LINEar EQuations:

AlGeBrA II

Translations& Reflections

Geometry

Output

& Free OnlineComputer Graphing Applications

Teachers can utilize Geogebra & Online Graphing Calculators to enhance instruction

Angles

**Technology in Mathematics**

Integrating Graphing Aides Into Core Curriculum

Geogebra.org

Slopes & Intercepts

Polygons

Parallel Lines

Perpendicular Lines

D i a l a t i o n s

**ALGEBRA I**

Understanding SLOPE

Compressions

Using Geogebra and a pen & tablet to show why the Equation of a slope is :

Prepare Ahead In order to Focus on Instruction

Slope =

rise

run

or

Start with basic concepts to develop upon

Images can be toggled on/off

Teacher is able to give instruction while providing visuals. Tablet and pen allow instructor to write directly on graph

Intercepts :

Graphically show how the y-intercept is where the line crosses the y-axis and the x-intercept is where the line crosses the x-axis

Coordinates :

Geogebra lists the algebraic parts of the graphs (i.e. the coordinates of each of the points A and B)

Parallel lines

Teachers & Students can use Geogebra to graph parallel lines through given points

graph the first line and then select the parallel line option

Scroll over the icon for instructions of how to create a new line that is parallel to the first

Equations of the two lines can be viewed in standard or slope-intercept form

Shows that the slopes of parallel lines are equal

Perpendicular Lines

created the same as parallel lines but use the perpendicular lines option

shows that slopes are negative reciprocals

points & other objects can be color coded to highlight specific items or concepts

**Geometry**

Angles

**Polygons**

Characteristics of Regular Polygons

**technology**

Circles

Identifying types of angles

grid & axes can be toggled on/off

points & angle size are labeled, color options available

all sides and angles are equal

measures the angle between 3 points

Text can be entered, sized & moved freely

segments can be placed to show length of sides

http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

Online GRAPHING CALCULATORS

**Circles**

Area & Circumference

equation of a circle with center & radius

Instruction can show how formulas for area & circumference work

Geogebra calculates area & distance (circumference/perimeter)

Reflections

students can access online no download needed

provides features that work for many different areas of math

**ALGEBRA II**

Parabolas

in mathematics

**Reflections of**

y = x

2

equations listed & color coded

table of x & y values can be altered

**Translations of**

shows how graph is shifted right then up

**y = x**

2

graphs can be toggled on/off

new vertex at (2,3)

Compressions

**D i a l a t i o n s**

parabola widens

vertex stays at (0,0)

graph window size can be adjusted in settings

equations can be changed to see how it affects the graph of y=x

2

vertex stays at (0,0)

Intersection: will find the point where two graphs intersect

multiplying by a positive whole number narrows the parabola

y = x

2

narrows

students learn to use the technology in class and then can download/access at home for free

Students can explore concepts further by manipulating the applications themselves

SELF DISCOVERY

EASY ACCESS

INSTRUCTION

m =

y - y

2 1

x - x

2 1