got geoboards?
DESCRIPTION
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 Types. - PowerPoint PPT PresentationTRANSCRIPT
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Got Geoboards?
They are not just for Geometry!!
September 2011
Math In-service
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Geoboards -- Agenda
Types of Geoboards Rubber bands Mathematical Connections
Rational Numbers Algebra/Graphing Statistics/Probability Geometry/Measurement
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Geoboards Types
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Geoboards Types
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Geoboards Rubber bands
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Geoboards
Rational Numbers
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Geoboards and fractions
Using your Geoboard, divide it into fourths as many ways as you possibly can. Record your answers on the given paper.
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Geoboards and fractions
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Geoboards and fractions
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Geoboards and fractions
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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.
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Geoboards and fractions
Subtraction? How would you show:
1/3 – ¼? 1 – 1/6?
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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.
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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?
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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?
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Decimals and Geoboards
How would you show: 0.34 + 0.25?
0.34 + 0.3?
0.45 + 0.55
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Decimals and Geoboards
How would you show: 0.34 - 0.25?
0.7 - 0.35?
1 - 0.21?
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Decimals and Geoboards
How would you show: 2 X 0.42?
3 X 0.3?
5 X 0.12?
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Percents and Geoboards
How would you show: 25%?
40%?
105%
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Percents and Geoboards
How would you show:
50% of 1?
50% of 2?
25% of 2?
20% of 4?
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Rational Numbers and Geoboards
Questions?
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Geoboards
Algebra and Geoboards
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Coordinates
Think of your Geoboard as the 1st Quadrant
(0,0) x
y
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Coordinates Graph the
following points on your Geoboard: Red dot (1,2) Blue dot (5,3) White dot (8,7)
(0,0) x
y
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Coordinates
We can also think of the Geoboard as 4 Quadrants
(0,0) x
y
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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
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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
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Slope
What is the slope of the line that passes through: (2, -3) and (-4, 3)?
(0,0) x
y
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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
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Algebra Graph the
following line on your Geoboard: y=2x-4
(0,0) x
y
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Algebra
Graph the following line on your Geoboard:
(0,0) x
y
12
1 xy
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Algebra
Graph the following line on your Geoboard:
(0,0) x
y
33
2 xy
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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
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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
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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)
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Geoboards and Algebra
Questions?
Suggestions?
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Geoboards, Tangrams, and Algebra
How can we relate the Geoboard and Tangrams with Algebra?
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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)
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Geoboards
Statistics and Geoboards
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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
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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
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Scatter Plots
x
y
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Scatter Plots
x
yRelationship?
Line of Regression
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Back of Geoboard
Circle Graphs
Remember that they need to be in sections of ?
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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
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Geoboards
Probability and Geoboards
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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.
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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.
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Geoboards– Prob/Stat
Questions?
Suggestions?
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Geoboards and Geometry/Measurement
Parallel Lines and transversals
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Parallel Lines
Graph y=1 and y=3 Graph transversal
line through (-2,3) and (1,0)
Measure the angles(0,0) x
y
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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
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Transformations
Draw triangle WVY and translate it (3,-1).
W(-1,0) V(-3,-3) Y(2,-3) (0,0) x
y
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Transformations
Draw triangle RST and reflect it over the y-axis. R(-5,0) S(-2,-5) T(-1,-1)
(0,0) x
y
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Transformations
Draw triangle RST and reflect it over the x-axis. R(-5,0) S(-2,-5) T(-1,-1)
(0,0) x
y
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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
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Triangles
B
Find three locations for a point P, above segment AB, so that triangle APB is a right triangle.
A
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Triangles
B
Find three locations for a point P, above segment AB, so that triangle APB is an isosceles triangle.
A
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Triangles
B
Find three locations for a point P, above segment AB, so that triangle APB is an acute triangle.
A
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Triangles
B
Find three locations for a point P, above segment AB, so that triangle APB is an obtuse angle.
A
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Perimeter
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Perimeter
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Perimeter
Create another figure, that is NOT a rectangle, with the same perimeter.
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Perimeter
Create another figure, that IS a rectangle, with the same perimeter.
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Area Establish that each “square” is 1 unit
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Area Establish that each “square” is 1 unit
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Area and Perimeter
Create a rectangle whose perimeter and area are the same
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Area of triangles
Determine the area of this triangle as many ways as you can--- discuss
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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?
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Area of triangles
Determine the area of this triangle.
Does your method work for this triangle too?
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Area of quadrilaterals
Determine the area of this polygon.
Does your method from the triangle work for this polygon?
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Area of quadrilaterals
Determine the area of this polygon.
Does your method from the triangle work for this polygon?
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Area of quadrilaterals
Create these trapezoids on your Geoboard.
Prove the formula for determining the area of a trapezoid
2
)( 21 hbb
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Area of quadrilaterals
Create a trapezoid with an area of 8 square units
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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)
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Geoboards and Tangrams
What is the area of each piece?
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Geoboards and Geometry
What other areas of Geometry could we use the Geoboard for in our classrooms?