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Manipulating Math
Presented by Juli DeNiscoCrowder 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!
Materials:
Yarn or StringRulerCalculatorCircular ObjectPaper and Pencil
o Wrap a string or yarn around a circular object.
o Using a ruler measure the amount of stringo Record this amount. This is Circumferenceo Next measure the diameter of the circle
Manipulating Math with M&M’s
Math topics reviewed in this lesson:
o Organizing Data with Charts and Tableso Converting Fractions, Decimals, and
Percentso Finding the Mean and Mediano Determining Probabilityo Finding Percentageso Graphing Datao Creating a Bar Graph and a Pie Graph
Manipulating Math with M&M’s
Organizing Data with Charts
YOUR BAG CLASSROOM
COLOR #
FRAC DEC % COLOR #
FRAC DEC %
Blue Blue
Brown Brown
Green Green
Orange Orange
Red Red
Yellow Yellow
Total Total
Manipulating Math with M & M’sFinding the Mean (Average) and
Median1. 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’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?
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?
Use the information from YOUR BAG on the M&M’s Color Chart. Put the information into the bar graph in color.
Manipulating Math with M&M’s
Blue Brown Green Orange Red Yellow
Graphing Information
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.
Manipulating Math with M&M’s Graphing Relationships
Thinking Inside the Box to Solve Percents
The Part
The Percent
The Whole
100
All percent problems have four parts:
PART %
WHOLE 100
What is 70% of 150?
How to Solve for the Part
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.
150 X 70 =10,500
10,500 / 100 =105
X = 105
PART %
WHOLE 100
15 is what percent of 30?
15 x 100=1,500
1,500 / 30 = 50
X= 50%
Solving for the Percent
ProportionsUsing 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
ProportionsUsing a proportion box
Answer:125 X 12 = 1,500 1500 / 5 =300 X =300
STUDENT TOOL BOX:Note the relationship between the percent box and the proportions box
Part
%
Whole
100
Sample Ship Box Sample Student Graph
Cartesian Coordinate Graph
Master Map has 10 ships HITS in RED MISSES in BLUE
Plotting X-Y Coordinates
(X,Y) Points
STUDENT TOOLBOX:(X, Y) Z
The horizontal axis is called the x-axis. And the vertical one is the y-axis.
Define Terms:
Right Angle
Sides
Hypotenuse
Pythagorean Theorem
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
Pythagorean Theorem
Plug in the numbers and SOLVE.
Pythagorean Theorem
c² = a² + b² c² = 4² + 3² c² = 16 +9 c² = 25 Square root of 25 = 5 C = 5
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 Demystify Algebra Immediately
Algebra Tiles
X2
X2
X X
1 1 1
Positive
1 1 1
Negative
Algebra TilesSolving 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 +3 = 8 X
=
Algebra TilesSolving 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
Algebra TilesSolving Two-Step Equations
2x + 3 = 11
X=
X
Algebra TilesSolving Two-Step Equations
2x + 3 = 11
X=
X
Algebra TilesSolving Two-Step Equations
2x + 3 = 11
X=
XX = 4
Using Algebra Tiles to Teach Negative and Positive Computation
http://mathbits.com/MathBits/AlgebraTiles/AlgebraTiles.htm
Algebra Tiles
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.
Addition and Subtraction of Negative and Positive Numbers
FLIP cards
Addition and Subtraction of Negative and Positive Numbers
-6 + (+5) = -1
Also written -6+5= -1
You will now move five places in the positive direction.
Financial Math
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 adults and adults
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!
Whole Numbers
Manipulating Math Toolkit
Manipulating Math Toolkit
RESOURCES CONTACT:
Juli DeNisco AEL Director Crowder College601 Laclede AveNeosho, MO 64850
Collaboration Activity
Partner Activity