Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
Defining Reasoning and Proof
|Introduction | Pattern Recognition | Repeating Patterns | Reasoning About Repeating Patterns | Growing Patterns | Classification | Your Journal|
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.
Clap Snap Clap Snap
In another example, the teacher modeled this AAB pattern:
Here is a student's response:
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: 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:
These are all forms of an AAB pattern.
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