Got Geoboards? They are not just for Geometry!! September 2011 Math In-service
Dec 26, 2015
Geoboards -- Agenda
Types of Geoboards Rubber bands Mathematical Connections
Rational Numbers Algebra/Graphing Statistics/Probability Geometry/Measurement
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 fractionsAddition of Rational NumbersTo 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
Multiplication of Rational NumbersFinding 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?
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 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
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) x
y
What is the equation of the line that goes through the two points? y=-x
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
12
1
12
1
xy
xy and
What is the point of intersection? (2,0)
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)
Bar Graphs
Create a bar graph with the following data on your Geoboard:
Class Number of students
A 27
B 24
C 24
D 30
E 30
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.
AbsencesFinal Exam
Score
0 90
1 100
3 80
3 70
4 80
5 60
6 60
7 50
10 40
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.
Flavor Frequency Percent DegreesRocky Road 12Chocolate
Chip18
Chocolate 24Oreo 12
Vanilla 6Total 72 100% 360
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.
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 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
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 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
2
)( 21 hbb
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)