Transcript Lassoing Answers by Manipulating Math

Manipulating
Math
Presented by Juli DeNisco
Crowder College AEL Director
Finding Pi
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).
Try some Pi for yourself!
MATERIALS:
Yarn or String
Ruler
Calculator (optional)
Circular objects
Paper and pencil
 Wrap a string or yarn around a circular object.
 Using a ruler measure the amount of string
 Record this amount. This is the Circumference
 Next measure the diameter of the circle.
 Multiply this number by 3.14 or π. It should be the same amount
as what you recorded for the circumference of the object
Manipulating Math with M&M’s
Math Topics Reviewed in these Lessons
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
Manipulating Math with M&M’s
Organizing Data with Charts
YOUR BAG
COLOR
#
CLASSROOM
FRAC
DEC
%
COLOR
Blue
Blue
Brown
Brown
Green
Green
Orange
Orange
Red
Red
Yellow
Yellow
Total
Total
#
FRAC
DEC
%
Manipulating Math with M & M’s
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?
Manipulating Math with M & M’s
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?
Manipulating Math with M & M’s
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?
Manipulating Math with M&M’s
Use the information from YOUR BAG on the M&M’s Color
Chart. Put the information into the bar graph in color.
12
11
10
9
8
7
6
5
4
3
2
1
Blue
Brown
Green
M&M Colors Bar Graph
Orange
Red
Yellow
Manipulating Math with M&M’s
Pie Charts
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.
Thinking Inside the Box to Solve Percents
All percent problems have four parts:
PART
WHOLE
%
1.The Part
100
3.The Whole
2.The Percent
4. 100
How to Solve for the Part
What is 70% of 150?
1.
2.
3.
4.
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.
X
70
150 100
150 X 70 =10,500
10,500 / 100 =105
X = 105
Solving for the %
15 is what percent of 30?
15
x
15 x 100=1,500
1,500 / 30 = 50
30
100
X= 50%
Proportions
MILES TRAVELED
LAST’S WEEK’S TRIP
125
NEXT TRIP
GALLONS OF GAS
5
X
Set up a proportion
box:
12
125 X 12 = 1500
1500 / 5 =300
X =300
5
125
12
125
5
x
12
300
125 is to 300 as 5 is to 12
(x,y) Battleships
Sample Ship Map
Master Map has 10 ships
Sample Student graph
HITS in RED
MISSES in BLUE
Pythagorean Theorem
Define Terms:
•Right Angle
•Sides
•Hypotenuse
Pythagorean Theorem
•
•
•
•
Arrange Squares
Trace Triangle
Measure Sides
Observe the
relationship between
sides and hypotenuse
Pythagorean Theorem
Plug the
numbers in
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
Algebra Tiles
Positives
X
Negatives
X
2
X
X
1
1
2
1
1
1
1
Algebra Tiles
Solving Equations
Remember to 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+3
=
8
Algebra Tiles
Solving Equations
Remember to 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=5
Algebra Tiles
2x + 3 = 11
X
X
1
1
1
1
=
1
1
1
1
1
1
1
1
1
1
Algebra Tiles
2x + 3 = 11
X
X
=
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Algebra Tiles
2x + 3 = 11
1
1
X
=
1
1
1
1
1
1
1
1
1
X=4
1
1
X
1
Algebra Tiles
Using Algebra Tiles to Teach
Negative and Positive Computation
http://mathbits.com/MathBits/AlgebraTiles/Alg
ebraTiles.htm
Addition and Subtraction of
Negative and Positive Numbers
• This activity helps students to understand the concept of subtracting a
negative number and changing both of the
– signs to + 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 these cards
-6
-6
-
-5
+ +5
-6 + (+5) = -1
Also written -6+5= -1
You will now move five places
in the positive direction.
Financial Math
Free Financial Literacy curriculum
available online from Wells Fargo Bank!
• Free Interactive online program for students
HANDS ON BANKING
• Free PRINTABLES – comprehensive lesson plans
and worksheets for kids, teens, young adults and
adults
PIG DICE GAME
 Practice Addition Skills
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
your entire bank.
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!
Manipulating Math Toolkit
Manipulating Math Toolkit
Manipulating Math Toolkit
RESOURCES
FunTastic Math
Games grades 5-8
CONTACT:
 Abebooks.com
 Fantastic Math Games
ISBN 1-56822-747-7
 Reproducible card
games, board games,
dice games, word and
picture games to
reinforce math skills
Juli DeNisco
AEL Director
Crowder College
601 Laclede Ave
Neosho, MO 64850
[email protected]