by itself = 1

• Remember “of” means multiply in mathematics.•“Per” means division in mathematics.

Solve the Problems3a = 21

To solve a, divide both sides by 3:

a = 7

b + 17 = 59To solve a, subtract 17 from both sides:b = 42

c – 22 = 100To solve c, add 22 to both sides

d = 505To solve for d, multiply both sides by 5d = 250

Exponents

Vocabulary

exponent – the number of times a number is multiplied by itself.

base – the number that is being multiplied.

83base

exponent

This is read “8 to the 3rd power” or “8 cubed.”

It means 8 x 8 x 8.

Evaluating Exponents

25= 2 x 2 x 2 x 2 x 2 = 32

63 = 6 x 6 x 6 = 216

1.34 = 1.3 x 1.3 x 1.3 x 1.3 = 2.8561

Exponents with a base of 10

• Any multiple of ten can be expressed as an exponent with a base of ten.

• The base is 10. The number of zeroes gives us the exponent.

• Example: 100 = 102

• 10,000 = 104

1,000,000 = 106

Writing in Expanded Form Using Powers of 10

• First, write the problem in expanded form.

• Then, change each term to a multiplication of the value and its place.

• Change the place values to exponents with powers of 10.

Example 7, 946

7, 000 + 900 + 40 + 6(7 x 1,000) + (9 x 100) + (4 x 10) + (6 x 1)

7 x 103 + 9 x 102 + 4 x 101 + 6

Percentages

Simply a fraction of 100 (meaning “cent)

Examples:

•1/3 = 33.33% (1÷3x100)

•¾ = 75% (3÷4x100)

•1½ = 150% (3÷2x100)

•15% of 3267 = 490

•230 expressed as a % of 430 = 230÷430x100 = 53,5% On the calculator –

use “shift, %” to do it faster.

Percents Have Equivalents in Decimals and Fractions

20% .2020100

15= = =

Decimal FractionFraction

SimplifiedPercent

Finding a Percent of a Number

Using a Proportion

• Set up a proportion that uses the percent over 100.

• Cross multiply to write an equation.

• Solve the equation.

To set up your proportion, think, “IS over OF equals PERCENT over 100.”

Example – What is 20% of 30?

= 20100

part

whole30x

=100x 30(20)=100x 600

100 100=x 6

Using a Decimal

• Change the percent to a decimal.

• Multiply that decimal by the number you are finding the percent of.

Example – What is 18% of 70?

18% = 0.18

0.18 x 70 = 12.6

Vocabulary

• A percent is a ratio that compares a number to 100. It means “per 100.”

• 49 out of 100 is 49%.

Writing Percents as Decimals

• Imagine a decimal point in the place of the percent sign, and move the decimal two spaces to the left (the same as dividing by 100).

26% .26

40% .40 .47% .07

Writing Percents as Fractions• Place the percent in a fraction with a

denominator of 100.• Simplify the fraction.

26% 26100

1350

75%75

10034

Writing Decimals as Percents

• Move the decimal point two spaces to the right, and add a % symbol (this is the same as multiplying by 100).

.34 34%

.19 19%

.125 12.5%.6 60%

1 100%

Included %When asked to work out the % of reserve fuel when it’s already included in the total given, care must be taken with the mathematics:

Example:

We have 11 500 Lt of fuel which include 15% reserve – how much fuel do we have available without using the reserve fuel?

If we started with 10 000 Lt and then had to add 15% reserve it means:

10 000 x 15% = 1500 + 10 000 = 11 500 Lt total fuel.

To reverse the calculation (how much fuel do we have without the 15%), we have to divide the total with 1.15 (or 115%).

Or 11 500 ÷ 1.15 = 10 000 Lt

Averages

Simply add all the quantities and divide it by the number of quantities

Example:

7, 11, 14, 8, 3, 26

means

(7 + 11 + 14 + 8 + 3 + 26) ÷ 6 = 11.5

Hint

• If you don’t see a negative or positive sign in front of a number it is positive.

9+

Rounding of Decimal Numbers

• When the digit to the right of the last retained digit is 5 or greater, round up by 1

• When the digit to the right of the last retained digit is less than 5, keep the last retained digit unchanged

Example:

23.46 becomes 23.5

And 2.1938 becomes 2.2

Note: Only do rounding at the

final calculation…..

Ratios• A comparison of two numbers

• Can be expressed as:– a fraction– A colon (:)– The word “to”

Example:

A gear ratio of 5:8 can be express as:

⅝ or 5:8 or 5 to 8

Ratios in Aviation

• Compression Ratio• Mach Number• Aspect Ratio• Air-Fuel Ratio• Glide Ratio• Gear Ratio• Interpolation• Trigonometry• Map Scales

No Unit of Measure….

i.e.: cm, lt or nm, etc.

Ratios

• A ratio is a comparison between two numbers by division.

• It can be written in three different ways:

5 to 25 : 2 5

2

Equal Ratios

• When two ratios name the same number, they are equal. It’s like writing an equivalent fraction.

20 : 30Equal Ratios:

10 : 15 2 : 3 80 : 120

Example:If the cruising speed of an airline is 200knots and its maximum speed is 250knots, what is the ratio of cruising speed to the maximum speed?• Solution:

• First express the speeds as a fraction:– Or Ratio =

• Then reduce fraction to smallest terms:– Or Ratio = = or 4 to 5, or 4:5

200

250

200

250

4

5

Angles

Vocabulary

• An angle has two sides and a vertex.

• The sides of the angles are rays. The rays share a common endpoint (the vertex)

• Angles are measured in units called degrees.

Types of Angles

When lines intersect to form right angles, then they are classified as perpendicular lines.

Measuring Angles

• Place the center point of the protractor on the vertex of the angle and turn the protractor so that one side lines up with 0 on the inner scale.

Measuring Angles (strategy 2)

• Place the center point of the protractor on the vertex of the angle. Note where both rays cross the protractor. Subtract the two numbers (from the same scale)

Property of triangles

• The sum of all the angles equals 180º degrees.

90º 30º

60º

What is the missing angle?

70º70º

?+180º70º 70º

?

40º

Classifying Triangles

Classifying by Angle

•Acute triangles have three acute angles.

•Obtuse triangles have one obtuse angle.

•Right triangles have one right angle.

Classifying by Sides

•Equilateral triangles have three congruent sides.

•Isosceles triangles have two congruent sides.

•Scalene triangles have zero congruent sides.

Finding Missing Angles•The three angles of a triangle always add to 180°.

•Use a variable to stand for the missing angle and set an equation equal to 180.

x + 49 + 47 = 180x + 96 = 180 – 96 = -96

x = 84

Trigonometry

The Right Angled Triangle

Trigonometric functions are

commonly defined as ratios of two sides

of a right triangle containing the angle

Study Tip

Acronym's to use:

• Sin-oh

• Cos-ah

• Tan-oa

Example: There is a hill 250’ high, 3000’ from the threshold of the runway.

What must the angle of climb be to clear the hill by 100’?

350’

3000’

Answer:

Tan ∞ = 350

3000

Tan ∞ = 0.116

∞ = 0.116

tan

AoC = 6.65º

90º∞

Can you see it’s a Right Angled Triangle?

Threshold

Hill

•Sin-oh•Cos-ah•Tan-oa

Which ratio to use?

Opposite

Adjacent

Hypotenuse

Thus we use

Tan…

The SINE Rule.A

C

B

c

a

b

aa

SIN ASIN A

bb

SIN BSIN B

cc

SIN CSIN C== ==

Non-Right Angle Triangle

The COSINE Rule.

A

C

B

c

a

b

a² = b² + c² - 2bc x COS A

b² = a² + c² - 2ac x COS B

c² = a² + b² - 2ab x COS C

COSINE RULE is used in NON-RIGHT ANGLED

TRIANGLES when given the length of two sides and one angle and the unknown is the length of the side

opposite the known angle or when given the length of all three sides

and the unknown is any angle.

Example:

Solve the length of Side a.a² = b² + c² - 2bc COS Aa² = 3² + 7² - (2 3 7 COS 40)a² = 9 + 49 - 32,17a² = 25,83a = √25,83 a = 5,08 UNITS

SINE RULE is used in NON-RIGHT ANGLED

TRIANGLES when given the length of two sides and one angle and the unknown is the length of the side

adjacent to the known angle.

SIN B =

SIN B =

At 1205, aircraft A and B are 75 nm's apart and are on a collision course. Aircraft A 330 Kts. Aircraft B 360 Kts. The relative bearing from A to B is 075. What angle needs to be closed by aircraft B to intercept aircraft A?

SIN B = 0.885

B = 62.3º

Example:

?

• Sine– The most fundamental sine wave has the

graph shown. – It fluctuates from 0 to a high of 1, down to –1,

and back to 0, in a space of 2.

Graphs of the Trig Functions

• Cosine– The graph of cosine resembles the graph

of sine but is shifted to the left. – It fluctuates from 1

to 0, down to –1,

back to 0 and up to 1.

Graphs of the Trig Functions

THE CIRCLE

Various questions may be asked relating to the radius, diameter, surface or circumference of a circle.FORMULA

d (diameter) = 2rc (circumference) = 2rs (surface) = r²

EXAMPLE 1:If the radius of a circle is 7 units, determine its circumference?

c = 2r= 2 3,14 7= 43,98 UNITS

rd

c

s

To Calculate the Radius of a TurnTAS 240 KtsRATE 1 TURNRATE 1 TURN = 2 mins. (360º)

What is the radius of the turn in feet?

Circ =240 x 6080' x

Circ =48640’

Circ = 2 r

r = Circ/ 2

r =48640/ 2

r =7741'

2

60

Example:

Convergency = Dlong x sin Mid Lat

Example:

What is the value of Convergency between Point A(26º40’S 24º15’E) and Point B (26º40’S 55º15’E)?

Solution:

The difference in longitude is: 55º15’ - 24º15’ = 31º

And: Convergency = Dlong x sin Mid Lat

Convergency = 31º x sin 26º40’

Convergency = 31º x 0,449

Convergency = 13,91º

Pythagoras• Used with Right Angle Triangles• Used for DME Slant Range Calculation

90º

A

B

C

a

b

c

a² = b² + c²

Example:

An aircraft at 35 000' is 60 DME from a ground station. What is the ground range?

90º

A

B

C

a

b

c35000

60

?

Solution:

a² = b² + c² or

b² = a² - c²

b² = 60² - (36000÷6080)²

b² = 3564.9

b = √ 3566,8

b = 59,72 nm (Ground Dist.)

Triangle of Velocities

DepartDestination

Air Position

Ground Position

THDG/TAS

Air Vector/Air Plot

Alw

ays from

Air to Track

W/V

Ground

Vector

Track Plot

TRK/GS

Drift

Angle

Vectors - Lines with Direction and speed

Interpolation: 1. to insert between or among others2. to change by putting in new material3. to estimate a missing value by taking an average of known values at neighboring points

Interpolate one series at a time:

PALT 14 000 16 000

AUW 12 000 LBS 1237 1268

15 500 1268 – 1237 = 31/2000 X 1500 = 23,25 (+1237)

= 12601260

AUW 10 000 LBS 1098 1120 1120 – 1098 = 22/2000 X 1500 = 16,5 (+1098)

= 1114.5

1115

AUW 10 750 LBS1260 – 1115 = 124/2000 X 750 = 54,37 (+1115)

= 1169

1169

Exercises:

1. Subtract the following numbers:

5920

-2744

-4889

3921

-492

= 10 124

2. Express as a %:

13/44

= 29.54%

26/85

= 30.58%

1/33

= 3.03%

3. If full tanks of fuel = 90 000 kg of fuel, and 15% reserves are carried, what is the fuel without reserves?

90 000 ÷ 1.15

= 78269.86 kg

4. Logging the following hours per week, what is the average trip length (hour and minutes)?

3.73

4.5

1.9

2.5

5.7

3h39min57sec

5. Sin A = .0876. What is value of A?

A = 5.02º

Primary Radar RangingA radar system has the following specifications : PRF of 400 PPS and a pulse width of 2µ seconds. Find the maximum and minimum range.

Range (M) = Speed X Time

2

Range (M) = 3 x 108

Meters / second X

2

Range (M) =600 Meters

2

Range (M) = 300 Meters Or 0.3 KM

106

2 X Seconds

Minimum Range :

LSS

TASMachNumber

If the Local Speed of Sound is 1100 feet per second, what is the TAS If the Local Speed of Sound is 1100 feet per second, what is the TAS of an aircraft flying at Mach 0.73?of an aircraft flying at Mach 0.73?

We can not work in feet per second as TAS is in knots. To We can not work in feet per second as TAS is in knots. To convert feet per second proceed as follows : 1100 x 60 = 66000 convert feet per second proceed as follows : 1100 x 60 = 66000 feet / minute: 66000 x 60 = 3960000 feet / hour: 3960000 / 6080 feet / minute: 66000 x 60 = 3960000 feet / hour: 3960000 / 6080 = 651 Kts = 651 Kts

32.651 73.0TAS

Knots .5475 .32651 73.0

LSS

TASMachNumber

Two aircraft flying at the same Flight Level, Aircraft A has a Mach Two aircraft flying at the same Flight Level, Aircraft A has a Mach Number of 0.815 and a TAS of 500 Knots, Aircraft B has a Mach Number of 0.815 and a TAS of 500 Knots, Aircraft B has a Mach Number of 0.76. At what Flight Level are the aircraft flying and Number of 0.76. At what Flight Level are the aircraft flying and what is the TAS of aircraft B?what is the TAS of aircraft B?

273 945.38 coatLSS

KnotsLSS 5.613

273 945.38 5.613 coat

273 945.38

5.613 coat

273 75.15 coat

273 275.15 coat

273 06.248 coat

coat 273 06.248

9.24 coat

Problem Solving

Problem Solving is easy if you follow these steps

Understandthe

problem

Step 1 – Understand the problem

• Read the problem carefully.• Find the important information.• Write down the numbers.• Identify what the problem wants

you to solve.• Ask if your answer is going to be

a larger or smaller number compared to what you already know.

Step 2 - Decide how you’re going to solve the problem

Choose a method

Use a graph Use formulasWrite an equationMake a listFind a pattern Work backwardsUse reasoning Draw a pictureMake a table Act it out

Step 3 - Solve the problem

LSS

TASMachNumber

Example:

Step 4 - Look Back & CheckReread the problem

Substitute your new number Did your new number work?

Strategy

• When a problem contains difficult numbers (like fractions or mixed numbers), then imagine the problem with simpler numbers.

• Solve a problem using the simpler numbers.• Check to see if the strategy worked. Does the

answer make sense?• Go back and use the same strategy, only this

time you can use the more difficult numbers.

If you get stuck…

• Remember, there are only four operations to choose from: multiply, divide, add, or subtract.

• Try a few operations and see which answer makes the most sense.

Words that mean “Add”

• In all

• Increased by

• How many / how much

• Sum

• Total

• Added to

• Altogether

Words that mean “Subtract”

• How many / how much MORE

• Decreased by

• Difference

• Less than

• Fewer than

• Left / left over

• Reduced by

Words that mean “Multiply”

• Of

• Product

• Times

• Multiplied by

• In all / total / altogether (when referring to repeated addition)

Words that mean “Divide”

• Quotient

• Out of

• Per

• Ratio

• Percent

E:\Cx-2e220.exeNavigation Computer

Study Methods

How to Mind Map1. Use just key words, or wherever possible images. 2. Start from the center of the page and work out. 3. Make the center a clear and strong visual image that depicts the

general theme of the map. 4. Create sub-centers for sub-themes. 5. Put key words on lines. This reinforces structure of notes. 6. Print rather than write in script. It makes them more readable and

memorable. Lower case is more visually distinctive (and better remembered) than upper case.

7. Use color to depict themes, associations and to make things stand out.

8. Anything that stands out on the page will stand out in your mind. 9. Think three-dimensionally. 10. Use arrows, icons or other visual aids to show links between

different elements. 11. Don't get stuck in one area. If you dry up in one area go to

another branch. 12. Put ideas down as they occur, wherever they fit. Don't judge or

hold back. 13. Break boundaries. If you run out of space, don't start a new

sheet; paste more paper onto the map. (Break the 8x11 mentality.)

14. Be creative. Creativity aids memory. 15. Get involved. Have fun.

Your mind think in

Pictures!!!

Eggs Pencils

Bacon Spaghetti

Knife Yoghurt

Bananas Syrup

Dough Nuts Red Paint

Memorize the following shopping list in 10

seconds….

Body List Method

1 = Toes

2 = Knees

3 = Thighs

4 = Back side

5 = Love Handles

6 = Shoulders

7 = Throat

8 = Face

9 = Point

10 = Ceiling

1. Eggs2. Bacon3. Knife4. Bananas5. Dough Nuts6. Pencils7. Spaghetti8. Yoghurt9. Syrup10.Red Paint

Now create your own house list….

Always use something that

you know already as your list….

11 Tips to Improve Studying Results 1  Study in Short, Frequent Sessions – no more than one hour at a time, with 10min break.

2  Take Guilt-Free Days of Rest.

3  Honor Your Emotional State. Do not study if you are tired, angry, distracted, or in a hurry.

4  Review the Same Day.

5  Observe the Natural Learning Sequence. if you try first to grasp the big picture and then fill in the details, you often have a more likely chance of success.

6  Use Exaggeration. Why do runners sometimes strap lead weights to their legs?

7  Prepare Your Study Environment. For example, do you need special lighting, silence, music, privacy, available snacks, etc.?

8  Respect “Brain Fade.” As you place more information on top, the lower levels become older and less available to your immediate recall. The trick here is simply to review.

9  Create a Study Routine. An effective way to do this is to literally mark it down in your datebook calendar as if you have an appointment, like going to the doctor. For example: “Tuesday 3-4:30 P.M. — Study.

10   Set Reasonable Goals. Set your vision on the long-term dream, but your day-to-day activity should be focused exclusively on the short-term, enabling steps.

11   Avoid the Frustration Enemy. Don’t waste energy blocking, getting upset, and thinking that you’re not good enough — simply keep moving forward at a slower (but un-blocked) pace.

The 7 Habits of Highly Effective People

Habit 1: Be Proactive

Habit 2: Begin with the End in Mind

Habit 3: Put First Things First

Habit 4: Think Win-Win

Habit 5: Seek First to Understand, then to be Understood

Habit 6: Synergize

Habit 7: Sharpen the Saw

Use a Diary – any plan is not a plan untill it’s written down. That includes a study plan..

The Time Management Quadrant

•Crises

•Pressing Problems

•Deadline driven projects, meetings, preparations

•Interruptions, phone calls

•Some mail, some reports

•Some meetings

•Many popular activities

•Preparation

•Prevention

•Values clarification

•Planning

•Relationship building

•Empowerment

•Trivia, busywork

•Some telephone calls

•Time wasters

•“Escape” activities

•Excessive TV

NOT URGENTURGENT

IMP

OR

TA

NT

NO

T IM

PO

RT

AN

T

1

43

2

Make it FUN!!