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.
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.
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.
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.
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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