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

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

Geoboards Types

Geoboards Rubber bands

Geoboards Rational Numbers

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

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.

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

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.

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?

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?

Decimals and Geoboards How would you show:  ?  ? 

Decimals and Geoboards How would you show:  ?  ?  ?

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

Percents and Geoboards How would you show:  25%?  40%?  105%

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

Rational Numbers and Geoboards Questions?

Geoboards Algebra and Geoboards

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

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

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

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

Algebra and Pre-Algebra 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? (0,0) x y

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

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) xy What is the equation of the line that goes through the two points? y=-x

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

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

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

Algebra 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? (0,0) x y

Algebra 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? (0,0) x y

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

Geoboards and Algebra Questions? Suggestions?

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

Geoboards and Tangrams Use your Geoboard and bands to form a special geometric shape following the steps below. 1. Band together: (0,0) (0,8) (8,8) and (8,0) 2. Band together: (0,8) and (8,0) 3. Band together: (0,4) and (4,0) 4. Band together: (2,2) and (8,8) 5. Band together: (2,2) and (2,6) 6. Band together: (6,2) and (4,0)

Geoboards Statistics and Geoboards

Bar Graphs Create a bar graph with the following data on your Geoboard: ClassNumber of students A27 B24 C D30 E

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. Absences Final Exam Score

Scatter Plots x y

x y Relationship? Line of Regression

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

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. FlavorFrequencyPercentDegrees Rocky Road 12 Chocolate Chip 18 Chocolate 24 Oreo 12 Vanilla 6 Total 72100% 360 

Geoboards Probability and Geoboards

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.

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.

Geoboards– Prob/Stat Questions? Suggestions?

Geoboards and Geometry/Measurement Parallel Lines and transversals

Parallel Lines Graph y=1 and y=3 Graph transversal line through (-2,3) and (1,0) Measure the angles (0,0) x y

Parallel Lines Connect (-3,-2) and (3,2) Connect (-4,-1) and (2,3) Create a transversal (-4,2) and (3,-3) What angles are congruent? (0,0) x y

Transformations Draw triangle WVY and translate it (3,-1). W(-1,0) V(-3,-3) Y(2,-3) (0,0) x y

Transformations Draw triangle RST and reflect it over the y-axis. R(-5,0) S(-2,-5) T(-1,-1) (0,0) x y

Transformations Draw triangle RST and reflect it over the x-axis. R(-5,0) S(-2,-5) T(-1,-1) (0,0) x y

Transformations Draw triangle RST and rotate it 90° clockwise. R(-5,0) S(-2,-5) T(-1,-1) Can use graph paper too (0,0) x y

Triangles B Find three locations for a point P, above segment AB, so that triangle APB is a right triangle. A

Triangles B Find three locations for a point P, above segment AB, so that triangle APB is an isosceles triangle. A

Triangles B Find three locations for a point P, above segment AB, so that triangle APB is an acute triangle. A

Triangles B Find three locations for a point P, above segment AB, so that triangle APB is an obtuse angle. A

Perimeter

Create another figure, that is NOT a rectangle, with the same perimeter.

Perimeter Create another figure, that IS a rectangle, with the same perimeter.

Area Establish that each “square” is 1 unit

Area Establish that each “square” is 1 unit

Area and Perimeter Create a rectangle whose perimeter and area are the same

Area of triangles Determine the area of this triangle as many ways as you can-- - discuss

Area of triangles Determine the area of this triangle as many ways as you can--- discuss How efficient was your approach? Would you approach it differently now?

Area of triangles Determine the area of this triangle. Does your method work for this triangle too?

Area of quadrilaterals Determine the area of this polygon. Does your method from the triangle work for this polygon?

Area of quadrilaterals Determine the area of this polygon. Does your method from the triangle work for this polygon?

Area of quadrilaterals Create these trapezoids on your Geoboard. Prove the formula for determining the area of a trapezoid

Area of quadrilaterals Create a trapezoid with an area of 8 square units

Geoboards and Tangrams Use your Geoboard and bands to form a special geometric shape following the steps below. 1. Band together: (0,0) (0,8) (8,8) and (8,0) 2. Band together: (0,8) and (8,0) 3. Band together: (0,4) and (4,0) 4. Band together: (2,2) and (8,8) 5. Band together: (2,2) and (2,6) 6. Band together: (6,2) and (4,0)

Geoboards and Tangrams What is the area of each piece?

Geoboards and Geometry What other areas of Geometry could we use the Geoboard for in our classrooms?