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Got Geoboards?

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Got Geoboards?

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  1. Got Geoboards? They are not just for Geometry!! September 2011 Math In-service

  2. Geoboards -- Agenda Types of Geoboards Rubber bands Mathematical Connections Rational Numbers Algebra/Graphing Statistics/Probability Geometry/Measurement

  3. Geoboards Types

  4. Geoboards Types

  5. Geoboards Rubber bands

  6. Geoboards Rational Numbers

  7. Geoboards and fractions • Using your Geoboard, divide it into fourths as many ways as you possibly can. Record your answers on the given paper.

  8. Geoboards and fractions

  9. Geoboards and fractions

  10. Geoboards and fractions

  11. Geoboards and fractions • Addition of Rational Numbers To find the sum of 1/3 and 1/2, the student models both in the same unit, then covers the islands with other islands of a single color that could be used to fill the unit. In this model, a pink island represents 1/3, and a brown island represents 1/2. Red islands may be used to cover both of the islands. The five red islands represent the sum 5/6 in this unit. Another student may cover both islands with yellow islands, each of which covers one Geoboard square, showing the sum as 10/12; but 5/6 and 10/12 are equivalent, so represent the same rational number.

  12. Geoboards and fractions • Subtraction? • How would you show: 1/3 – ¼? • 1 – 1/6?

  13. Geoboards and fractions Multiplication of Rational Numbers Finding the product of 1/3 and 1/2 is modeled as “1/3 of 1/2.” 1/2 is modeled with one brown island in this unit. Since three red islands cover the brown island, then one red island models one-third of the brown area. The one red island represents 1/6 in this unit; thus the product is 1/6.

  14. Fractions and Geoboards • Problem: Mr. McGregor has a garden that is a rectangle 3 units by 2 units. He wants to plant flowers on half of the garden Show how he would divide his garden on the geoboard. Then draw it on the paper and shade in the part that would be flowers with one of the colors. • How much of the garden will be flowers? How much is 1/2 of a whole? • Is the result more or less than the whole?

  15. Decimals and Geoboards • How would you show 0.34 on your geoboard? • How would you show 0.3 on your geoboard? • How would you show 1.34 on your geoboard?

  16. Decimals and Geoboards • How would you show: • 0.34 + 0.25? • 0.34 + 0.3? • 0.45 + 0.55

  17. Decimals and Geoboards • How would you show: • 0.34 - 0.25? • 0.7 - 0.35? • 1 - 0.21?

  18. Decimals and Geoboards • How would you show: • 2 X 0.42? • 3 X 0.3? • 5 X 0.12?

  19. Percents and Geoboards • How would you show: • 25%? • 40%? • 105%

  20. Percents and Geoboards • How would you show: • 50% of 1? • 50% of 2? • 25% of 2? • 20% of 4?

  21. Rational Numbers and Geoboards Questions?

  22. Geoboards Algebra and Geoboards

  23. y x (0,0) Coordinates • Think of your Geoboard as the 1st Quadrant

  24. y x (0,0) Coordinates • Graph the following points on your Geoboard: • Red dot (1,2) • Blue dot (5,3) • White dot (8,7)

  25. y x (0,0) Coordinates • We can also think of the Geoboard as 4 Quadrants

  26. y x (0,0) Coordinates • Graph the following points on your Geoboard: • Red dot (-1,2) • Blue dot (3,-3) • White dot (-2,-3) BINGO

  27. Algebra and Pre-Algebra y • We can use the Geoboard to help with graphing equations and determining slope: • Connect (-3,-3) and (3,3) • What is the slope of the line that connects these points? x (0,0)

  28. y x (0,0) Slope What is the slope of the line that passes through: (2, -3) and (-4, 3)?

  29. y x Algebra • Graph the following points on your Geoboard: • Red dot (-1,1) • Blue dot (3,-3) • Use a band to draw the line that goes through both points (0,0) What is the equation of the line that goes through the two points? y=-x

  30. y x (0,0) Algebra • Graph the following line on your Geoboard: • y=2x-4

  31. y x (0,0) Algebra • Graph the following line on your Geoboard:

  32. y x (0,0) Algebra • Graph the following line on your Geoboard:

  33. Algebra y Connect (-3,-2) and (3,2) • What is the slope of the line that connects these points? Connect (-2,2) and (2,-4) • What is the slope of the line that connects these points? x (0,0)

  34. Algebra y Connect (-3,-2) and (3,2) • What is the slope of the line that connects these points? Connect (-4,-1) and (2,3) • What is the slope of the line that connects these points? x (0,0)

  35. y x (0,0) Algebra • Graph the following line on your Geoboard: (2,0) What is the point of intersection?

  36. Geoboards and Algebra Questions? Suggestions?

  37. Geoboards, Tangrams, and Algebra How can we relate the Geoboard and Tangrams with Algebra?

  38. Geoboards and Tangrams Use your Geoboard and bands to form a special geometric shape following the steps below. • Band together: (0,0) (0,8) (8,8) and (8,0) • Band together: (0,8) and (8,0) • Band together: (0,4) and (4,0) • Band together: (2,2) and (8,8) • Band together: (2,2) and (2,6) • Band together: (6,2) and (4,0)

  39. Geoboards Statistics and Geoboards

  40. Bar Graphs Create a bar graph with the following data on your Geoboard:

  41. Scatter Plots • Create a scatter plot with the following data on your Geoboard: • The table shows the number of class absences and final exam scores for 9 students in Mr. Hayes’ class.

  42. Scatter Plots y x

  43. y x Scatter Plots Relationship? Line of Regression

  44. Back of Geoboard Circle Graphs Remember that they need to be in sections of ?

  45. Back of Geoboard- Circle Graph A group of 72 randomly selected 8th graders were asked about their favorite ice cream flavor. The results are shown below.

  46. Geoboards Probability and Geoboards

  47. Back of Geoboard Creating spinners The probability of landing on an even number is ½ and the probability of landing on an odd number is ¼.

  48. Back of Geoboard Creating spinners The probability of landing on a multiple of seven is 3/8 and the probability of landing on a multiple of eight is 3/8.

  49. Geoboards– Prob/Stat Questions? Suggestions?

  50. Geoboards and Geometry/Measurement Parallel Lines and transversals