# Eighth Grade Online Demonstration/Exploration Tools

## Page Contents:

Number and Operations
Algebra
Geometry
Measurement
Data Analysis and Probability

### Number and Operations

 Broad Expectation* Topic Link to Applet and Description How good for teacher demos (1-3)? How easy for students (1-3)? How good for exploration (1-3)? Available activities Understand numbers, ways of representing numbers, relationships among numbers, and number systems Integer Addition Color Chips-Addition - Use color chips to illustrate addition of integers. 3 3 3 built in Integer Subtraction Color Chips-Subtraction - Use color chips to illustrate subtraction of integers. 3 3 3 built in Percent Percentages - Solve __% of __ is __ problems. ("What percent of a number is a number") 3 3 3 Fractions/Decimals/ Percents Fraction Model Applet - Set model, length model, and circle (area) model. Nice multiple representation tool from NCTM. 3 3 2 Understand meanings of operations and how they relate to one another Factoring Numbers Factor Tree - Prime factorization. Computer generated numbers or make your own. 3 3 2 built in Integer Multiplication Rectangle Multiplication of Integers – Visualize multiplication of integers using an area representation. 3 3 3 Prime Numbers Sieve of Eratosthenes - an (ancient, but still good) way to find the primes. Sieve of Eratosthenes – another one - click at the bottom of the table. Sieve of Eratosthenes – another one. 3 3 3 Compute fluently and make reasonable estimate

### Algebra

 Broad Expectation* Topic Link to Applet and Description How good for teacher demos (1-3)? How easy for students (1-3)? How good for exploration (1-3)? Available activities Understand patterns, relations, and functions Represent and analyze mathematical situations and structures using algebraic symbols Expressions Pan Balance-Expressions - Interactive pan balance allows numeric or algebraic expressions to be entered and compared. This balance is a natural extension of Pan Balance-Numbers and Pan Balance-Shapes. 3 3 3 Included online Distributive Property, Multiplying Binomials, and Factoring Algebra Tiles - Visualize multiplying and factoring algebraic expressions using tiles. 3 2 3 Use mathematical models to represent and understand quantitative relationships Analyze change in various contexts

### Geometry

 Broad Expectation* Topic Link to Applet and Description How good for teacher demos (1-3)? How easy for students (1-3)? How good for exploration (1-3)? Available activities Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships Shapes Geoboard – Use geoboards (virtual rubber bands) to illustrate area, perimeter, and more. 3 3 3 built in Specify locations and describe spatial relationships using coordinate geometry and other representational systems 2D relationships Turtle Geometry – Explore numbers, shapes, and logic by programming a turtle to move. 3 3 3 Apply transformations and use symmetry to analyze mathematical situations Transformations Transformations - Composition – Explore the effect of applying two of the following: translation, rotation, and reflection. 3 3 3 built in Transformations - Dilation – Dynamic dilation transformation. 3 3 3 built in Combining Transformations - Four levels of play. Use translation, rotation, reflection, and dilation. 3 3 3 Tessellations Tessellations – Tile the plane. 3 3 3 built in Tessellate! - This tool allows you to make your own shape to tessellate the plane. (Shodor) 3 3 3 Use visualization, spatial reasoning, and geometric modeling to solve problems Polyhedra Platonic Solids - Investigate the solids (cube, tetrahedron, ...). Rotate the shape. Shift-click the edges, vertices, and the faces to color (and count them). V - E + F =   ? Platonic Solid Duals - Investigate the solids and their duals. 3 2 3 Platonic Solids Platonic Solids - Nets Cut-out, Nets - Manipulate nets for the five Platonic Solids. Click and drag! See them open and close. 3 3 3

### Measurement

 Broad Expectation* Topic Link to Applet and Description How good for teacher demos (1-3)? How easy for students (1-3)? How good for exploration (1-3)? Available activities Understand measurable attributes of objects and the units, systems, and processes of measurement Rates Understanding Distance, Speed, and Time Relationships - Simulation of two runners along a track. Explore slope and starting points. 3 2 3 Apply appropriate techniques, tools, and formulas to determine measurements Angle Measure Protractor applet - Very nice. Has an introduction (which can be skipped). Various interactive activities with and without a virtual protractor. 3 3 3 included online Surface Area & Volume Surface Area and Volume - Manipulate dimensions of polyhedra, and watch how the surface area and volume change. Also manipulate the solid. 3 3 3 use compute mode

### Data Analysis and Probability

 Broad Expectation* Topic Link to Applet and Description How good for teacher demos (1-3)? How easy for students (1-3)? How good for exploration (1-3)? Available activities Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them Graphing Data Create a Graph Tool - for students (others) to make statistical graphs (NCES). 3 2 3 Bar Graph - You may enter data to create a bar graph, then change the settings for the graph's appearance. 3 2 3 Select and use appropriate statistical methods to analyze data Mean, Median, Mode Plop It! - allows the user to experiment with mean, median, and mode by using a bar graph (Shodor). 3 3 3 Available under the Learner tab Mean and Median - user experiments with mean, median, and applet shows the box-and-whisker plot (NCTM). 3 3 3 Available under the Exploration Comparing Properties of the Mean and the Median - Simplified version of "Mean and Median" above (only 7 data points and no box-and-whisker plot). 3 3 3 On web page Develop and evaluate inferences and predictions that are based on data Understand and apply basic concepts of probability Experimental probability Ball-Dropping applet - Ball drops down through a series of pins. Probability and Pascal's Triangle. 3 3 3

Click here for the Index for >> Online Math Games, Demonstration/Exploration Tools, and Puzzles

(This page is organized using the five content areas in school mathematics, as articulated in the NCTM Principles and Standards, 2000.)

• Broad Expectation - from NCTM Principles and Standards (2000) for each of the five NCTM Content Standards
• Topic - Mathematical topic
• Link to Applet and Description - A description of the applet and hyperlink to the page.
• How good for teacher demonstrations (1-3)? - Is this applet good for the teacher to use in a class demonstration?

3=Excellent for class demonstrations of mathematics
2=Fair to Good for class demonstrations of mathematics
1=Not designed for class demonstrations of mathematics

• How easy for students (1-3)? - How easy is the applet for students to use, without instruction?

3 = No advance instruction needed (very easy to use).
2 = Short demonstration helpful (pretty easy to use).
1 = Extensive demonstration needed (hard to use without an explanation).

• How good for exploration (1-3)? - Is this applet designed for student exploration?

3=Excellent for student exploration of mathematics.
2=Fair to Good for student exploration of mathematics.
1=Not designed for student exploration of mathematics.

• Available activities - Are there student activities already written to accompany this applet? If so, links are provided.

by: James R. Olsen, Western Illinois University
updated: December 14, 2011