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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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