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

julidenisco@crowder.edu

Collaboration Activity

Partner Activity