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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.

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got geoboards

Got Geoboards?

They are not just for Geometry!!

September 2011

Math In-service

geoboards agenda

Geoboards -- Agenda

Types of Geoboards

Rubber bands

Mathematical Connections

Rational Numbers

Algebra/Graphing

Statistics/Probability

Geometry/Measurement

geoboards

Geoboards

Rational Numbers

geoboards and fractions
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 fractions4
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 fractions5
Geoboards and fractions
  • Subtraction?
    • How would you show: 1/3 – ¼?
    • 1 – 1/6?
geoboards and fractions6
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
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
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 geoboards1
Decimals and Geoboards
  • How would you show:
    • 0.34 + 0.25?
    • 0.34 + 0.3?
    • 0.45 + 0.55
decimals and geoboards2
Decimals and Geoboards
  • How would you show:
    • 0.34 - 0.25?
    • 0.7 - 0.35?
    • 1 - 0.21?
decimals and geoboards3
Decimals and Geoboards
  • How would you show:
    • 2 X 0.42?
    • 3 X 0.3?
    • 5 X 0.12?
percents and geoboards
Percents and Geoboards
  • How would you show:
    • 25%?
    • 40%?
    • 105%
percents and geoboards1
Percents and Geoboards
  • How would you show:
    • 50% of 1?
    • 50% of 2?
    • 25% of 2?
    • 20% of 4?
geoboards1

Geoboards

Algebra and Geoboards

coordinates
y

x

(0,0)

Coordinates
  • Think of your Geoboard as the 1st Quadrant
coordinates1
y

x

(0,0)

Coordinates
  • Graph the following points on your Geoboard:
    • Red dot (1,2)
    • Blue dot (5,3)
    • White dot (8,7)
coordinates2
y

x

(0,0)

Coordinates
  • We can also think of the Geoboard as 4 Quadrants
coordinates3
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

algebra and pre algebra
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)

slope
y

x

(0,0)

Slope

What is the slope of the line that passes through:

(2, -3) and (-4, 3)?

algebra
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

algebra1
y

x

(0,0)

Algebra
  • Graph the following line on your Geoboard:
    • y=2x-4
algebra2
y

x

(0,0)

Algebra
  • Graph the following line on your Geoboard:
algebra3
y

x

(0,0)

Algebra
  • Graph the following line on your Geoboard:
algebra4
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)

algebra5
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)

algebra6
y

x

(0,0)

Algebra
  • Graph the following line on your Geoboard:

(2,0)

What is the point of intersection?

geoboards and algebra

Geoboards and Algebra

Questions?

Suggestions?

geoboards tangrams and algebra

Geoboards, Tangrams, and Algebra

How can we relate the Geoboard and Tangrams with Algebra?

geoboards and tangrams
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)
geoboards2

Geoboards

Statistics and Geoboards

bar graphs
Bar Graphs

Create a bar graph with the following data on your Geoboard:

scatter plots
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.
scatter plots2
y

x

Scatter Plots

Relationship?

Line of Regression

back of geoboard
Back of Geoboard

Circle Graphs

Remember that they need to be in sections of ?

back of geoboard circle graph
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.

geoboards3

Geoboards

Probability and Geoboards

back of geoboard1
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 geoboard2
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

Geoboards– Prob/Stat

Questions?

Suggestions?

geoboards and geometry measurement

Geoboards and Geometry/Measurement

Parallel Lines and transversals

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

y

x

(0,0)

parallel lines1
Parallel Lines

y

Connect (-3,-2) and (3,2)

Connect (-4,-1) and (2,3)

Create a transversal (-4,2) and (3,-3)

  • What angles are congruent?

x

(0,0)

transformations
Transformations

y

Draw triangle WVY and translate it (3,-1).

W(-1,0) V(-3,-3) Y(2,-3)

x

(0,0)

transformations1
Transformations

y

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

x

(0,0)

transformations2
Transformations

y

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

x

(0,0)

transformations3
Transformations

y

Draw triangle RST and rotate it 90° clockwise. R(-5,0) S(-2,-5) T(-1,-1)

Can use graph paper too

x

(0,0)

triangles
Triangles

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

A

B

triangles1
Triangles

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

A

B

triangles2
Triangles

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

A

B

triangles3
Triangles

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

A

B

perimeter2
Perimeter

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

perimeter3
Perimeter

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

slide65
Area
  • Establish that each “square” is 1 unit
slide66
Area
  • Establish that each “square” is 1 unit
area and perimeter
Area and Perimeter
  • Create a rectangle whose perimeter and area are the same
area of triangles
Area of triangles
  • Determine the area of this triangle as many ways as you can--- discuss
area of triangles1
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 triangles2
Area of triangles

Determine the area of this triangle.

Does your method work for this triangle too?

area of quadrilaterals
Area of quadrilaterals

Determine the area of this polygon.

Does your method from the triangle work for this polygon?

area of quadrilaterals1
Area of quadrilaterals

Determine the area of this polygon.

Does your method from the triangle work for this polygon?

area of quadrilaterals2
Area of quadrilaterals

Create these trapezoids on your Geoboard.

Prove the formula for determining the area of a trapezoid

area of quadrilaterals3
Area of quadrilaterals

Create a trapezoid with an area of 8 square units

geoboards and tangrams1
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)
geoboards and tangrams2
Geoboards and Tangrams

What is the area of each piece?

geoboards and geometry
Geoboards and Geometry

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

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