### Manipulating Math

```Presented by Juli DeNisco
Crowder College AEL Director
Pi = 3.14 or 22/7
The symbol for Pi looks like this
The idea of Pi is that the circumference of a circle
is approximately 3.14 times the diameter.
The formula for circumference is
distance (d)
circumference (C).
Materials:
Yarn or String
Ruler
Calculator
Circular Object
Paper and Pencil
o
o
o
o
Wrap a string or yarn around a circular object.
Using a ruler measure the amount of string
Record this amount. This is Circumference
Next measure the diameter of the circle
Math topics reviewed in this lesson:
o
o
o
o
o
o
o
Organizing Data with Charts and Tables
Converting Fractions, Decimals, and Percents
Finding the Mean and Median
Determining Probability
Finding Percentages
Graphing Data
Creating a Bar Graph and a Pie Graph
Organizing Data with Charts
COLOR
#
FRAC
CLASSROOM
DEC
%
COLOR
Blue
Blue
Brown
Brown
Green
Green
Orange
Orange
Red
Red
Yellow
Yellow
Total
Total
#
FRAC
DEC
%
Finding the Mean (Average) and Median
1. What is the average (mean) number of orange M&M’s in
this size bag?
2. What is the average number of blue M&M’s in this size
bag?
3. What is average number of yellow M&M’s?
4. What is that average number of brown M&M’s?
5. What is the average number of red M&M’s in the bag?
Probability
6. If you put all of the M&M’s in a cup and mixed
them up, what is the probability that you would
pick a red M&M?
7. If you put all of the M&M’s in a cup and mixed
them up what is the probability that you would
pick a blue M&M?
8. Under the same circumstances what is the
probability that you would pick a green M&M?
9. What is the probability you would choose a purple
M&M?
Finding Percentages and Median
10. Using the percentage of red from the Classroom Color
Chart what number of red M&M’s would you expect to
find in a bag of 300 M&M’s?
11. Using the percentage of green from the Classroom Color
chart what number of green M&M’s would you expect to
find in a bag of 300 M&M’s?
12.Using the percentage of blue from the Classroom Color
chart what number of blue M&M’s would you expect to
find in a bag of 300 M&M’s?
13. What is the median number of M&M’s in a ‘fun size’ bag?
Graphing Information

Use the information from YOUR BAG on the M&M’s
Color Chart. Put the information into the bar graph
in color.
Blue
Brown
Green
Orange
Red
Yellow
Graphing Relationships

STEP 1: Cut out colored bars and
tape end to end into bracelet.

STEP 2: Place the bracelet on paper
and trace the circle. Use the colors
to determine the size of each piece
of pie.

All percent problems have four parts:
PART
WHOLE
%
100

The Part

The Percent

The Whole

100

1.
2.
3.
4.
What is 70% of 150?
PART
%
WHOLE
100
Place the known numbers in the
BOX
Use an X for the unknown
number
Multiply the numbers that are
diagonally opposite from each
other.
Divide the answer by the number
that wasn’t used.
150 X 70 =10,500
10,500 / 100 =105
X = 105

15 is what percent
of 30?

15 x 100=1,500

1,500 / 30 = 50

X= 50%
Using a proportion box
Question: Last week Meredith traveled 125 miles on 5
gallons of gas. If she buys 12 gallons of gas
approximately how far will she be able to travel on her
next trip?
STUDENT TOOL BOX:
Note the relationship between the
percent box and the percentage box
Using a proportion box
125 X 12 = 1,500
1500 / 5 =300
X =300
Part
%
Whole
100
STUDENT TOOL BOX:
Note the relationship between the
percent box and the proportions box
Plotting X-Y Coordinates

Sample Ship Box
Master Map has 10 ships

Sample Student Graph
HITS in RED
MISSES in BLUE
The horizontal axis is called the x-axis.
And the vertical one is the y-axis.
STUDENT TOOLBOX:
(X, Y) Z

Define Terms:

Right Angle

Sides

Hypotenuse
STUDENT TOOLBOX:
The Hypotenuse is always C.
It can be remembered as the C
for Cut across.

Arrange Squares

Trace Triangles

Measure Sides

Observe the
relationship between
sides and hypotenuse

Plug in the
numbers and
SOLVE.
c² = a² + b²
 c² = 4² + 3²
 c² = 16 +9
 c² = 25
 Square root of 25 = 5
C = 5

Demystify Algebra Immediately
If your student says one of these statements:
•
•
•
I can’t do Algebra
I don’t understand Algebra
I don’t understand why there are letters and number
Show them a simple algebra problem and demystify it.
“You can do algebra you just don’t realize it.”
_ + 5 = 12 …”what is it?”
“Yes, 7 + 5 = 12”
“In algebra we use a letter instead of a blank!”
x + 5 = 12
X
2
X
X
1
1
Positive
2
X
1
1
1
Negative
1
Solving Equations


Balance the equation.
What you do to one side of the equal sign, you must do the same to
the other side.
X +3 = 8
X
=
X+3
8
Solving Equations


Balance the equation.
What you do to one side of the equal sign, you must do the same to
the other side.
X +3 = 8
X
X
=
X=5
=
Solving Two-Step Equations
2x + 3 = 11
X
X
=
Solving Two-Step Equations
2x + 3 = 11
X
X
=
Solving Two-Step Equations
2x + 3 = 11
X
=
X=4
X
Using Algebra Tiles to Teach
Negative and Positive Computation

http://mathbits.com/MathBits/AlgebraTiles/AlgebraTiles.htm
Understanding the concept of subtracting a negative
number and changing both of the negative signs to
positive signs
•
•
Make cards with positive numbers from 1-9 on
one side and negative numbers on the back.
Also make a card with - on one side and + on the
back.
FLIP cards
-6 + (+5) = -1
Also written -6+5= -1
You will now move five
places in the positive
direction.
Free Financial Literacy online curriculum
From Wells Fargo Bank!
•
•
Free Interactive online program for students
HANDS ON BANKING
Free PRINTABLES – comprehensive lesson
plans and worksheets for kids, teens, young
•
DICE GAME
• Each player takes turns rolling dice. If you roll a double you
loss your turn. If you roll a snake eyes (2 ones) you loss
• Add the two dice for points and total results
• First one to 100 wins!
•
Practice Multiplication Skills
• Use two sets of dice one set will represent one of the
numbers to be multiplied
• Multiply the total of first two dice times the total of the other
set of dice. If you roll a double you loss your turn. If you roll
a snake eyes (2 ones) you loss your entire bank.
• First player to 500 wins!

CONTACT:
Juli DeNisco
AEL Director
Crowder College
601 Laclede Ave
Neosho, MO 64850
[email protected]
```