Patterns

Ag_math_patterns

Construct repeating pattern scenes using geometric shapes, objects, colors and textures
Grades K-2

Introduction
Repeating patterns can be found in many everyday things such as flowers, seashells, quilts, numbers, housing developments and snowflakes. Basic shape manipulation is used over and over in the development of beautiful geometric designs found in advanced architectural forms. Mathematics is a science of patterns and order, and recognition and discrimination among patterns is one of the foundations of children's mathematical development. Children's mathematics learning builds on their natural curiosity and enthusiasm for doing it themselves. With experience, children begin to identify and categorize increasingly complex patterns, and are eager to communicate their findings. With teacher-scaffolding, these students may begin to generalize their findings, one of the key components of learning algebra.

Preparation
Gather pictures showing a variety of patterns. Discuss these pictures moving from the concrete to the general (e.g., show a pineapple; ask what it is; ask children to share what they notice about the pineapple; with questioning, focus their attention on the spiral patterns and how these repeat.)

Procedure
The teacher begins the class with a teacher-generated pattern. Students copy and then extend the pattern.

The teacher/classroom aide views copied and extended pattern. Discussion/questioning is encouraged.

Students create their own patterns using 2 or more shapes and repeat the processes used with the teacher-generated pattern of extending the pattern, rotating, reflecting, translating, and dilating this pattern.

Evaluation
The student may be required either to create the task for teacher review
on-screen or as a printout.

The students' understanding may be assessed by questioning and discussion that
results from the exploration of  rotating, reflecting, translating, and dilating
the original pattern.  Discussion and questioning will emphasize what remained the
same, what differed, and how it differed from manipulation.

Model and encourage GENERALIZATIONS and the use of mathematically accurate vocabulary.

Extensions
The teacher will have students create 4-shaped patterns, then 5-, 6-, etc. Students print these patterns, copy several sets, and categorize the different kinds of patterns. The students should be ready to explain how they grouped their sheets. The teacher leads a discussion about same and different.

The teacher assigns a value to each basic shape and has students calculate the value of the various patterns, discuss their results, and look for patterns with equal value. The student should be encouraged to generalize their findings.

Students look for and copy down patterns that they spot in the classroom/school/outside environment (books, buildings, clothing, nature, animals). For example, they may see a pattern in the grouping of their desks, on the calendar, as the second hand on the clock moves through a minute, etc.

Some learners may be ready to start learning how to write a general expression for a pattern. The student begins by setting values for shapes using units to which they relate easily. For example, rather than using n or x, use the program objects such as the farm girl, truck, horse, etc.

The students will print out scenes and write a story using their patterns as part of the story-line or illustration.

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