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No part of this publication may be reproduced in whole or part, stored in a

retrieval system, or transmitted in any form or by any means, electronic,

mechanical, photocopying, recording, or otherwise without written permission

of the author.

Copyright 2009 By Scott P Hicks

All rights reserved.

Book and cover design by Scott P Hicks

Growing with Mathematics is a trademark of The McGraw-Hill Companies,

Inc. 2004

Printed in the U.S.A.

ISBN: 978-1-929179-55-8


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Table of Contents

TOPIC 1 MATHEMATICS IN OUR WORLD 3

TOPIC 2 PROPERTIES OF POLYGONS AND CIRCLES 6

TOPIC 3 USING DIVISION 11

TOPIC 4 INVESTIGATING LENGTH AND PERIMETER 13

TOPIC 5 ADDING AND SUBTRACTING COMMON FRACTIONS 15

TOPIC 6 ANALYZING EVERYDAY DATA 21

TOPIC 7 WORKING WITH LARGE NUMBERS 22

TOPIC 8 USING MULTIPLICATION 24

TOPIC 9 THINKING VISUALLY 26

TOPIC 10 WORKING WITH TIME 30

TOPIC 11 ADDING AND SUBTRACTING DECIMAL FRACTIONS 32

TOPIC 12 RELATING VOLUME, CAPACITY, AND WEIGHT 37

TOPIC 13 EXPLORING MULTIPLICATION AF FRACTIONS 39

TOPIC 14 USING DIVISION TO FIND RATES 43

TOPIC 15 RELATING CIRCUMFERENCE AND DIAMETER 45

TOPIC 16 WORKING WITH FRACTIONS 48

TOPIC 17 WORKING WITH AREA 53

TOPIC 18 PROBABILITY AND STATISTICS 56

TOPIC 19-20 ALGEBRAIN THINKING / POLYGONS & POLYHEDRA 58

TOPIC 21 MONEY AND TIME 60

TOPIC 22 WORKING WITH DIVISION 63

TOPIC 23-24EXPLORING PERCENT / APPLYING MATH WE KNOW

67

MUST KNOW VOCABULARY 68


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Topic 1Whole Numbers:

Whole numbers are 0, 1, 2, 3, 4, 5 and so on. They are numberswithout fractions or decimals.

Common Fractions and Decimal Fractions areNOTWhole Numbers.


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Thousands Hundreds Tens Ones

9,256


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TimeHours : Minutes : Seconds

6:32:201 Hour = 60 Minutes

1 Minute = 60 SecondsRemember! When you add or

subtract time you MUST carry or

borrow at 60!

(Fractions of an hour)

hour = 30 minutes

hour = 15 minutes


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Topic 2Shapes


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Surface

(or Face)

Vertex

Edge


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How to use a ruler

Parts of a circle

8 centimeters

First step:

Line up the end ofthe line on the zero.

Second step:

Round to the nearest unit

of measurement

Radius

Diameter

Circumference


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How to use a protractor

Step one:

Put the vertex of the anglein the center of the hole at

the bottom of the

protractor

Step two:Start at the zero

where the linecrosses. (In this

example the line is

going to the side

where the zero is theon the outside of the

protractor)

Step three:

Read the number where the other linecrosses. (Remember in step two of this example we

found that we are using the outside numbers.)

79


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Flipping a shape:

Turning (rotating) a shape:

90

90 turns change

horizontal lines to

vertical lines.

What is a 90 turn?


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Topic 3

Dividing

Remember:

Showing your work helps you in math.


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3)372124

3076

1212

0

Dividing by two digit numbers is exactly the same process aswith one digit numbers


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Topic 4

1 kilometer = 1000 meters

1 meter = 100 centimeters

1 centimeter = 10 millimeters

PREFIXES

KILO = THOUSAND

CENT = HUNDRED

DEC = TEN


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Perimeter

To find the perimeter, simply add all the sides of a shape.

A

B

C

D

A + B + C + D =Perimeter

A B

C

A + B + C = Perimeter


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Topic 5


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When adding fractions withcommon denominators, simply add

the numerators.

When adding fractions withuncommon or different

denominators, you must find acommon denominator first.

2

5

1

5

+ =3

5

The denominator doesnot change.

25 13+ =

101520

2530

6912

1518

First:

Find a common multiple ofthe denominators.


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2

51

3

=

This number is your newdenominator for both

fractions.

=

6

155

1555

3

3

What ever you do to thedenominator of a

fraction you must do

the same to the

numerator!

6

15

5

15+ =

Now add the new fractions

11

15Subtracting fractions has the same

procedure as adding them.

1

3

Parts of a fraction

Numerator

Denominator

Fraction Bar


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What is a fraction?It is a piece of a whole

What is the fraction of blue?

There are 5 blue pieces

There are 8 total pieces

5

8


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12

20

35

2

2

2

2

2

2

There are 20 stars.12 of the stars are circled.

That fraction is

We also see that 3 out of 5 columns arecircled. We can use this to show the

simplified fraction of

Finding Equivalent FractionsRemember:

To find equivalent fractions whatever

you do to the denominator you mustdo to the numerator

12

24

48

816

= = =


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How do I find equivalent fractions with

the same denominators?1

2

13

=

=

??

??

Our first step is to find a

common denominator.

First:

Find a common multiple of thedenominators.

(That is the new denominator for

both fractions.)

2

4

6

8

3

6

9

12

1

2

1

3

=

=

3

6

2

6

What did we do to thedenominators?

2

2

3

3REMEMBER!

What ever you do to the

denominator of afraction you must do the

same to the numerator!


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Topic 6Finding the Mean is the same thing as finding the Average.

2+5+6+6+8+9 = 36 36 6

How do I find a Median?The middle number of a set of numbers is called the median.

Finding equivalent fractions

There are 6

numbers

To find the mean or average you add all of the numbers,

then you divide by the number of numbers.

5, 12, 35, 110, 115

13

39

=To find the equivalent fraction

we need to find out whathappened to the denominator.

In this example 3 is multipliedby 3 to get nine.

REMEMBER!

Whatever you do to thedenominator you must do to

the numerator

3

3


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Topic 7

SpellingOne (1)

Two (2)

Three (3)

Four (4)

Five (5)

Six (6)

Seven (7)

Eight (8)

Nine (9)

Ten (10)

Eleven (11)

Twelve (12)

Thirteen (13)

Fourteen (14)

Fifteen (15)

Sixteen (16)

Seventeen (17)

Eighteen (18)

Nineteen (19)

Twenty (20)

Thirty (30)

Forty (40)

Fifty (50)

Sixty (60)

Seventy (70)

Eighty (80)

Ninety (90)

Hundred (100)

Thousand (1,000)

Million (1,000,000)Billion (1,000,000,000)

Trillion (1,000,000,000,000)

Look for a pattern:

258,632,123

Hundreds, Tens, Ones, Hundreds, Tens, Ones, Hundreds, Tens, Ones

No matter how big the number is, it ALWAYS follows the same pattern(ones, tens, hundreds)

5 2 6 8 9 1

Five hundred twenty six thousand, eight hundred ninety one


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One hundred twenty five THOUSAND six hundred thirty eight

Million = 250,000 Million = 500,000

Million = 750,000

Whenever you come to a comma you mustput words showing the value of the

numbers before the comma.(Million, Thousand etc)


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Topic 8

Order of Operations

Please ParenthasesExcuse Exponants

MyDear

MultiplicationDivision

AuntSallie

AdditionSubtraction

Multiplying Double Digit Numbers

43

x2521586

1075

1

NOTICEWhen you multiply with

the tens you MUST linethem up under the tens.


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Multiplying with a Decimal

This is done the EXACT same waywith one extra step at the end.

43x0.25

21586

10.75

+

Extra step:Count the number of

digits AFTER any

decimal in the problem

Put the decimal so thatthe same number of

digits are after thedecimal in the answer.


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Topic 9Birds-Eye View means looking at something like you were a

bird flying over it.

What would it look like from the top?

The box in the back is

higher than the rest of

the boxes. This means

that it must be sitting

on another box.

Even with the box sitting ontop of another box it still

would look the same from abirds-eye view.


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FLIP

Slide

Flipping something just meansturning it over (like flipping a card)

Sliding something just meansmoving it over (like pushing a toy)


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Line of Symmetry

Vertical means up and down

Horizontal means side by side

The line of

symmetry is

the line in anobject or shape

where it can be

folded in half


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