Learning Tools List
Note: There is a shortcut to this page: maine.edc.org/tools All learning tools on this list were created using the open educational resource (OER) GeoGebra. Selecting a tool name launches the tool in a new browser window. Your computer must be connected to the Internet to open GeoGebra files using this list. 
#  Name (link) 
Description (starts with content tag(s).) 
1  Are They Linear? (1) 
Algebra. Functions. Linear Relationships. Provides four sample relationships in table form. Students determine if the tables represent linear relationships and check by clicking to plot points and draw lines of best fit. 
2  Are They Linear? (2) 
Algebra. Functions. Linear Relationships. Provides two equations. Sliders change the value for x in each equation. As the value of x changes, the point changes on the graph. Check by graphing the equations. 
2a  Are They Linear? (2a) 
Algebra. Functions. Linear Relationships. Display and type in five given equations of different forms to determine if they are linear. Check boxes show each equation, the graph of each equation, and the equation in modified form. 
3  Are They Linear? (3) 
Algebra. Functions. Linear Relationships. Quadratic Relationships. Two equations are shown; both include terms with x^{2}. Sliders change the value for x in each equation. As the value of x changes, the point changes on the graph. Check by graphing the equation. 
3b  Are They Linear? (4) 
Algebra. Functions. Linear Relationships. Quadratic Relationships. Provides nine example relationships in table form; some are not linear. A tenth example allows users to create a table by moving points on the graph. Users can show or hide the table, slope table, slope calculation between two selected points, graph, and function or line of best fit. 
4  Comparing Rational Numbers (Decimals)  Number. Rational Numbers. Decimals. Create two rational numbers using sliders for each digit (units, tenths, hundredths, thousandths). Compare, then check using a number line. 
5a  Comparing Rational Numbers (Fractions)  Number. Rational Numbers. Fractions. Create two rational numbers (fractions) using sliders for the numerators and denominators. Compare, then check using area models and a number line. 
5b  Comparing Rational Numbers (Fractions)  2  Number. Rational Numbers. Fractions. Create two rational numbers (fractions) using sliders for the numerators and denominators. Compare, then check using area models and a number line. A red line can be used to compare the area models. 
5c  Comparing Rational Numbers (Fractions)  2 (Revised)  Number. Rational Numbers. Fractions. Create two rational numbers (fractions) using sliders for the numerators and denominators. Compare, then check using area models and a number line. A red line can be used to compare the area models. This revised version includes separate check boxes for the relationship and the common denominators. 
6  Difference of Squares (1)  Algebra. Expressions. Explore evaluating the difference of squared terms. An interactive visual model represents the relationship between the expressions a^{2}  b^{2} and (a+b)(ab). 
7  Difference of Squares (2)  Algebra. Expressions. Explore, both arithmetically and geometrically, the values of the expressions a^{2}  b^{2} and (a+b)(ab). 
8  Difference of Squares (3)  Algebra. Expressions. Explore the relationship between the expressions a^{2}  b^{2} and (a+b)(ab) using a visual model with trapezoids. 
9  Equivalent Expressions  Circle Area and Circumference  Algebra. Geometry. Formulas. Expressions. Graphing. Explore the relationship between the formulas for circle area and circumference. Compare equations, table values, graphic representations, and visual models. 
10  Equivalent Expressions  Commutative Property  Algebra. Expressions. Explore the relationship between two different formulas, l•w•h and h•w•l, for the volume of a rectangular prism. Sliders change the values of each variable. 
11  Equivalent Expressions  Distributive Property (1)  Algebra. Expressions. Explore the relationship between two different formulas, a(l+w) and a(l) + w. Sliders change the values of each variable and the set models. 
12a  Equivalent Expressions  Distributive Property (2)  Algebra. Expressions. Explore the relationship between two different formulas, a(b+c) and a(b) + c. The expression a(b+c) is shown in both expanded and factored form. Sliders change the values of each variable and the set models. 
12b  Equivalent Expressions  Distributive Property (3)  Algebra. Expressions. Explore the relationship between two different formulas, a(b+c) and a(b) + c. The expression a(b+c) is shown in both expanded and factored form. Sliders change the values of each variable and the set models. This version is the same as Equivalent Expressions  Distributive Property (2) except the sliders start with different values. 
13  Equivalent Expressions  Powers  Algebra. Expressions. Compare a*n to a^{n}. Shows a visual model for n < 4. 
14  Fishing from a Boat with a Fish Finder  Algebra. Geometry. Trigonometry. Explore triangle relationships with a simulation of fishing from a boat with a fish finder. Check boxes modify what is seen and sliders change the fish finder depth and angle. Determine the length of line necessary to put the lure at the fish. 
15  Fractions (Set Model)  Number. Fractions. Set Model. Explore the meaning of fractions using a set model. Sliders change the number of blue circles and the number of circles in a set. Check boxes allow students to check the values for the fraction, decimal, and percentage. Improper fractions are possible. 
16  Integer Addition and Subtraction (Number Line Model)  Number. Operations. Integers. Explore addition and subtraction of integers from 10 to 10 with a number line model. Sliders change the values of the first and second term. Options allow modeling both addition, subtraction, and the distance (difference) between the sum and difference simultaneously. Another option models subtraction of the first term [e.g.  (4) + (5) ]. 
17  Ladder on a Wall  Geometry. Triangles. Angles. A simulation of a ladder against a wall. Displays triangle leg dimensions and hypotenuse dimension. Check boxes show the angles. A free window is included! 
18  Locating Rational Numbers (1) Fractions  Number. Fractions. Locate rational numbers on a number line. Drag fractions to the number line and check your answer. (See also the ParticipantDesigned list for another tool in this series.) 
19  Locating Rational Numbers (2) Decimals  Number. Decimals. Locate rational numbers on a number line. Drag decimal numbers to the number line and check your answer. (See also the ParticipantDesigned list for another tool in this series.) 
20 
Locating Rational Numbers (3) Mixed Numbers  Number. Mixed Numbers. Fractions. Decimals. Locate rational numbers on a number line. Drag fractions and mixed numbers to the number line and check your answer. Use the pointer to find a location on the number line and check your answer. (See also the ParticipantDesigned list for another tool in this series.) 
21a  Multiplying Fractions  Area Model  Operations. Number. Fractions. Explore the multiplication of fractions using an area model. Sliders change the values of the numerators and denominators, and you can check the product. 
21b  Multiplying Fractions  Area Model: Problem Set 1  Operations. Number. Fractions. Explore the multiplication of fractions using an area model and fifteen problems. A slider changes the problem shown, and the area model allows you to drag one square to overlap the other square. Select your answer using sliders for the numerator and the denominator, then check your answer. 
21c  Multiplying Fractions  Area Model: Problem Set 2  Operations. Number. Fractions. Explore the multiplication of fractions using an area model and ten problems. A slider changes the problem shown, and the area model allows you to drag one square to overlap the other square. Select your answer using sliders for the numerator and the denominator, then check your answer. 
22 
Multiplying Unit Fractions  Area Model 
Operations. Number. Fractions. Explore the multiplication of unit fractions using an area model. Sliders change the values of the denominators, and you can check the product. 
23 
Representing Rational Numbers  Number Line Model 1 
Number. Fractions. Decimals. Percents. Explore fractions, decimals, and percents by changing the number of divisions and the number of shaded divisions on a number line from 0 to 1. 
24 
Representing Rational Numbers  Number Line Model 2 
Number. Fractions. Decimals. Percents. Explore fractions, decimals, and percents by changing the number of divisions and the number of shaded divisions on a number line. A slider changes the total length of the number line from 0.1 to 2 units. 
25a 
Powers (1) 
Algebra. Operations. Powers. Exponents. Explore the relationship between (x + y)^{2} and x^{2} + y^{2}. Sliders change the values of x and y, and check boxes show the resulting expressions simplified and evaluated. 
25b 
Powers (2) 
Algebra. Operations. Powers. Exponents. Explore the relationship between (x + y)^{2} and (x + y)(x + y). Sliders change the values of x and y, and check boxes show the resulting expressions simplified and evaluated. 
25c 
Powers (3) 
Algebra. Operations. Powers. Exponents. Explore the relationship between (xy)^{2} and x^{2}y^{2}. Sliders change the values of x and y, and check boxes show the resulting expressions simplified and evaluated. 
26 
Addition or Multiplication of Powers 
Algebra. Operations. Powers. Exponents. Addition. Multiplication. Explore the relationship between x^{y} and a^{b} + c^{d} or a^{b} • c^{d}. Sliders change the variable values and check boxes show the resulting expressions in expanded form, simplified, and evaluated. 
27 
Division of Powers 
Algebra. Operations. Powers. Exponents. Division. Explore the relationship between x^{y} and a^{b} ÷ c^{d} or a^{b}/c^{d} (written as a fraction). Sliders change the variable values and check boxes show the resulting expressions in expanded form, simplified, and evaluated. 
28 
Rates of Change 
Algebra. Graphing. Explore rates of change with three different lines. Check boxes allow viewing lines individually or simultaneously, as well as the calculations for the slopes. Sliders change the values of x for each line and display a corresponding slope triangle starting at the origin. 
29 
Triangle Equal Regions 
Number. Geometry. Explore dividing an equilateral triangle into regions by dragging points on the legs of the triangle. Check boxes show examples of triangles divided into 2, 3, or 4 equal regions. 
30a 
Effects of Scale Interval Changes 
Graphing. Scale. Algebra. Functions. Slope. Show the effects of scale interval changes on four different graphs. Sliders change the axes scale intervals and two points can be used to explore scale interval changes on slope. 
30b 
Effects of Scale Interval Changes (2) 
Graphing. Scale. Algebra. Functions. Slope. Show the effects of scale interval changes on two different graphs. Sliders change the axes scale intervals and two points can be used to explore scale interval changes on slope. This version shows graphs A and B from the original tool and the points to determine slope stay on the function when the scale is changed. Adapted from the Effects of Scale Interval Changes tool (on this list). 
31a 
Distance  Time Graph 
Graphing. Line Plot. Slope. Explore line plots with an interactive distance vs. time graph. Users can create custom graphs with up to six sections. The tool also can show the slope triangle and the slope calculation for each section. 
31b 
Slope  Line Graph 
Graphing. Slope. Explore slope or other concepts using a line plot or scatter plot. Modify the plot by changing the axes variables, adding plot sections (16), adjusting the points between the plot sections, extending the section segments, and showing the slope triangle and/or slope for each plot section. 
32a 
Solve by Trace 
Algebra. Equations. Solving. Substitution. Graphing. The tool illustrates a method of solving equations by graphing, tracing, and substitution. It models a variety of equations of the form ax + b = c, and aids the user finding a solution for the variable x that will make the expression on the left side of the equation equivalent to the expression on the right side of the equation. 
32b 
Wind Chill Problem 
Algebra. Equations. Solving. Substitution. Graphing. Apply a method of solving equations by graphing, tracing, and substitution. The tool models the equation used to determine wind chill. The tool aids the user finding solutions for the 3 problems given; the solution is when the expression on the left side of the equation is equivalent to the expression on the right side of the equation. 
33a 
Balloons & Sandbags  Exploring Integer Operations 
Number. Operations. Integers. Explore integer operations using two different balloons and sandbags models. Drag balloons, sandbags, and/or zero pairs onto the board and see how the total result shown on the board changes the models. Nine preset integer addition and subtraction problems are given, as well as the ability to create your own problems (option 10). An alert is given when the first term of each expression is formed. (The models can also be used during discussions of multiplication and division, although no problems are included.) 
33b 
Balloons & Sandbags  Exploring Integer Operations (2) 
Number. Operations. Integers. Explore integer operations using two different balloons and sandbags models. Drag balloons, sandbags, and/or zero pairs onto the board and see how the total result shown on the board changes the models. Nine preset integer addition and subtraction problems are given, as well as the ability to create your own problems (option 10). An alert is given when the first term of each expression is formed. (The models can also be used during discussions of multiplication and division, although no problems are included.) This version can show the solution and a solution model for each of the nine preset example problems. 
34 
Measures of Center 
Data. Graphing. Measures of Center. Explore mean, median, and mode through the use of an interactive line plot. Modify the line plot by dragging on Xs representing data. The measures of center are shown graphically and the values are computed dynamically as data is added to the graph. The maximum data can be adjusted to accommodate a wide array of values. One to ten data points can be displayed at a time. 
35a 
Comparing Whole Number Products (12x12) 
Number. Multiplication. Area. Array. This tool allows users to compare two whole number products visually using area or array models. Users can change the factors (from 0 to 12) using sliders; the numerical product can be shown. Compare the products visually by dragging the second area or array model over the first model. Side, remaining, and additional lengths, as well as region areas, can be shown with the area model. 
35b 
Comparing Whole Number Products (30x30) 
Number. Multiplication. Area. Array. This tool allows users to compare two whole number products visually using area or array models. Users can change the factors (from 0 to 30) using sliders; the numerical product can be shown. Compare the products visually by dragging the second area or array model over the first model. Side, remaining, and additional lengths, as well as region areas, can be shown with the area model. 
36 
Growing Patterns 
Algebra. Patterns. Expressions. Multiple Methods. Explore multiple equivalent expressions for two patterns (tiling around a square pool and an X with lengthening arms). Colorcoded pattern figures are shown. For the pool border pattern, the expressions in terms of n are given and solved for each n (04), and each expression is explained in writing. The X pattern is left unsolved for students to investigate. 
37a 
Snow Melt (1) 
Graphing. Algebra. Slope. Rate of Change. Explore rate of change in the context of snow melting. 
37b 
Snow Melt (2) 
Graphing. Algebra. Slope. Rate of Change. Explore rate of change in the context of snow melting. Users can adjust the graph using multiple points, to display multiple scenarios with both new snowfall and snow melting. 
38a 
Algebraic Expressions (1) 
Algebra. Expression. Evaluate. Integer. Coefficient. Substitution. Choose from four algebraic expressions and use sliders to select the value of the variable (10 to 10) and any parameters. Show or hide the algebraic expression, the expression with substitution, the notation shown for multiplication or division, and the result. Values range from 10 to 10 and can be integers or intervals of one tenth. 
38b 
Algebraic Expressions  Number Line Model for Multiplication 
Algebra. Multiplication. Number Line. Evaluate. Coefficient. Choose from two algebraic expressions, the first a variable with no coefficient and the second the multiplication of a variable by a coefficient. Use sliders to select the value of the variable (10 to 10) and the coefficient. Show or hide the algebraic expression, the expression with substitution, the notation shown for multiplication, the result, and a model for the multiplication, shown as jumps along a number line. Values for the variable and coefficient are integers from 10 to 10. 
39 
Addition and Subtraction with Blocks 
Number. Addition. Subtraction. Blocks. Commutative Property. Users create one or two addition and/or subtraction expressions using blocks (single and a rod/column of ten). Users can see the expressions evaluated and a representation of each expression on a number line. The use of negative numbers and blocks can be turned on or off. 
40 
Plot Points on Linear Equations 
Algebra. Plot Points. Graphing Linear Equations. Slope. Plot three points on the line for each of 10 example equations; an eleventh example allows users to change the slope and yintercept values of a slopeintercept equation. For each example, other alternate forms of the the equation can be shown. Check boxes can show the ordered pairs for each point and verify the positions of the points, show the best fit line for the three points, or graph the example equation. 
41a 
Calculating Slope 
Algebra. Slope. Linear Equations. Drag two points to determine a line. Check boxes can show the ordered pairs for the points, the slope triangle, the calculation of the slope of the line, and the equation of the line in slopeintercept form. A check box allows the use of delta notation. 
41b 
Calculating Slope (2) 
Algebra. Slope. Linear Equations. Drag two points to determine a line. Check boxes can show the ordered pairs for the points, the slope triangle, the calculation of the slope of the line, and the equation of the line in slopeintercept form. A check box allows the use of delta notation. This version enables rightclick features and show the Input bar. 
42 
Exploring Scale Factors 
Scale Factor. Transformations. Dilate. Resize. Multiplication. Modify the dimensions of a rectangle and see a representation of it multiplied by a scale factor (from 1 to 6). Check boxes show the original figure, it's grid and area, and the scaled figure and it's grid, area, and divisions of it marking the dimensions of the original figure. 
43 
Exponential Graphs 
Algebra. Exponents. Exponential Functions. Explore exponents with three expressions: 1^{x}, 2^{x}, and 5^{x}. See each expression and the evaluation of the expression, as well as the expanded form of the expression and the graph of the related equation (for example, y=2^{x}). 
44 
Exploring Exponents 
Algebra. Powers. Exponents. Functions. Graph. Explore exponents with a graph of y=x^{n}. Sliders change the value of n and a substitution value for the base, so a point is traced along the function. Check boxes can show the negative of the function, hide the base slider and points, and hide all options. Double clicking on the applet opens it in a new frame to allow users to move the grid and adjust the axes scales using GeoGebra tools. 
45 
Absolute Value (1) 
Absolute Value Graph. Algebra. Function. Inequality. Explore absolute value using a graph of the absolute value function. A slider controls the position of a point on the graph. Set up an inequality problem and solve it using a second slider to control the position of another point on the graph. 
46 
Visualizing Equivalent Fractions (Proper Fractions) 
Number. Fraction. Equivalence. Area Model. Create a rectangular area model of a proper fraction and explore related models of equivalent fractions by subdividing the original model. Users can subdivide the original whole horizontally or vertically. 
47 
Adjacent Complementary and Supplementary Angles 
Geometry. Adjacent Angles. Complementary. Supplementary. Explore adjacent angles in degree measures, up to 180 combined (total) degrees. Show angle measures using check boxes, and control the total and one angle measure using sliders. One mode allows only combined measures of 90 degrees and 180 degrees, and the second mode allows combined angle measures from 0 to 180 degrees by one degree increments. 
48 
Fraction Bars (Strips): Addition Problem Set 1 
Number. Fraction. Addition. Use sliders to make fraction bars model ten addition problems. Choose a common denominator value and check your answer. Visual, numeric, and written feedback can be shown. 
49 
Similar Triangles SAS 
Geometry. Similarity. SAS. Ratio. Explore similar triangles that show sideangleside values. Side values for triangle 1 are rounded to the nearest whole number. Angle values are rounded to the nearest whole degree. Drag points on triangle 1 and see triangle 2 change. Adjust the ratio of corresponding sides from 1/4 to 2 by quarters and thirds. Drag triangle 2 onto triangle 1. 
50 
Pythagorean Theorem 1 
Geometry. Right triangle. Formulas. Pythagorean Theorem. Explore the Pythagorean Theorem using a right triangle showing squares drawn off each of the sides. Show or hide values for the side lengths, areas of the squares. Show the Pythagorean Theorem, including with selected values shown. If the values of two sides or areas are shown, users can see the solution steps to find the third side. 

The list is NOT alphabetical by tool name.  The descriptions begin with content tag(s). You can use your browser's Find feature ("apple + F" on an Apple/MLTI computer) to search by content tags and key words. 
Switch to the ParticipantDesigned Resources and Starter Tools List.  
Switch to the Interactive Mathematics Tools for Assessment & Instruction List. 
Helpful Tips
To automatically trust the GeoGebra certificate and speed up loading these pages, click on: Show Certificate > Trust (select the arrow) > When using this certificate > pull down to Always Trust; then click Trust at the bottom right corner.
*Note: Opening GeoGebra using the button at the top right requires that your computer is connected to the Internet, and loading time may be affected by your connection speed, local network settings, and other factors. Closing this browser window/tab will also close the GeoGebra window created by this button (be careful to save your work). You can save and open files on your computer's hard drive when using this button, and work offline only AFTER GeoGebra is opened (this is different from the WebStart version). This version of GeoGebra runs through your Internet browser and should work even if you are not able to save the GeoGebra application or WebStart version to your computer.
Depending on your local connection speeds and Internet settings, you may experience faster loading times using GeoGebra offline as an application or with the WebStart version (both versions are free; see www.geogebra.org). Download all the tools on this page as individual GeoGebra files.
These tools require Java 1.4.2 or later. If you have trouble opening the files, please make sure that Java 1.4.2 (or later) is installed and active in your browser. (Click here to install Java now.)
If Java 1.4.2 or later is installed and you experience trouble, try quitting the browser and restarting, or use a different browser (e.g. if you are using Firefox and the applets stop loading, try using Safari).
If you continue to have problems loading these applets, contact Peter TierneyFife at ptierneyfife@edc.org.
Credits, License, and Contact Information
GeoGebra applets collaboratively designed by MSP project partners and staff of EDC in Maine (Download this free application from the GeoGebra Web site, www.geogebra.org).
Covered under the Creative Commons License (AttributionNoncommercialShare Alike). Under this license you are free to to copy, distribute, display, and perform the work, and to make derivative works, under the following conditions: attribution is given, the use is noncommercial (unless you have permission from the author), and if you alter or build on this work you may distribute the resulting work only under a license identical to this one.
Report errors and send comments to Peter TierneyFife at ptierneyfife@edc.org.
Back to the EDC in Maine home page.