## Reflection: Developing a Conceptual Understanding Patterns in the graph - Section 3: Exploration

I am sometimes tempted to move on as soon as a single student has come to a correct conclusion. I get so excited when someone comes up with an insight, I forget that hearing or seeing it once is not enough for the rest of the students in the class. Even that student needs to be able to investigate, verify, confirm, and see it in another way before he/she has a firm understanding.

I don't want them to just be able to plot points from a table to a graph.

I want them to understand the relationships between the numbers in the table, the points on the graph, and what they represent. I think working in a group and hearing each others responses to purposeful questions help them build meaning.

• "what does this [number] represent?"
• "where do we find it on the graph?" (along a single axis - one dimension)
• "what does the [tile floor] look like at this point on the graph?"

I want my students to understand how each of the points on the graph are related to each of the others.

• "how are the points related to each other?"
• "what is the same about each point on the graph?"
• "what patterns do you notice on the graph?"
• "is that pattern true for all the points on the graph?"

I want them to understand how the graph represents the constant change represented by the ratio.

• "how do we get from one point to the next?"
• "could you use the pattern to predict where other points might be located on the graph?"
• "why does that make sense?"
• "does it make sense to connect the dots? why/why not?"

Discussing these in their collaborative 'math family groups' helps them incorporate all the different viewpoints for a more complete understanding of proportional relationships.I have sentence starters taped to each of their desks to help them conduct productive group discussions.

I am always listening for their ideas and questions to help me plan future lessons. In this lesson I would specifically listen for any discussion of the origin (0,0).

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Developing a Conceptual Understanding: Don't rush it!

# Patterns in the graph

Unit 6: Proportionality on a graph
Lesson 1 of 10

## Big Idea: The ideas of scale factor and equivalent ratios show up in the graph as the constant of proportionality.

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Standards:
Subject(s):
Math, graphical techniques, Number Sense and Operations, graphing equivalent ratios, proportionality on a graph, patterns in a graph, discovery, ratios, pattern
46 minutes

### Erica Burnison

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