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|
Although most patterning experiences for young students will focus on repeating patterns, students can also begin to visualize and talk about growing patterns in the early grades.
A linear growing pattern is a pattern that increases or decreases by a constant difference. For example:
Let's take a look at a classroom experience with another growing pattern.
Teacher: What do you notice about these houses?
Teacher: Describe what you mean by "bigger."
Teacher: What do you think the fifth house will look like?
Teacher: Can you show me?
Teacher: Describe your house to me.
Teacher: What about the next house?
The students continue to build and describe the houses until Martha notices another pattern.
Martha: I see something else: The number of the house is the number of triangles and squares.
Teacher: So, what do you think House 20 will look like?
Teacher: How do you know that's correct?
Teacher: What do you think House 100 would look like?
Teacher: Do you think if you knew how many squares and triangles there were, you could figure out what house it is? Let's try. I have a house with 10 squares and 10 triangles.
A great deal of reasoning is occurring in this activity. The children begin by describing the pattern and extending it with physical materials. They make conjectures about the pattern and predict the number of tiles in elements that come later in the series. Finally, they make generalizations about the number of squares and the number of triangles for any house, based on the patterns they have discovered. Throughout the entire activity, the children explain their reasoning. The teacher challenges their thinking by asking probing questions and extending the activity.
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