In this unit, students use logical thinking to create, identify, extend, and translate patterns. They make patterns with objects, numbers, and shapes. They also explore a variety of patterns in mathematics, in physical education, in science, and in social studies.
The lessons in this unit give students an opportunity to make patterns with a variety of objects. After a review of classification and seriation, the students will extend and translate patterns in many modalities and in several mathematical settings. Although all lessons should be used with students to ensure that they can recognize, extend, and create patterns, you may wish to exclude some of them in the interest of time.
Since the value of patterning may not be apparent to some parents, you may wish to explain that the students are engaging in a true problem solving activity, one which builds a foundation for much of later mathematics.
The core is the shortest string of elements within a pattern that repeats. When presenting patterning tasks, it is important to repeat the core at least twice.
| Pattern Cores Explored in this Unit |
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| AB |
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ABB |
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| AAB |
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|
ABC |
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| ABCD |
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|
ABA |
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There is no significant difference in difficulty among the first five pattern cores listed (AB, ABB, ABC, AAB, and ABCD). Because the same element is used both first and last in the ABA pattern, however, this is a more difficult pattern for students to create, extend and translate. Work with ABA patterns is best delayed until students are comfortable with the other pattern cores.
Math Content
Mathematics has been called the science of patterns. In a pattern, a core unit
is repeated in predictable ways. Although patterns can be found at the most
advanced levels of mathematics, even young students can begin to explore
patterns. Classification and seriation, both, form the basis for
patterning ability, which in turn is fundamental to an understanding of place
value, multiplication, functions, and many other topics. This unit offers rich
opportunities for communication, representation, and reasoning in a variety of
mathematical settings and is a highly motivating topic for most students.
Individual Lessons
Lesson 1 - Order, Order In this lesson students seriate objects and review the meaning of ordinal numbers. They describe orderings in words and in pictures. [This lesson gives you an opportunity to review or teach vocabulary such as before, after, and next.] At the conclusion of the lesson, students make an entry in their portfolios. A Science extension is suggested.
[At this point you may wish to make pretty pasta for the students to use in this unit. Simply place uncooked pasta of various shapes in a plastic bag; add a few drops of food color and a few drops of rubbing alcohol. Shake the bag until the pieces are coated, then spread them out to dry.]
Lesson 2 - Sorting Time Students sort objects and symbols and make patterns with sorted objects. They make Venn diagrams and use their sortings to create linear patterns. They extend a pattern created by the teacher. Students will begin identifying pattern cores and reading patterns. A Social Studies connection is suggested as an extension. Lesson 3 - What’s Next? In this lesson, students make patterns with objects, read patterns and find patterns in the environment. They should be encouraged to classify patterns by type (i.e. AAB, ABC). They continue learning about patterns by extending a given pattern, identifying missing elements in a pattern, and recording a pattern. Lesson 4 - Playing With Patterns Students use objects and symbols to make repeating linear patterns. They extend patterns and translate patterns from one modality (auditory, visual, and kinesthetic) to another. A Physical Education connection is suggested as an extension. This lesson is intended to take two class periods to ensure that all students have multiple opportunities to create original patterns. Lesson 5 - More Patterns Students extend their knowledge of linear patterns by recognizing and discussing familiar patterns. Students make auditory and visual patterns from names. An art activity is suggested as an extension. Lesson 6 - Multiple Patterns Students explore patterns which involve doubling. They use objects and numbers in their exploration and record them using a table. Lesson 7 - Exploring Other Number Patterns Students make and extend numerical patterns using hundred charts. They also explore functions at an intuitive level. This lesson integrates technology. Lesson 8 - Growing Patterns Students explore growing patterns. They analyze, describe, and justify their rules for naming patterns. Since students are likely to see growing patterns differently, this is an opportunity to engage them in communicating about mathematics. Lesson 9 - Looking Back and Moving Forward This final lesson reviews the work of the previous lessons. Students explore patterns in additional contexts and record their investigations. Students will rotate through center activities. Teachers may add other centers they feel will benefit the students.
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