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Got Geoboards? - PowerPoint PPT Presentation

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?

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

Rational Numbers

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

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.

• Subtraction?

• How would you show: 1/3 – ¼?

• 1 – 1/6?

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.

• 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?

• 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?

• How would you show:

• 0.34 + 0.25?

• 0.34 + 0.3?

• 0.45 + 0.55

• How would you show:

• 0.34 - 0.25?

• 0.7 - 0.35?

• 1 - 0.21?

• How would you show:

• 2 X 0.42?

• 3 X 0.3?

• 5 X 0.12?

• How would you show:

• 25%?

• 40%?

• 105%

• How would you show:

• 50% of 1?

• 50% of 2?

• 25% of 2?

• 20% of 4?

Questions?

Geoboards

Algebra and Geoboards

x

(0,0)

Coordinates

x

(0,0)

Coordinates

• Graph the following points on your Geoboard:

• Red dot (1,2)

• Blue dot (5,3)

• White dot (8,7)

x

(0,0)

Coordinates

• We can also think of the Geoboard as 4 Quadrants

x

(0,0)

Coordinates

• Graph the following points on your Geoboard:

• Red dot (-1,2)

• Blue dot (3,-3)

• White dot (-2,-3)

BINGO

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)

x

(0,0)

Slope

What is the slope of the line that passes through:

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

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

x

(0,0)

Algebra

• Graph the following line on your Geoboard:

• y=2x-4

x

(0,0)

Algebra

• Graph the following line on your Geoboard:

x

(0,0)

Algebra

• Graph the following line on your Geoboard:

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)

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)

x

(0,0)

Algebra

• Graph the following line on your Geoboard:

(2,0)

What is the point of intersection?

Questions?

Suggestions?

Geoboards, Tangrams, and Algebra

How can we relate the Geoboard and Tangrams with Algebra?

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

Statistics and Geoboards

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

• 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.

x

Scatter Plots

Relationship?

Line of Regression

Circle Graphs

Remember that they need to be in sections of ?

A group of 72 randomly selected 8th graders were asked about their favorite ice cream flavor. The results are shown below.

Geoboards

Probability and Geoboards

Creating spinners

The probability of landing on an even number is ½ and the probability of landing on an odd number is ¼.

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.

Questions?

Suggestions?

Geoboards and Geometry/Measurement

Parallel Lines and transversals

• Graph y=1 and y=3

• Graph transversal line through (-2,3) and (1,0)

• Measure the angles

y

x

(0,0)

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)

y

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

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

x

(0,0)

y

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

x

(0,0)

y

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

x

(0,0)

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)

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

A

B

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

A

B

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

A

B

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

A

B

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

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

• Establish that each “square” is 1 unit

• Establish that each “square” is 1 unit

• Create a rectangle whose perimeter and area are the same

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

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

Would you approach it differently now?

Determine the area of this triangle.

Does your method work for this triangle too?

Determine the area of this polygon.

Does your method from the triangle work for this polygon?

Determine the area of this polygon.

Does your method from the triangle work for this polygon?

Create these trapezoids on your Geoboard.

Prove the formula for determining the area of a trapezoid

Create a trapezoid with an area of 8 square units

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)

What is the area of each piece?

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