Learning Resources Welding System LRM320B GUD User Manual

Look for these other great products from  
®
Learning Resources !  
®
LER 0913 Mini GeoSolids  
LER 0921 Folding Geometric Shapes  
LER 0922 Large Geometric Shapes  
For a dealer near you, call:  
(847) 573-8400 (U.S. & Int’l)  
(800) 222-3909 (U.S. & Canada)  
+44 (0)1553 762276 (U.K. & Europe)  
© Learning Resources, Inc., Vernon Hills, IL (U.S.A.)  
Learning Resources Ltd., King’s Lynn, Norfolk (U.K.)  
Please retain our address for future reference.  
Made in China.  
LRM3208-GUD  
 
2
 
Introduction  
®
The transparent Giant GeoSolids set includes 10 plastic, three-dimensional  
shapes that allow for hands-on study of volume. These shapes can expand  
daily math lessons while introducing, teaching, and reviewing geometric  
concepts effectively. They allow students to make concrete connections between  
geometric shapes and their associated formulas for volume, as  
well as compare the volumetric relationship between each shape.  
Most shapes in this set are variations of a prism or a pyramid, both of  
which are polyhedrons. Polyhedrons are solid figures with flat sides, or  
faces. Faces may meet at a point, called a vertex, or at a line, called an  
edge. A prism has two congruent bases; the remaining faces are rectangles. A  
pyramid has one base and the remaining faces are triangles.  
Three shapes in this set have curved faces rather than flat ones: the cylinder,  
cone, and sphere. Technically, they are not polyhedrons. Even so, a cylin-  
der can be thought of as a circular prism: a figure with congruent circular bases  
and a single, rectangular face. A cone can be thought of as a pyramid with a  
circular base and a face that is a wedge. A sphere is a unique shape with no  
parallel to prisms or pyramids.  
At the outset, learning formulas for the volume of more than a dozen geometric  
shapes may seem daunting to your students. However, formulas become much  
easier to remember when students recognize that only the method for calculating  
the area of a base changes from formula to formula; the other variables of a  
polyhedron are calculated the same way, regardless of shape.  
Getting Started with Transparent Geometric Shapes  
Allow students to become familiar with the manipulatives before beginning  
directed activities. You may want to explore prisms and pyramids on separate  
days. Encourage students to handle, observe, and discuss the shapes. Ask them  
to write down their observations as they make the following comparisons:  
How are the shapes similar? (With the exception of the sphere, all shapes have  
the same height. They are all three-dimensional. They all have empty spaces  
inside them.) How are they different? (Some have flat sides, some have curved  
sides. Some are box-shaped, some are round, and some are triangle-shaped.)  
Where have students seen these shapes in the world around them? (Great  
Pyramids  
of Egypt, traffic pylons, film canisters, soccer balls, pieces of chalk, boxes,  
lipstick tubes, and so on.)  
Introduce and identify the following terms: face, edge, vertex or corner,  
and base. Mention to students that the base of each shape can be identified  
by its color.  
Ask students how they might organize the shapes into categories based on their  
3
 
features. Write students' answers on the board. Then, define pyramids and  
prisms. Hold up an example of a prism and a pyramid for the class.  
Encourage students to organize the shapes again based on this information.  
Discuss and explain the cylinder, sphere, and cone as exceptions.  
Geometric  
Shape  
Number of Shape of Number of Number of Number of  
Bases Base(s) Faces Edges Vertices  
Square Prism  
Rectangular Prism  
Hexagonal Prism  
Triangular Prism  
Square Pyramid  
Triangular Pyramid  
Sphere  
Hemisphere  
Cylinder  
Cone  
Work with students to create a table like this one to record their observations:  
Show students a cardboard box. Ask if the box is a prism or a pyramid.  
(Prism.) Have a student volunteer identify the box's bases, faces, edges, and  
vertices. Have another student do the same for an oatmeal container. You may  
need to cut the container to make identification easier.  
This would be a good time for your students to make constructions of the  
various models. You can construct models using toothpicks and gum drops,  
straws and yarn, or even pipe cleaners. As you go through formulas, encourage  
students to refer to their models to visualize why the formulas work.  
Introducing Volume  
Volume, or the capacity of an object, is sometimes confused with surface  
area. At first glance, the formulas for finding each appear somewhat similar. A  
helpful way to compare the two is to explain surface area is the amount of  
4
 
room on the outside of a shape, and volume is the amount of space inside a  
shape. Discuss the importance of measuring volume, giving such examples as  
knowing how much water a pool will hold, how much air fills a SCUBA tank,  
or how much cement fits in a cement mixer. Ask students for other examples.  
Students will benefit from practice with building, measuring, and filling  
containers to understand volume. Each shape has openings in the base and  
can be filled with water, sand, rice, or other materials. By filling one shape  
and pouring its contents into another shape, students can explore volume  
relationships between shapes. If you intend to have students perform exact  
measurements using a graduated cylinder, be sure they are comfortable  
reading the bottom edge of the water level, or meniscus.  
Note: The bottoms of each shape are not removable.  
Challenge students to estimate the volume of each shape and place them in  
order from largest to smallest volume. You may want to allow students to  
fill their shapes to make more accurate estimations. As you introduce the  
formulas for finding the volume of each shape, encourage students to refer  
to the shapes for reference. You may wish to distribute copies of the table  
on page 2 for reference.  
Once you have finished your discussion, students can mathematically  
calculate the volume of each shape to confirm the accuracy of their initial  
guesses about volume.  
These models were built using the metric system. Although they can be used  
with any measurement system, metric is easiest. Because of the thickness of  
the plastic, measurements between students might be slightly “off,” depending  
on if they measure from the inside edges or the outside edges. If students round  
to the nearest centimeter, this will not be a problem.  
Volume Formulas  
Prism  
Finding the volume of a general prism is simply a matter of multiplying the  
area of the base times the height of the prism:  
×
Volumegeneral prism = A  
H
A = Area of the base.  
H = Height of the prism.  
The formula for the area of the base of the prism  
depends upon the shape  
of the base.  
H
l
Rectangular Prism  
×
Volumerectangular prism = A  
H
w
5
 
= (l × w) × H  
H
Square Prism  
Volumesquare prism = A × H  
= (w × l) × H  
l
w
b
A = Area of the square base.  
H = Height of the prism.  
s = Length of the side.  
h
H
Triangular Prism  
Volumetriangular prism = A × H  
= ( b× h) × H  
A = area of the triangle base ( b× h)  
h = altitude, or height of the triangle.  
H = height of the prism.  
H
Hexagonal Prism  
Volumehexagonal prism = A × H  
= (w × s) × H  
A = Area of the hexagonal base.  
H = Height of the prism.  
Explain that the area for a hexagon is calculat-  
ed as follows:  
w
A = w × s  
s
w = Width of hexagon as shown.  
s = Length of side.  
r
H
Cylinder  
Volumecylinder = A × H  
6
 
2
= (πr ) × H  
Pyramid  
Introduce the general formula for finding the volume of a pyramid.  
Volumepyramid = A × H  
Ask students to identify the difference between this general formula and the one  
for the prism. (There is one more variable:  
volume formula for a prism, it is easy to  
remember the volume formula for  
.)If students remember a  
a pyramid with the same-size base and  
H
height: simply multiply by . You  
can demonstrate this concept by pouring  
three filled pyramids into the  
corresponding prism in the Geometric  
Shapes set.  
l
w
Square Pyramid  
H
Volumesquare pyramid = A × H  
--------------  
= (l × w) × H  
h
b
Triangular Pyramid  
H
Volumetriangular pyramid = A × H  
_
= (b × h) × H  
r
Cone  
r
Volumecone = A × H  
2
= (πr ) × H  
_
Sphere  
Volumesphere = πr  
r
3
7
 

Leica Microscope Magnifier DMI3000B User Manual
Lennox International Inc Furnace ML180DFE SERIES User Manual
Life Fitness Home Gym 909101 User Manual
Life Fitness Treadmill 97TE XXXX 08 User Manual
Lindy Switch 25040 User Manual
Logitech Computer Keyboard mk220 User Manual
Magnasonic Car Stereo System MM171K User Manual
Maxtor Computer Drive 51024U2 User Manual
Mazda Automobile 2008 5 User Manual
Meridian Audio Projector D ILA 1080MF2 User Manual