||Making Patterns (applet)
Includes an interactive figure for creating, comparing, and viewing
multiple repetitions of pattern units. The interactive figure
illustrates how students can create pattern units of squares, then
predict how patterns with different numbers of squares will appear when
repeated in a grid and check their predictions.
Create pattern units of two
to five squares and display them on the grid. Can you visualize how the grid
will look when your pattern is repeated? Try these challenges:
- Make different patterns with
units of varying size. The units you create should all result in a pattern
with vertical stripes when displayed on the grid.
- Make a unit that will create a
pattern with red squares appearing diagonally on the grid.
- Create a pattern whose eighteenth
square is green.
How to Use the Interactive Figure
Use the interactive
figure to create pattern units. Then predict how units with different numbers
of squares will appear when they are repeated in a grid.
Click on the
Arrow Up or Arrow Down buttons at the top right to adjust the number of squares
to be included in the pattern unit.
To color a square, click on a square displayed in the rectangle in the upper
left and then click on a color button.
Click on the Arrow Up or Arrow Down buttons in the lower right to adjust the
speed of the displayed pattern.
Other features can be accessed from the following buttons:
the unit of squares shown in the upper left box until the grid is filled.
one unit to the pattern shown in the grid.
again to resume.
Making Predictions from
Patterns in the Classroom
The ability to create and
analyze simple patterns and make predictions about them is a major learning
goal for students in the primary grades. Using cubes and a grid or the
interactive computer applet, students can create and study different pattern
units. With physical manipulatives, they can repeat their pattern units in a
linear fashion, predicting what the next cube will be or what color the
sixteenth cube will be. The interactive applet is designed so that students can
place squares one at a time as they extend their patterns, place entire units on
the grid one at a time, or have the computer fill the entire grid. Students can
complete the task using either method.
This example encourages
students to explore what new designs their pattern units will generate when
repeated on the grid. Teachers should help students focus on the number of
squares in students' pattern units and how these units will look when repeated
in a ten-by-ten grid. Questions such as these are helpful:
- How many squares are in your
- How many times can you repeat your
pattern unit in one row?
- Does your pattern unit fit one
- What happens if you make your
pattern unit one square longer (or shorter)?
Through the pattern activity
students can also explore the divisibility of 10 by 2, 3, 4, and 5. A similar activity,
"Mr. Stripes Paper Company," appears in Burton et al. (1992).
Creating pattern units with
the interactive applet can be beneficial for students who are not yet
successful in creating their own patterns with physical manipulatives. With
physical objects, students may simply make strings of objects without order or
repetition instead of creating units that are repeated. The computer
environment provides a structure for success and for reflection on the idea of
a repeating unit.
Take Time to Reflect
- What realistic applications
could teachers suggest to give students additional opportunities to
create and repeat pattern units?
- Why are conversations about the
pattern units students create important in helping them learn to analyze
patterns made by others?
Burton, Grace, Douglas
Clements, Terrence Coburn, John Del Grande, John Firkins, Jeane Joyner, Miriam
A. Leiva, Mary M. Lindquist, and Lorna Morrow. Third-Grade Book. Curriculum and Evaluation Standards for
School Mathematics Addenda Series, Grades K–6, edited by Miriam A.
Leiva. Reston, Va.: National Council of Teachers of Mathematics, 1992.
- 4.1 Creating, Describing, and Analyzing Patterns to Recognize Relationships and Make Predictions
- 4.1.2 Describing Patterns
- 4.1.3 Extending Pattern Understanding