Interactive Mathematics Tools for Assessment & Instruction
This page will be updated as project activities progress and project participants provide information related to curricula and student needs.
Many learning tools on this list were created using the open educational resource (OER) GeoGebra. Selected others link to interactive applets from other sites. Selecting a tool name launches the tool in a new browser window. Selecting an associated resource downloads the resource to your computer. Your computer must be connected to the Internet to open GeoGebra files or download resources using this list. 
Interactive Technology Resources
#  Tool Name (link) 
Associated Resources (link) 
Description (starts with content tag(s).) 
1 
Freudenthal Institute: Solving Equations 1 
Solving Equations 1 (.pdf) Solving Equations 1 (.doc) Tutorial 
Algebra. Solving Equations. Balanced Equation. Explore how to most efficiently solve equations by interacting with an interactive solutions tool using the balanced equation strategy. This version does the computation while users are required to focus on the process. This tool supports student exploration and discovery of multiple and efficient solution strategies. The supporting resources are created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
2  Freudenthal Institute: Solving Equations 2 
Solving Equations 2 (.pdf) Solving Equations 2 (.doc) Tutorial 
Algebra. Solving Equations. Balanced Equation. Explore how to most efficiently solve equations by interacting with an interactive solutions tool using the balanced equation strategy. This version requires the user do the computation and supply the solution. Each step of the process is checked for accuracy. This tool supports student exploration and discovery of multiple and efficient solution strategies. The supporting resources are created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
3  NLVM: Algebra Balance Scales 
No print resource available. Tutorial 
Algebra. Solving Equations. Balance Method. This tool allows users to solve simple linear equations through the use of a balance beam. © 19992010 Utah State University. The supporting resources are created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
4a  Trace Method (1) 
Solve Eq Trace Method 1 (.pdf) Solve Eq Trace Method 1 (.doc) Tutorial 
Algebra. Solving Equations. Trace Method. This tool allows users to use the trace method to solve a simple linear equation. The tools and resources are created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
4b  Trace Method (2) 
Solve Eq Trace Method 2 (.pdf) Solve Eq Trace Method 2 (.doc) Tutorial 
Algebra. Solving Equations. Trace Method. This tool allows users to use the trace method to solve a simple linear equation. The equation can be modified by the user. The tools and resources are created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
5a  Graphing & Substitution (1) 
Solve Eq Graph & Substitution_1 (.pdf) Solve Eq Graph & Substitution 1 (.doc) Tutorial 
Algebra. Solving Equations. Substitution Method. This tool allows users to solve simple linear equations through the use of substitution. This is also represented through the use of graphing. The tools and resources are created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
5b  Graphing & Substitution (2) 
Solve Eq Graph & Substitution 2 (.pdf) Solve Eq Graph & Substitution 2 (.doc) Tutorial 
Algebra. Solving Equations. Substitution Method. This tool allows users to solve simple linear equations, which can be modified, through the use of substitution. This is also represented through the use of graphing. The tools and resources are created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
6  Freudenthal Institute: Algebra Arrows 
No print resource available. Tutorial 
Algebra. Solving Equations. Substitution. Flowchart. Graphing. This tool allows users to represent and solve simple linear equations through the use of interactive flowcharts, substitution or/or graphing. The supporting resources are created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
7  Jim Reed: What is a linear equation? 
No print resource available. Tutorial 
Algebra. Solving Equations. Algebra Tiles. This tools uses algebra tiles to represent and solve linear equations. Equations are also shown graphically. This is the "Algebra Tiles and the Distributive Property" applet; choose the button "Tiles Practice". The supporting resources are created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
8a  Comparing Ratios including Percent (1) 
No print resource available.  Ratio. Proportion. This tool allows users to compare a ratio (whole from 1 to 200) to a percent visually and change the whole and part using sliders. A proportion and decimal values are shown. The tool and resources are created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
8b  Comparing Ratios (2) 
No print resource available.  NOTE: This is a test tool and may be changed significantly without notice. Ratio. Proportion. Percent Change. This tool allows users to compare a ratios (wholes from 1 to 500, parts up to 2 times the whole) visually and change the wholes and parts using sliders. A proportion and decimal values are shown. The tool and resources are created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
8c  Comparing Ratios including Percent (3) 
No print resource available.  Ratio. Proportion. This tool allows users to compare ratios visually and change the whole and part using sliders. A percent (whole set to 100) and two other ratios are shown, as well as poportions and decimal values. The tool and resources are created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
8d  Comparing Number Lines: Ratios & Proportions 
No print resource available.  Users use up to three number lines to compare ratios. The top number line has the whole as 100 and the part shows percent; the wholes on the other two number lines can be changed from 1 to 200. Check boxes show proportions and decimal values. 
9  Double Number Line  No print resource available.  Ratio. Proportion. Fraction. This tool allows users to compare a proper fraction (denominator a whole number from 0 to 10) to a whole (from 1 to 300) visually and change the numerator, denominator, and whole using sliders. The value of the part of the whole and the equivalent percent can be shown. The tool and resources are created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
10a  DVD Rental Plans Problem  DVD Problem (.pdf) DVD Problem (.doc) 
Algebra. Systems of Equations. Linear Functions. Applications. Users compare two DVD rental plans from a video store. The user can change the monthly fee and perDVD charge for each plan. The equations, graph, and table can be shown and adjust automatically as the values change. The tool and resources are created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
10b  Song Downloads  No print resource available.  Algebra. Systems of Equations. Linear Functions. Applications. Users compare two online music purchase plans. The user can change the monthly fee and persong charge for each plan. The equations, graph, and table can be shown and adjust automatically as the values change. Adapted from the DVD Rental Plans Problem tool by the same authors. 
10c  Cost of Songs  No print resource available.  Algebra. Linear Functions. Applications. See the graph of an equation representing the cost of buying songs with a purchase plan that includes a monthly fee and a cost per song. users can change the monthly fee, cost per song, and trace the point on the graph representing a specific number of songs. 
11a  Sliding Rod (1)  No print resource available.  Geometry. Functions. Observe the trajectory of a ball in the midpoint of a vertical rod against a wall when the bottom of the rod is pulled away from the wall. The tool was created by D. Bowie for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
11b  Sliding Rod (2)  No print resource available.  Geometry. Functions. Explore the trajectory of a ball on a vertical rod against a wall when the rod is pulled away from the wall or when the top is pulled down, and when the ball is at different heights on the rod. The tool was adapted by EDC in Maine staff from a tool by D. Bowie (11a, above). Created for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
12a  Analysis of Cubic Polynomials (1)  No print resource available.  Calculus. Algebra. Functions. Slope. Derivative. Analyze the relationship between a cubic polynomial and its derivative. Drag a point on the cubic function and observe the trace of the derivative function. Shows the slope triangle. You can change the cubic polynomial by dragging the graph of the function or by adjusting the function values in the Algebra window. Minimum, maximum, roots, and inflection points are all shown and values displayed in the Algebra window. Created by D. Bowie for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
12b  Analysis of Cubic Polynomials (2)  No print resource available.  Calculus. Algebra. Functions. Slope. Derivative. Analyze the relationship between a polynomial and its derivative. Drag a point on the function and observe the trace of the derivative function. You can change the polynomial using sliders. Minimum, maximum, roots, and inflection points and point coordinates can be displayed. You can show or hide the trace of the derivative, the derivative function, the tangent line, the slope triange, the function, and the grid. The tool was adapted by EDC in Maine staff from a tool by D. Bowie for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
13  Pythagorean Theorem  No print resource available.  Geometry. Algebra. Triangles. Explore the Pythagorean Theorem dynamically by dragging the triangle vertices or the squares. Areas for the squares are given, as well as a computation of a^{2} + b^{2} that can be compared to the value of c^{2}. Created by D. Bowie for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
14  Pythagorean Theorem with Circles  No print resource available.  Geometry. Algebra. Triangles. Explore the Pythagorean Theorem dynamically by dragging the triangle vertices. Circles (each centered on the midpoint of a leg or hypotenuse, with diameter the length of the leg or hypotenuse) are shown, as well as the area of each circle. Created by D. Bowie for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
15  Ferris Wheel Unit Circle  FerrisWheelUnitCircle32 (.pdf)  Trigonometry. Functions. Unit Circle. Users create a graph of the height of a seat on a Ferris wheel to explore the sine function and characteristics of the unit circle. Users can pivot the Ferris wheel to emphasize the change in height of a seat, show the sine and cosine functions, turn on coordinates, degrees, and/or radians associated with the eight benchmark points on the unit circle, and see values for sine, cosine, and tangent of the seat position. Created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. Adapted from Trigonometry Functions and the Unit Circle (2) which was adapted from the Trigonometry Functions and the Unit Circle tool by J. Lawlis. 
16a  Arithmetic Rack (1)  No print resource available.  Number. Addition. Subtraction. Simulates an arithmetic rack with 10 beads per rod. One or two rods can be shown, as well as the total number of beads on each side of each rod, and the sum or difference of the beads on the left of the rods. Checkboxes allow users to hide the beads on the right side of each rod. Problems for which students make the total value can be generated randomly, and feedback appears when the total on the left side matches the target number. Created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
16b  Arithmetic Rack (2) Beads on Left 
No print resource available.  Number. Subtraction. Addition. Simulates an arithmetic rack with 10 beads per rod. Beads start on the left, which can be useful for subtraction problems. One or two rods can be shown, as well as the total number of beads on each side of each rod, and the sum or difference of the beads on the left of the rods. Checkboxes allow users to hide the beads on the right side of each rod. Created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
17  5 Frame & 10 Frame  No print resource available.  Number. Addition. Users drag chips onto a 5 frame or a 10 frame. Options include showing totals, hiding frames or remaining chips, and showing the sum or difference of the two rows in the 10 frame. Created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
18a  Addition Models: PartPartWhole and Number Line 
No print resource available.  Number. Addition. Drag counters into the two boxes of the partpartwhole model and see the total (whole) in the box underneath. The number line model reflects the parts and the whole in the partpartwhole model. Options include showing or hiding numbers, counters, and aspects of the number line. Created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
18b  Addition Models: PartPartWhole and Number Line Problems (version 1) 
No print resource available.  Number. Addition. Drag counters onto the two boxes of the partpartwhole model and see the total (whole) in the box underneath. The number line model reflects the parts and whole in the partpartwhole model. This version includes problems for users to solve and a checkbox shows the answer. Options include showing or hiding numbers, counters, and aspects of the number line. Created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
18c  Addition Models: PartPartWhole and Number Line Problems (version 2) 
No print resource available.  Number. Addition. Drag counters onto the two boxes of the partpartwhole model and see the total (whole) in the box underneath. The number line model reflects the parts and whole in the partpartwhole model. This version includes problems for users to solve and a checkbox shows the answer; problem 4 includes a slider to set the number subtracted. Options include showing or hiding numbers, counters, and aspects of the number line. Created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
19a  Broken Rulers (1)  No print resource available.  Measurement. Number. Measure different objects using various rulers. Checkboxes show measurement aids and allow you to check answers. Select from nine objects and five U.S. (customary) rulers. Rulers divided into 1/4 inch intervals. Created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
19b  Broken Rulers (2)  No print resource available.  Measurement. Number. Measure different objects using various inch and centimeter rulers. Checkboxes show measurement aids and allow you to check answers. Select from twenty objects and eight rulers. U.S. (customary) rulers divided into 1/16 inch intervals. Created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
19c  Broken Rulers: Measure Me  No print resource available.  Measurement. Number. Use a broken ruler to measure three pets. Checkboxes show measurement aids and allow you to check answers. U.S. (customary) ruler is divided into 1/16 inch intervals. Created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
19d  Locating Numbers on a Ruler  No print resource available.  Measurement. Number. Locate numbers on a U.S. Customary ruler. Activity options include two sets of values to drag onto the ruler, a way to generate random values to locate on the ruler, and a randomly generated distance (span) that can be marked using the two pointers and checked for accuracy. The ruler intervals can be adjusted. 
19e  Measuring with a Ruler  No print resource available.  Measurement. Number. Measure objects and segments with a U.S. Customary ruler. Activity options include a set of objects to measure and a way to generate segments of random lengths to measure and check. The ruler intervals can be adjusted. 
20  What is the Number?  No print resource available.  Number. Create a number line by setting minimum, maximum, and number of intervals. Use up to 7 pointers to mark locations on the number line. Check pointer values using a checkbox. Choose between fraction or decimal values for hash marks and pointers. Created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
21  Perimeter Example 1  No print resource available.  Geometry. Perimeter. Circumference. Explore a visual strategy for finding the perimeter of a region defined by three arcs in an equilateral triangle. Designed and created by Pam Buffington and Peter TierneyFife of EDC in Maine. 
22  Visualizing Square Roots  No print resource available.  Number. Square Root. Users adjust a slider to see a visualization of a square root as the side length of a square with the area shown. Users can estimate square roots by showing the area and checking their estimate using a check box for the square root. Checkboxes turn on and off the grid, side lengths, area, and square root. Designed and created by Pam Buffington of EDC in Maine. 
23a  Where Is The Fraction (1)  No print resource available.  Number. Fractions. Locate or identify fractions on a number line from zero to one. Users can move up to five pointers (four blue and one red) and select the precision of the pointers. Users can adjust the number line by changing the number of intervals and the hash mark labels. Labels can be hidden or shown with (1) denominators the same as the number of intervals (hash marks, up to 20ths) or precision value (pointers, up to 100ths); (2) in reduced form, or (3) as decimals. Please note that all label values may be rounded. For blue and red pointers, the precision sliders control the amount to which the pointer value labels are rounded. Created by staff of EDC in Maine. Adapted from the What Is The Number tool. 
23b  Where Is The Fraction (2)  No print resource available.  Number. Fractions. Locate or identify fractions and mixed numbers on a number line from zero to two. Users can move up to five pointers (four blue and one red) and select the precision of the pointers. Users can adjust the number line by changing the number of intervals and the hash mark labels. Labels can be hidden or shown with (1) denominators the same as the number of intervals (hash marks, up to 10ths) or precision value (pointers, up to 100ths); (2) in reduced form, or (3) as decimals. Please note that all label values may be rounded. For blue and red pointers, the precision sliders control the amount to which the pointer value labels are rounded. Created by staff of EDC in Maine. Adapted from the Where Is The Fraction (1) tool. 
23c  Locating Fractions on a Number Line  No print resource available.  Number. Fractions. Number Line Location. Locate four given fractions on a number line that includes dots/points at possible locations. There are six sets of fractions, and the number line includes labels at 0 and either 1 or 2 (depending on the set). Once all four fractions are placed on the line, check boxes allow you to check the locations and show a hint. 
24  Water Triangle  No print resource available.  Ratio. Proportion. Geometry. Area. Manipulate a model of a water triangle. Users can choose from three different scenarios and adjust variables such as water area, water height, and distance of the water level along one triangle leg. Check boxes allow users to show values for leg distances, water height, and water area. Created by staff of EDC in Maine. 
25  Rolling Paper (Exploring Cylinders)  No print resource available.  Geometry. Cylinder. Volume. Area. Surface Area. Explore cylinder volume and surface area by comparing two cylinders made by rolling up two rectangles (pieces of paper). Change the dimensions of the paper and use check boxes to show the radius, area of the circular end, volume, and total surface area for each cylinder. 
26  Cylinder Volumes  No print resource available.  Geometry. Cylinder. Volume. Area. Surface Area. Explore cylinder volume by comparing two cylinders. Change the dimensions of the cylinder (below each cylinder as length and width of a rectangle) and use check boxes to show the radius, area of the circular end, and volume for each cylinder. 
Assessment Probes and Intervention Resources
#  Probe (link) 
Associated Resources (link) 
Description (starts with content tag(s).) 
1 
Solving Equations Probe (.pdf) Solving Equations Probe (.doc) 
SolveEq Probe Resources (.pdf) SolveEq Probe Resources (.doc) 
Algebra. Solving Equations. A brief formative assessment probe designed to elicit student understandings and misconceptions related to core concepts for solving algebraic equations. The supporting resources were created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
Workshop Resources
#  Associated Resources (link) 
Description (starts with topic tag(s).) 
1 
GeoGebra Sequence Command handout (.pdf) GeoGebra Sequence Command Tool (Web page) GeoGebra Sequence Command Tool (download as .zip) 
GeoGebra. Commands. Sequence. This activity is designed engage participants with exploring possible uses of the Sequence command in GeoGebra. The resources were created by EDC in Maine staff for the Maine Learning Technology Initiative (MLTI) to support the integration of technology in mathematics learning and teaching. 
2 
GeoGebra Wiki (English) 
A link to the GeoGebra Wiki English Resources page. 
3 
Area of a Circle Triangle Areas Area Formulas 
Geometry. Area. Formula. Link to selected GeoGebra Wiki resources related to area formulas. The first two links are GeoGebra tools. The third link (Area Formulas) is a list of additional tools. 
4 
Geometry Relationships: Rectangle and Triangle Rational Number Products 
Geometry. Area. Number. Products. Link to selected resources related to the relationship between rectangles and triangle areas and products of rational numbers. Both resources are GeoGebra tools. 
5 
Equivalent Expressions  Distributive Property 2 Comparing Whole Number Products (12 x 12) Comparing Whole Number Products (30 x 30) Distributive Property Matrix Multiplication (2b) Distributive Property Matrix Multiplication (1) 
Number. Products. Properties. Link to selected resources related to equivalent expressions, the distributive property, and comparing products. All resources are GeoGebra tools. 
6 
Multiplying Fractions with a Scaling Model (Quadrivium) Multiplying Fractions – Area Model (EDC) Triangle Inequality Theorem (GeoGebra Web site) Triangle Inequality (GeoGebra Web site) Triangle Inequality (EDC) Compare Perimeters and Areas of Rectangles (2) (EDC) Exploring Rectangle Areas (EDC) Compare Perimeters and Areas of Squares (EDC) Compare Perimeters and Areas of Rectangles (1) (EDC) Area and Perimeter of Similar Rectangles (GeoGebra Web site) 
Geometry. Number. Triangle. Perimeter. Area. Fractions. Scaling. Link to selected resources related to topics in Number and Geometry. All resources are GeoGebra tools. 

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