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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).
Finding Pi
Try some Pi for yourself!
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
MATERIALS: Yarn or StringRulerCalculator (optional)Circular objectsPaper and pencil
Manipulating Math with M&M’sMath Topics Reviewed in these Lessons
Organizing Data with Charts and TablesConverting Fractions, Decimals, and PercentsFinding the Mean and MedianDetermining ProbabilityFinding PercentagesGraphing DataCreating a Bar Graph and a Pie Graph
Manipulating Math with M&M’sOrganizing Data with Charts
YOUR BAG CLASSROOMCOLOR # FRAC DEC % COLOR
# FRAC DEC %Blue Blue
Brown Brown
Green Green
Orange Orange
Red Red
Yellow Yellow
Total Total
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’sFinding the Mean (Average) and Median
Manipulating Math with M & M’sProbability
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?
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’sFinding Percentages and Median
12
11
10
9
8
7
6
5
4
3
2
1
Blue Brown Green Orange Red Yellow
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.
M&M Colors Bar Graph
Manipulating Math with M&M’sPie 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
PART %
WHOLE 100
All percent problems have four parts:
1.The Part
2.The Percent
3.The Whole
4. 100
How to Solve for the PartWhat is 70% of 150?
1. Place the known numbers in the BOX
2. Use an X for the unknown number
3. Multiply the numbers that are diagonally opposite from each other.
4. 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 30 100
15 x 100=1,500
1,500 / 30 = 50
X= 50%
Proportions
MILES TRAVELED GALLONS OF GAS
LAST’S WEEK’S TRIP 125 5
NEXT TRIP X 12
Set up a proportion
box: 125 X 12 = 1500 1500 / 5 =300
X =300
125 5
x 12
125
5
300
12
125 is to 300 as 5 is to 12
(x,y) Battleships
Sample Ship Map Sample Student graph
HITS in RED MISSES in BLUE
Master Map has 10 ships
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
Pythagorean Theorem
• c² = a² + b² • c² = 4² + 3²• c² = 16 +9
• c² = 25 • Square root of 25 = 5
• C = 5
Plug the numbers in and SOLVE!
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 Negatives
X 2
X
X2
X
1 11 111
Algebra Tiles
Solving EquationsRemember 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
Algebra Tiles
Solving EquationsRemember 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
XX
1 1
1
=1 1
1
1
1
1
1
1
1
1
1
Algebra Tiles
2x + 3 = 11
XX
1
1
1
=
1
1
1
1
1
1 1
11
1
1
Algebra Tiles
2x + 3 = 11
X
X
1
1
1
=
1
1
1
1
1
1
1
1
1
1
1
X = 4
Algebra Tiles
Using Algebra Tiles to Teach Negative and Positive Computation
http://mathbits.com/MathBits/AlgebraTiles/AlgebraTiles.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 - -5
-6 + +5
-6 + (+5) = -1 Also written -6+5= -1
You will now move five places in the positive direction.
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
Financial Math
PIG DICE GAME
Practice Addition SkillsEach 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 resultsFirst one to 100 wins!
Practice Multiplication SkillsUse two sets of dice one set will represent one of the
numbers to be multipliedMultiply 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
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
CONTACT:
Juli DeNisco AEL Director Crowder College601 Laclede AveNeosho, MO 64850
