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Manipulating Math

Manipulating Math. Presented by Juli DeNisco Crowder College AEL Director . Finding Pi. Pi = 3.14 or 22/7

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Manipulating Math

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  1. Manipulating Math Presented by Juli DeNisco Crowder College AEL Director

  2. Finding Pi Pi = 3.14 or 22/7 The symbol for Pi looks like thisThe 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).

  3. Try some Pi for yourself! Materials: Yarn or String Ruler Calculator Circular Object 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 Circumference • Next measure the diameter of the circle

  4. Manipulating Math with M&M’s • Math topics reviewed in this lesson: • 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

  5. Manipulating Math with M&M’s Organizing Data with Charts

  6. 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?

  7. 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 greenM&M? • What is the probability you would choose a purple M&M?

  8. 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?

  9. Manipulating Math with M&M’s Graphing Information • Use the information from YOUR BAG on the M&M’s Color Chart. Put the information into the bar graph in color. Blue BrownGreen Orange Red Yellow

  10. Manipulating Math with M&M’s Graphing Relationships • 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.

  11. Thinking Inside the Boxto Solve Percents • The Part • The Percent • The Whole • 100 • All percent problems have four parts:

  12. 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. 150 X 70 =10,500 10,500 / 100 =105 X = 105

  13. Solving for the Percent • 15 x 100=1,500 • 1,500 / 30 = 50 • X= 50% • 15 is what percent of 30?

  14. Proportions Using 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

  15. Proportions Using 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

  16. Cartesian Coordinate Graph Plotting X-Y Coordinates • Sample Ship Box • Sample Student Graph Master Map has 10 ships HITS in RED MISSES in BLUE

  17. (X,Y) Points The horizontal axis is called the x-axis.  And the vertical one is the y-axis.  STUDENT TOOLBOX: (X, Y) Z

  18. Pythagorean Theorem • Define Terms: • Right Angle • Sides • Hypotenuse STUDENT TOOLBOX: The Hypotenuse is always C. It can be remembered as the Cfor Cut across.

  19. Pythagorean Theorem • Arrange Squares • Trace Triangles • Measure Sides • Observe the relationship between sides and hypotenuse

  20. Pythagorean Theorem • Plug in the numbers and SOLVE. • c² = a² + b² • c² = 4² + 3² • c² = 16 +9 • c² = 25 • Square root of 25 = 5 • C = 5

  21. Algebra 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

  22. Algebra Tiles X X 2 2 X X 1 1 1 1 1 1 Positive Negative

  23. Algebra Tiles Solving 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 + 3 8

  24. Algebra Tiles Solving Equations • Balance the equation. • What you do to one side of the equal sign, you must do the same to the other side. X = X +3 = 8 X X = 5 =

  25. Algebra Tiles Solving Two-Step Equations 2x + 3 = 11 X = X

  26. Algebra Tiles Solving Two-Step Equations 2x + 3 = 11 X = X

  27. Algebra Tiles Solving Two-Step Equations 2x + 3 = 11 X = X = 4 X

  28. Algebra Tiles Using Algebra Tiles to Teach Negative and Positive Computation • http://mathbits.com/MathBits/AlgebraTiles/AlgebraTiles.htm

  29. Addition and Subtraction of Negative and Positive Numbers 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.

  30. Addition and Subtraction of Negative and Positive Numbers FLIP cards -6 + (+5) = -1 Also written -6+5= -1 You will now move five places in the positive direction.

  31. Financial Math Free Financial Literacy online curriculum From Wells Fargo Bank! • Free Interactive online program for studentsHANDS ON BANKING • Free PRINTABLES – comprehensive lesson plans and worksheets for kids, teens, young adults and adults

  32. Whole Numbers 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!

  33. Manipulating Math Toolkit

  34. Manipulating Math Toolkit

  35. RESOURCES • CONTACT: Juli DeNisco AEL Director Crowder College 601 Laclede Ave Neosho, MO 64850 julidenisco@crowder.edu

  36. Collaboration Activity

  37. Partner Activity

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