# Sarah

Document Sample

```					  Sarah Costanzo

Math Mania, Hero of Math,
Explosion of Knowledge
2008-2009
Squaring Numbers
12 = 1
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100
112 = 121
122 = 144
1000 squared
is 1,000,000!
Multiplying 6’s
6x1=6
6 x 2 = 12
6 x 3 = 18
6 x 4 = 24
6 x 5 = 30
6 x 6 = 36
6 x 7 = 42
6 x 8 = 48
6 x 9 = 54
6 x 10 = 60
6 x 11 = 66
6 x 12 = 72
Combining Numbers
Combining numbers looks like this:

2y+4y=6y
2t-1t=1t
This is how you solve one.
Say y is a cookie. Your friend has six cookies
and you have eight cookies. If you wanted to see how
much you have, the problem would look like this: 6y
+8y =14y.
You just add up the cookies and get the
With addition, you’re buying more. You do it the same
with subtraction, except you’re eating the cookies that
you bought that are shaped like y’s. By the way, a
subtraction problem would look like this:
14y-8y=6y.
Explaining how to multiply two or
three digit numbers by one digit
numbers
If you have a multiplication problem
like this it can be a little hard.

•            82
•            x6
First you multiply the two on the
end.

•           82
•           x6
12
Then carry the one and multiply
eight times six.
1

•          82
•          x6
482
Then you add 48 plus one, which
equals 49…

492
Multiplying by Lots and Lots of
Ones
Like 1, 11, 111, 1111, 11111, etc.
You all know 1 times 1, right?

1x1=1
Do you know 112?

11 x 11 = 121
There is a joke in there. Did you
see it? Well if you didn’t, this next
one will show you the joke. But if
you still don’t understand it,

Do you know 111 x 111?

1112 = 12321
NOW do you get the joke? Heh heh
heh heh. What? You don’t? You
don’t have good eyes.
Do you know 11112?

11112 = 1234321
Do you know 111112?

111112 = 123454321
1111112

12345654321
11111112

12345657654321
111111112

123456787654321
1111111112

12345678987654321
11111111112

25937424601
111111111112

285311670611
1111111111112

3138428376721
11111111111112

34522712143931
Riders of the Jungle Cats
This puzzle is called The Rider of the Jungle
Cats. You have to try to get the rider to ride
on both cats at the same time correctly.
This won’t work.
Hmmm……..
Do you give up? Well I’ll tell you the
solution on the next slide.
Solution to The Riders of the
Jungle Cats
• The cats are JUMPING, not walking as
they appeared before. Tricky, tricky, tricky.
You know what I’m saying? Who wants to
make a puzzle when the cats are walking?
It’s boring.
Diameter, Circumference
Meaning of Diameter and
Circumference:
Diameter is a line through the middle, and
Circumference is an outline of a circle.
(See the lines).
diameter   circumference
Factors
Factors are numbers that can
multiply into any number.
So the factors of 70 are 10, 7, 70,
and 1 because you can multiply
them into seventy. See?

7 x 10 = 70, 70 x 1 = 70
Here’s a test. Is 7 a factor of 24?

Yes              No
Congratulations if you got it right!
You have learned your factors! You
won a quarter!
CAWWNAAUVB0A10

(Calculating Averages With Whole
Number Answers and Using
Values Between 0 and 10.)
This is Our Math Problem.

1
9
2
Confusing, isn’t it? Well this
section in my math
PowerPoint will show how
to solve this.
Our numbers are one, two, and
nine right? So one plus two equals
three.

1         3          2
So you add three plus nine…
Divide the answer by three, and get
Area

The Area of the Auditorium
Area is…
• Area is the length times the width of a
shape. So if a rectangle was two meters
high, and six meters across, you would
multiply six times two and get 12, in this
case, 12 square meters.
The length of the auditorium (left to
right) was 13.6 meters. This is the
side we should be working on.
The Width of the Auditorium is 10.7
meters. This is the side we should
be working on.
So What is 10.7 times 13.6?
Please take your time to figure this
out.
If you said 145.52 you are correct!
You won a penny!
Explaining Volume Formula
You all know area, right?
It’s length times the width, right?
Well Volume is very similar.
It is length times the width, times
the height.
Length,
Times the Width,
Times the Height.
Lets say the length, that’s this line
here, is eight centimeters long.
We’ll put that on our little chart
here…

Ok, that’s recorded down.
Now lets say that the width, that’s
this line right here, is six
centimeters.
Now lets put that on our little chart
here…

Ok, there we go.
And now lets say the height is,
that’s this line right here, is two
centimeters.
So that’s on our little chart here, so
on the next slide you’ll see the
finished product of our little chart.
Height   Width   Length

cm       cm       cm
So you have to multiply two, times
six, times eight. Use this time to
figure it out.
If you said 96 you are right! You
have won a million dollars!
Gas Change
This is my graph of the Arco and
Mobil Gas Stations.
Sarah's Arco and Mobil Gas Prices Graph

\$3.000
\$2.500
\$2.000
Arco
\$1.500
Mobil
\$1.000
\$0.500
\$0.000
9

9

9

9

9

9
00

00

00

00

00

00
/2

/2

/2

/2

/2

/2
11

12

13

14

15

16
5/

5/

5/

5/

5/

5/
Did you notice the line going up and down a
little? Well if you did, you have good
eyesight. The Arco and Mobil gas stations
didn’t change the gas prices a whole lot in
a week. Personally, I think they should’ve
lowered their prices a little bit lower,
because the lines were a little bit high on
my chart.
Geometry
Point
Line
Line Segment
Ray
Vertex
Parallel lines
Intersecting lines
Perpendicular lines

90
Right Angle

90
Right Angle
ABC Angle/CBA Angle
A

C
B
Right Angle

90

0
Acute Angle
Obtuse Angle
straight angle

180
Triangles

( still in the geometry section)
Right Triangle

1 right angle
Scalene Triangle

no equal sides and no
equal angles
Isosceles Triangle

At least 2 equal sides and
at least 2 equal angles

( still in the geometry section)
Square

a parallelogram with four
equal sides and four right
angles
Parallelogram

Opposite sides are
equal and parallel
Rhombus

A parallelogram with
four equal sides
Rectangle

A parallelogram with
four right angles
Isosceles Trapezoid

One pair of parallel
sides and one pair of
equal sides
More geometry
pentagon
Perimeter
The Point

Sarah
(This may not be geometry to you, but
I think of it as geometry. So if you think
it is something else, too bad.)
There once was a point named
Fred. He was very greedy because
no one could see him because he
was so small.

Hi.

Who
said
that?
So he went to Billy Bob Joe, his
friend that could shift others into
greater shapes.

Sure.         Can you change
me into a shape
that people could
see?
So Billy Bob Joe turned him into
a…
…Line! So Fred said his thanks
and looked in a mirror. When he
saw himself, he went on…
And on…
And on…
Until he realized that he went on
forever!
So he went back to Billy Bob Joe to
turn into something shorter. So he
turned into some….
…Perpendicular Lines! So Fred
said his thanks and went to look in
a mirror. He looked like a giant
plus! But he had little squares
indicating right angles.
So he thought, if being a
perpendicular line meant he had
indicators saying there were right
angles, why couldn’t he just be a
right angle himself! So he went
back to Billy Bob Joe and turned
into a…
…Right Angle! He said his thanks
and looked in a mirror. He saw that
the angle on himself were just like
a square’s! That’s when he saw the
indicator.
Furious, he stomped back to Billy
Bob Joe and changed into a…
…Triangle! He looked into a mirror
and saw a face on a shape with no
indicators! He was really happy.
But not happy enough…
He saw only three sides. He
wanted more! So he went back to
Billy Bob Joe and turned into a…
…Square! He went to look in a
mirror and saw a shape with four
sides with right angles! He was
happier than with three! But not
enough…
He went back to Billy Bob Joe and
turned into a…
…Pentagon! He looked into a
mirror and saw a shape with FIVE
sides! He was WAY happier than
with three! But not happy enough…
He went back to Billy Bob Joe and
changed into a…
…Hexagon! He looked into a mirror
and saw a shape with six sides! He
LOVED this shape! But
unbelievably, not enough…
He wanted MORE! SO he went
back to Billy Bob Joe and turned
into a…
…Heptagon! He looked into a
mirror and saw a seven sided
shape! He REALLY REALLY
LOVED this shape! But not
enough!
He went back to Billy Bob Joe and
changed into a…
…Octagon! He looked into a mirror
and saw an eight sided shape! He
REALLY REALLY REALLY
REALLY LOVED this shape! But he
wasn’t happy enough…
He went back to Billy Bob Joe and
changed into a…
…Nonagon! He looked into a mirror
and saw a nine sided shape! He
loved this so much that he wanted
to explode! But he wanted more…
He ran back to Billy Bob Joe and
changed into a…
…Decagon! He looked into a mirror
and saw a TEN sided shape! But
he wasn’t happy anymore…
Because he exploded and had to
be swept away.
Algebra Puzzle

Room 18 Website
The Algebra Puzzle Starts Like
This.
The row that is highlighted will be
the row I am working on.
We will start with this row first.
Since it is Easy we will do it first.
• What is 6÷3? You’re right! It is 2! Since all
the items in that row are guitars, you slide
the bar that is below the guitar on the right
to 2. Like this:
Then you move on to the next
easiest one.
• Now, since the guitars are 2, 18-2=16, and
16÷2=8, there are 2 ladybugs that equal 8!
So now you know that the ladybugs are 8.
So now it’ll look like this:
Now we just have to figure out the
umbrellas!
The easiest one with umbrellas
should be this one.
• So 42-2=40, and 40÷2=20, so umbrellas
are 20! Just put it in, press check it, and
you’ll see if you won!
We solved the puzzle!
Strange things
Möbius Strip
Numbers
6,00   7,00   8,00
0      0      0
450   500
400
Rounding Numbers
Rounding to the nearest hundred
150

140         160

130                     170

120                             180

110                                       190

100                                         200
Rounding to the nearest thousand
2,500

2,400           2,600

2,300                      2,700

2,800
2,200

2,100                                             2,900

2,000
3,000
  5

4             6

3                       7

2
8

1                                         9

0                                                 10
Rounding to the nearest ten with a little surprise!
Graphs
This is a bar graph that I made in
Skittles Column Graph
• My mode is 6 & 5
Sarah

7
6
5
4
3
2
1
0
Lime   Lemon    Orange   Grape   Strawberry
Skittles Pie Graph
• My mode is 6 & 5 again

Sarah

Strawberry, 6,
Lime, 2, 8%
25%
Lemon, 6, 25%

Grape, 5, 21%
Orange, 5, 21%
Vons pears are \$1 every 3 pounds.
Pounds   3      6     9      12

Cost    \$1    \$2     \$3     \$4
Geometric Shapes

My Math Shapes
Small Red Square
Medium Green Circle
Large Blue Rectangle
Medium Orange Pentagon
Small Turquoise Hexagon
Medium Dark Red Trapezoid
Large Teal Triangle
Small Pink Cylinder
Medium Yellow Cube
Polygons
These are Polygons.
Taking apart Excel squares and
making them different
3 by 3
1 by 8
2 by 3
3 by 8
Mr. Gallon
Quart
Measurement
1 liter = 1000 ml
liter

milliliter
Decimals
0.5 = 5
10
0.1 = 1
10
0.9 = 9
10
0.8 = 8
10
1.0 = 1
0.2 = 2
10
0.3 = 3
10
0.7 = 7
10
0.4 = 4
10
Number Problems

With Base Ten Blocks
How Many?
1,000    100
10

1
In the last slide you saw base ten
blocks. Here is the answer!

3,328
Congruency
Congruency is…
• Congruency is two or more shapes that
are exactly the same size and shape. If
there were two shapes that were the
same, there would be two congruent
shapes.
These shapes would be congruent.
These shapes would not be
congruent.
Would these shapes be congruent?
Five Square Puzzle
The Five Square Puzzle is hard.
You just need twelve toothpicks.
The rules are, you have three
squares in the starting position.
You have to move exactly three
toothpicks and make five squares.
These are our toothpicks.
This is the starting position.
So this is the first toothpick you
should move.
Would these ones be congruent?
Explaining Area and Perimeter
Area
• Area is how many
figures or sections
that are in a shape.
The area is how many
squares are in this     For example, this
rectangle.              rectangles area is
eight
Perimeter
• Perimeter is how
many lines are on the
outside of a figure.
This penguin shows
the perimeter of this
square.
Explaining Percentage
Percentage is a fraction that always
has 100 on the bottom.
• 40% = 40            98% = 98
•      100                 100
You never change it, even if it is a
very high number.

1000
100
Decimals and Fractions
The shaded part of this square in a
fraction is 30/100.

The shaded part of this square
in a decimal is 0.030.
The shaded part of this square in a
fraction is 90/100.

The shaded part of this square in
a decimal is 0.090.
Sudoku Solving
4
4
4
1
4
1
4
3 1
4
3 1
3 4
4
3 1
Prime and Composite
Numbers
A Prime Number is,
• A number that is only divisible by itself and
one. Most all odd numbers are prime.

7 divided by 1 is 7, and 7 divided by 7 is
one. It can’t be divided by any other
number.
A Composite Number is,
• A number that can be divided by 3 or more
numbers. Almost all even numbers are
composite except 2 (which can only be
divided by itself or one.

8 can be divided by 1, 8, 2, and 4 so it is
composite.
On the next slide it will show you numbers
going into groups of Prime and Composite
numbers. There will be circles labeled
Prime and Composite.
19       72
1        2     31 13
18        6 5
40
14
PRIME

COMPOSITE
Mixed Numbers
This is how you use a Mixed
Number
A mixed number is made with whole
numbers (big number) and the fraction. An
example of a mixed number might look like
this.

5
7   4
These are the kinds of shapes you
use for Mixed Numbers.
Do you know the answer to this
problem?

It is easy to answer if you count the
shapes that are pink and say how
many pinks there are
It is easy to answer if you count the shapes
that are pink and say how many pinks
there are. Then on the bottom you say
how many shapes there is in all. You see
one block where there is all pink. So
before the fraction you put a big number
telling how many blocks are all pink.
(tip. When you do the bottom of the fraction
you only put the number of blocks for the
block you are trying to solve.)
You can guess the answer and I
will tell you on the next slide.
This is the answer to that problem.
Moving Frogs

Room 18 Excel Frog Challenge
Trying to Move the Frogs to the
Opposite Side in two Minutes
The First Frog
The next Frog
The next Frog
And the next
Next one
And the next Frog
Go Frogs!
Almost…
Getting VERY Close.
The End is Very Near
Moving the next frog
3 more Frogs to move
2 more
1 more
Ta-Daa!
The next slide shows an example
of tessellation.
These shapes Tessellate.
More Tessellating
• Shapes that tessellate.
Rectangles Tessellate.
Rhombuses Tessellate.
Trapezoids Tessellate.
Squares Tessellate.
Paperwork instructions
• You have 13 OLG shortbreads to share
fairly with TukTuk (the towel) Show exactly
how you could divide them up.
6

R1

6
• Problem, A ball rebounds 1 half of the
height from which it is dropped. Assume
the call is dropped from a building at a
height of 128 feet. How far will the ball
bounce up it when it bounces the fourth
time?
64

128 FEET
32

16
8
• problem, The farmer has to get three
things across the river. They are a fox,
chicken, and wheat. The fox and the
chicken can’t be alone together because
the fox will eat the chicken, and the
chicken can’t be alone with the wheat
because the chicken will eat the wheat.
Here is my answer to that problem.
How Many Days will J.J. need?
• A Frog named J.J. fell down a 10-foot well.
He cannot hop out. He has to climb out.
He climbs three feet a day, but during the
night, while sleeping, he slips down two
feet. At this rate, how many days will it
take for J.J. to climb out of the well?
Let’s help poor J.J. get out of this
large well! 
10
9

8

7

6

5
4
3

2
1             Help Me!
0
J. J. will
get out of
10
9
the well by
8    going up
7
three in the
6

5
day, and
4    going down
3
two in the
2
1    night! Let’s
0
Go!
J. J. is home! He’s free!

J. J.’s Home
Perimeter
The perimeter is 14.
The perimeter is 24.
The perimeter is 18.
Pythagorean Theorem
A2+B2=C2
32+42=52
3 meters
9+16=25
Side A

4 meters   Side B
Money Decimals
\$0.25 (also known as quarter)
\$0.25 = one fourth = twenty five
one hundredths.
\$0.50 (also known as half dollar)
\$0.50 = one half = fifty one
hundredths.
\$0.05 (also known as nickel)
\$0.05 = one twentieth = five one
hundredths.
\$0.01 (also known as penny)
\$0.01
Math Triangles

Multiplication and Division
This is a Multiplication Math
Triangle.

To find out the answer,       The question
you multiply the two          mark is the
eights that are already       answer to this
filled in.                    math problem.
8

8                    ?
This is an inch.
The Fibonacci Sequence
This is the Fibonacci Sequence.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 149,
and so on. If you may have noticed, the
Fibonacci Sequence is a sequence of
numbers adding the last two in the
sequence.
0+1=1…
1+1=2…
2+1=3…
And so on.
The New Penny
The New Penny Looks Like This.
The Other Side Looks Like This.
This Side
Probably
Won’t Ever
Change.
The Circumference of my Penny
is…

5.969021
The Mass of my Penny is…
The Radius of my Penny is…

0.95 cm
The Diameter of my Penny is…
The Area of my Penny is
2.8352849
Multiplying by 10, 100, and
1,000
This is the type of multiplication
problem we are working on.

50
x 40
?
To Solve a ten problem, you first
put the zeros in the trash can.

50
x 40
Then you multiply the remaining
numbers.

5
x4
20
Then after you’ve got the answer,
you take the zeros out of the trash
can and onto the answer!

20
00
Glossary
Bar Graph
Meaning:
• A Bar Graph is a graph with bars going up
to the requested amount.
100
80
60
40
20
Century
Meaning:
• A century is something that lives/is there
100 years.

He lived a
century! 100 years later.
2009
Congruent
Meaning:
Same length, size, color, and shape.

These rectangles are congruent.
Meaning:
• A decade is something that lives/is there,
for 10 years.

It has been a
2009                       10 years later.
Denominator
Meaning:
• The denominator is the bottom of a
fraction.

5
6
Dozen
Meaning:

• A dozen is 12 of something.
Gross
Meaning:
• A gross is 144 in math.
Since 12x12=144, this
is a gross.
Fortnight
Meaning:
• A fortnight is 14 days at a time.

Now                           14 days later.
Baker’s Dozen
Meaning:             This can not be!
There is a whole
• A baker’s dozen is 13. I don’t know why it
one extra donut! I
will be ruined!
is 13.                               Get it away! Get
it AWAY!
Millennium
Meaning:
• A millennium is something that is there
1,000 years. For example, a tree that has
been in the redwood forest for 1,000 years
means that it has been there for a
millennium.

2009       3009
Score
Meaning:
• A score is 20.

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