got geoboards?

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

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

Geoboards and fractions

Geoboards and fractions

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

Subtraction? How would you show:

1/3 – ¼? 1 – 1/6?

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?

Decimals and Geoboards

How would you show: 0.34 + 0.25?

0.34 + 0.3?

0.45 + 0.55

Decimals and Geoboards

How would you show: 0.34 - 0.25?

0.7 - 0.35?

1 - 0.21?

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 1st 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) x

y

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

12

1 xy

Algebra

Graph the following line on your Geoboard:

(0,0) x

y

33

2 xy

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 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:

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

Scatter Plots

x

y

Scatter Plots

x

yRelationship?

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.

Flavor Frequency Percent DegreesRocky Road 12Chocolate

Chip18

Chocolate 24Oreo 12

Vanilla 6Total 72 100% 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

Perimeter

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

2

)( 21 hbb

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?