Presented by Juli DeNisco Crowder College AEL Director 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 CLASSROOM COLOR # FRAC DEC % Blue Brown Green Orange Red Yellow Total

Manipulating Math with M & M’s Finding the Mean (Average) and Median What is the average (mean) number of orange M&M’s in this size bag? What is the average number of blue M&M’s in this size bag? What is average number of yellow M&M’s? What is that average number of brown M&M’s? 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? 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? 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 Orange Red Yellow M&M Colors Bar Graph

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 100 1.The Part 2.The Percent 3.The Whole 4. 100

How to Solve for the Part What is 70% of 150? 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? x 30 100 15 x 100=1,500 1,500 / 30 = 50 X= 50%

Proportions Set up a proportion box: 125 X 12 = 1500 1500 / 5 =300 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 5 300 12 125 5 x 12 125 is to 300 as 5 is to 12

(x,y) Battleships Sample Ship Map HITS in RED Master Map has 10 ships Sample Student graph HITS in RED MISSES in BLUE Master Map has 10 ships

Pythagorean Theorem Define Terms: Right Angle Sides Hypotenuse

Pythagorean Theorem Pythagorean Theorem Arrange Squares Trace Triangle Measure Sides Observe the relationship between sides and hypotenuse

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 X 2 2 X X 1 1 1 1 1 1

you must do the same to the other side. Algebra Tiles 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 =

you must do the same to the other side. 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 1 1 1 1 1 = X 1 1 1 1 1 1 1 1 1

Algebra Tiles 2x + 3 = 11 X 1 1 = X 1 1 1 1 1 1 1 1 1 1 1 1

Algebra Tiles 2x + 3 = 11 1 1 1 = 1 X 1 1 1 1 1 1 1 1 X = 4 1 1 X

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) = -1 Also written -6+5= -1 You will now move five places in the positive direction. -6 - -5 + +5

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 Practice Multiplication 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: Juli DeNisco 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 College 601 Laclede Ave Neosho, MO 64850 julidenisco@crowder.edu