Sample Lessons
Grades K - 2
The following are sample lessons for primary grades:
- Students at the primary level need to experience "hands on" work
with
concrete materials, pictures and drawings. Sample "hands on" materials
include pattern blocks, tangrams, Lego blocks, tinker toys. Miras,
mirrors, multilink cubes, jigsaw puzzles, and other construction toys.
With these and/or similar materials students should build various
constructions.
- Have students make figures with objects and/or drawings. Then have
the
students make mirror images of these objects and/or drawings. Have a
number of
mirrors available so that they can see how figures are reversed when they
look into the mirrors. Introduce the concepts of reflection and flipping
about a line.
- Introduce the concept of symmetry as being
able
to find a line through which an object, picture, or drawing can be flipped
to get the same looking object. Have students explore their own
constructions to see if they are symmetric. Also have available
additional objects, pictures, and drawings that are symmetric. Have
students discriminate between symmetric and nonsymmetric objects,
pictures, and drawings.
- Have students select a picture. Have the students hold the picture
at one
point and rotate/turn the picture about the one
point, and observe how it looks in different positions.
- Figure 1 shows a number of pictures. The pictures on the left are
the
original pictures. Have the children tell if each of the pictures on the
right were gotten by a flip or turn from the original picture on the left.
Figure 1
- Have students look around their environment and find objects that are
symmetric. Have
students work with appropriate software and
visit appropriate web sites.
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Grades 3 - 5
The following are sample lessons for Intermediate Grades:
- Students should continue work with construction toys at a more
complex level. Students at this age should be able to do more than
single-step transformations of slides, flips, and turns.
Have the students construct figures with "hands on" materials then
draw pictures of them. They can then copy these figures into a graphics
program such as HyperStudio. The graphics program can then allow the
students to
flip, turn, slide, and/or dilate the figure. Students can also make
animations of
their transformations.
- Figure 2 illustrates pictures with more than one step transformations
where the original picture is on the left and the transformed pictures are
on the right. Have the students tell which steps are involved for
generating each picture on the right.
Figure 2
- Have students develop an animation showing one of the pictures on the
left
transformed to the pictures on the right. Have
students work with appropriate software and
visit appropriate web sites.
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Grades 6 - 8
The following are sample lessons for Grades 6 - 8:
- Students can develop more mature transformations using computer
graphics,
including animations.
They should be able to work with multiple-step
transformations, including dilations as well
as slides, flips
and turns. Students should also be able to
work with
tesselations.
- Figure 3 demonstrates the applications of such transformations. Have
students predict how to transform the pictures at the left to the pictures
at the right. Have the students write animations for
one of the
pictures at the left to generate the corresponding pictures at the right.
Figure 3
- Have students explore tesselations. Then
have
students create a tesselation of their own, including an animation of the
generation of their tesselation.
- Have students explore concepts of congruency, similarity, perpendicularity, and parallelism as they relate to
transformations, as well as to other geometric concepts and relationships.
For example, if each of the three sides of one triangle are parallell to
the corresponding sides of another triangle, how do the triangles relate?
-
Have students work with appropriate software and
visit appropriate web sites.
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Geometry and
Spatial Sense: Sample Lessons