Seventh Grade Online Demonstration/Exploration Tools

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Explanation of Column Headings
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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
	Percent	Pie Chart - Percentages and fractions in a pie chart.	3	3	3
	Fractions/Decimals/ Percents	Bar Model - Fractions, decimals, and percents represented by a bar (divided into equal parts).	3	3	3	Fractions of a bar
	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
	Multiplication	Rectangle Multiplication – Visualize the multiplication of two numbers as an area.	3	3	2
	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
	Fractions - equivalent and comparison	In-between fractions - This is a multi-step activity which leads ultimately to finding fractions, on a number line, between two given fractions.	2	2	3	In-between fractions



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

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 shapes, symmetry, angles, 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	Translation	Transformations - Translation – Dynamic applet for exploring translations.	3	3	3	built in
	Reflection	Transformations - Reflection – Dynamic applet for exploring reflections.	3	3	3	built in
	Rotation	Transformations - Rotation – Dynamic applet for exploring rotations.	3	3	3	built in
Use visualization, spatial reasoning, and geometric modeling to solve problems

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	Perimeter and Area	Cyberchase Airlines Builder Game - Drag (and sometime rotate) segments to make a spaceship. A spaceship must be an enclosed shape. Fixed perimeter. Find the shapes.	1	3	3	Airline Game
	Mass	Pan Balance: Shapes - This double pan balance provides an environment in which to consider the concept of equivalence.	3	3	3	Find the Lightest Pan Balance 2 Pan Balance 3
Apply appropriate techniques, tools, and formulas to determine measurements

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

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	Spinners - Can make various spinners with equal or unequal regions. Spin once or multiple times. Results table provided.	3	3	3	Spinner Game

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Explanation of Column Headings

(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