Geometry is the branch of mathematics
dealing with the properties and relations of lines, angles, surfaces and
solids. All objects, whether the smallest protozoa to the largest
building in the world, can be described through geometric descriptions.
Symmetry is the ability to divide an object into parts, equal in size and
shape and similar in position on either side of a dividing line or around
a center. A pattern is an arrangement of shapes or colors in a design
with a repeatable quality.
In order for students to understand the difference
of these terms, they must practice and train their mind to observe and
pick out patterns and symmetry.
A pattern usually has a "unit cell" that
repeats itself. Even if one tree (unit cell) repeats itself in a
row, it is a pattern. A row of pegs can be a row of trees.
Patterns are all around us. A diamond shape is actually 4 points
(unit cells). If you combine several diamond shapes, you get an overall
pattern different from the original diamond.
The unit cell in the picture above is a 4
“rounded cornered rose.” The overall pattern is “rectangular.”
However, because the corners are not real rectangles the description is
This set of two activities, guides
students into defining a unit cell, which is very important in determining
a pattern. The repeatability of the unit cell, including the same
color and shape, is important to recognize. The more experience a
child has with identifying the unit cells the easier it becomes.
- Give each student a worksheet and crayons.
Instruct them to color or outline the unit cell on the worksheet.
(Answers: 1. circle; 2. square; 3. triangle; 4. circle; 5. square;
and 6. circle.)
After they complete that see if they can create
a pattern with any unit cell they decide on. Notice that we don’t
write in the colors for the unit cell, let them decide if color helps determine
the unit cell (it does!). This will give students practice on keeping
the unit cell the same.
- When students complete the worksheet
give them one box of pattern blocks per group. Instruct students
to work together to create a pattern with one or more unit cells.
Let their creativity go. Group cooperation is important.