# Geoboard Geometry

Sometimes geoboards are left on the shelf because we don’t know what to do with them. They can be powerful tools for students to study, length, area and perimeter. (But remember to be careful with the perimeter part because the length of one unit is only measured on the horizontal or vertical, not the diagonal.) Geoboards can help students experience area so that they can develop area formulas for themselves.

Geoboards in the Classroom
This unit deals with the length and area of two-dimensional geometric figures using the geoboard as a pedagogical device. Five lesson plans are provided.

The Online Geoboard
An applet simulates the use of an actual geoboard without the usual limitations of working with rubber bands. Most materials designed for real geoboards may be used with this online version.

Rectangle: Area, Perimeter, Length, and Width
This applet features an interactive grid for forming rectangles. The student can form a rectangle and then examine the relationships among perimeter, area, and the dimensions of the rectangle as the rectangle dimensions are varied.

Investigating the Concept of Triangle and the Properties of Polygons: Making Triangles
These activities use interactive geoboards to help students identify simple geometric shapes, describe their properties, and develop spatial sense.

National Library of Virtual Manipulatives: Geometry (Grades 6—8)
This site has a number of virtual manipulatives related to the NCTM geometry standards.

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# Hands-On Measuring

Students need active learning experiences to understand measurement concepts and develop important skills. These resources provide opportunities for students to problem solve with hands-on and virtual measurements in real-world and online environments.

The Global Sun Temperature Project
Bigger than hands-on, this is an annual real-world, international and interdisciplinary research project for students. Classes gather local data, post data online, and use the aggregated data to see how average daily temperatures and hours of sunlight relate to distance from the equator.

It Takes Ten
Students use metric units to estimate and measure weight, length, and volume, and to determine area.

Open-Ended Math Problems: Get Ready, Get Set
Select a month and scroll down to find open-ended measurement problems at three levels of difficulty. Students build mathematics understanding and see how mathematics is used in everyday life.

Pentagon Puzzles
This measurement lesson is one of 37 hands-on projects focused on mathematics. See http://www.math.nmsu.edu/~breakingaway/lessons.html for more lessons.

Popcorn Math
Here is a volume estimating activity for students to do on their own or with others.

Surface Area and Volume
Examine prisms from multiple views, adjust dimensions, rotate prisms, and see how dimension changes impact volume and surface area. Students can also calculate volume and surface area.

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# Linear Measurement

Sure middle schoolers know how to measure length! But if students need a little more experience with linear measurement, here are challenging resources that put linear measurement into a practical context, or can be used for review before introducing a new measurement topic.

Big Tree: Have You Ever Seen a Tree Big Enough to Drive a Car Through?
In this thought-provoking, discussion-generating challenge, students use common sense, given information, and their calculated tree diameters to answer the question. Teachers should investigate the links at the bottom of the web page. All activities on this site are printable.

Constant Dimensions
Students measure length and width of a rectangle using both standard and nonstandard units of measure. After creating a length vs. width graph, students observe an interesting and important fact — the ratio of length to width in a rectangle is constant.

Inclined Plane
Here is a terrific multiday lesson for teachers interested in having students apply their linear measurement skills and engage in mathematics discussions. Students use length and height data from hands-on experiments to draw conclusions. Useful teacher information is included.

Perimeter Explorer
Using this applet, students determine perimeters for irregular shapes on a grid. The applet is part of a complete lesson reinforcing students’ concept of perimeter and skills for finding perimeters. Shape area can be varied and a table comparing perimeter and area can be generated.

Reaching New Heights
Measuring, collecting and interpreting data, using variables—this complete lesson has it all! Students measure height and arm span, create a scatterplot, and draw conclusions about the correlation. This lesson is an excellent way to build the foundation for the study of functions. Teacher support and information about supporting research is included.

Rectangle: Area, Perimeter, Length, and Width
Using this simulation, students can instantaneously see the interplay among perimeter, area, and the rectangle dimensions. The rectangle size or shape is changed by dragging a point.

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# Area and Volume

Here are online resources with virtual manipulatives that can help make area and volume real for students. Be sure to check out the sites these resources are from — the sites contain many other interesting and useful mathematics learning resources.

Area Explorer
With this simulation, the student finds the areas for irregular shapes on a grid. Answers are checked and a table displays the perimeters and areas. The instructor page contains exploration questions to use to investigate the relationship between area and perimeter.

How High?
This virtual manipulative simulates pouring a liquid from one container to another container with different dimensions and the same or different shape. Students determine the volume of the liquid in the first container and predict the height of the liquid in the second. The container can be a cylinder, tank, or cone.

Neighborhood Math
Two of this site’s printable lessons, Math at the Mall and Math in the Park or City, feature hands-on activities where students use area or volume to explore their actual neighborhood.

Patios: Does Bigger Perimeter Mean Bigger Area?
This activity challenges students to think about the relationship between perimeter and area. Students must use a little ingenuity to find the dimensions of the tiles used to build two patios with the same area, but different shapes.

Scaling Away
In this hands-on lesson, students find the dimensions of a rectangular prism or cylinder and create a larger scale model of the same shape. After calculating surface areas and volumes, students draw conclusions about the relationship between surface area and volume.

Three Dimensional Box Applet: Working With Volume
Students create boxes by using their mouse to indicate how much of each corner should be cut from a grid. The dimensions of the box and its volume and surface are generated by the applet

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