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Reasoning and ProofSession 04 Overviewtab atab bTab ctab dtab eReference
Part C

Defining Reasoning and Proof
  Introduction | Pattern Recognition | Repeating Patterns | Reasoning About Repeating Patterns | Growing Patterns | Classification | Your Journal

 
 

A repeating pattern is a cyclical repetition of an identifiable core. The core is the shortest string of elements that repeat. For example:


Repeating Pattern

This is a repeating pattern in the form ABB, since it has three elements -- blue, red, red -- as the core.


Let's look at some examples of students' work with repeating patterns.


Physical and Auditory Patterns

Students are asked to copy a simple repeating pattern (AB):


Teacher: Listen carefully (claps her hands and snaps her fingers):


Clap Snap Clap Snap


Teacher: Now it's your turn.


Students:


Clap Snap Clap Snap


In another example, the teacher modeled this AAB pattern:


Teacher's AAB Model

Here is a student's response:


Students' AAB Model


It doesn't take long for students to develop skill in copying patterns. However, the more complex the pattern, the more sophisticated the reasoning involved. As students continue to copy patterns, teacher should ask questions or give prompts that encourage students to extend the pattern, for example:


Teacher: What do you think comes next in this pattern?


Teacher's Incomplete AB Model

Student: This


Student's AB Model


Teacher: Explain why you chose these tiles to continue the pattern.


Student: Well, I saw two green tiles and then two yellows and then two green, so the pattern seems to be two of each color. Since there is only one yellow at the end, I added one more yellow and then two greens.


This student's solution shows one of several possible patterns. For this reason, it is important for students to explain the reasoning they used to determine their solutions. A nice extension would be to have students find a variety of solutions and then justify their thinking for each.


Children should have a variety of experiences with repeating patterns and with using materials to explore and extend patterns. In the People Patterns video, we saw children acting out patterns in order to represent them, for example, stand stand sit stand stand sit. Manipulative materials provide additional ways for young children to show and develop patterns.


After children have had a variety of experiences with patterns, they will begin to recognize that two patterns represented in different ways are actually the same pattern. For example, look at the following:


AAB Patterns

SNAP SNAP CLAP SNAP SNAP CLAP


STAND STAND SIT STAND STAND SIT


These are all forms of an AAB pattern.

Next  See students begin to represent patterns in different ways

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