# Experimenting with Linear Patterns

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## Objective

SWBAT explain initial amount, rate of change, linear patterns, and limits to domain and range through completing a hands on lab.

#### Big Idea

Use a hands on lab to understand linear patterns, initial amount, rate of change, and real limits to domain and range.

## Bellringer Warm-up

10 minutes

I have a set rotation with bellringers, though this is flexible when I need to change the schedule.  Today is the Explore/ACT preparation day.  One day a week, all my classes practice three Explore or ACT questions in order to prepare them for this assessment that is taken as a junior and heavily weighed by in-state colleges for admission and scholarships.  I am including one of the Explore/ACT resources I have found online and use as question resources.

30 minutes

## Wrapping up the Lesson

10 minutes

Wrapping up the lesson is really discussing all the properties and vocabulary of the experiment.  It is not easy to stop students as they are completing the lab and questions so the closing on this day is very important to help students make connections and consolidate all those connections into one unit organizer.  Important vocabulary to add to the organizer include (MP6):

1. Initial amount (the beginning 60 ml of water)
2. Rate of change with Scatter Plot and Line of Best Fit (increase in water as marbles are added and discuss why it might only be close to perfectly linear because of imperfections in marbles so this is really a scatter plot with strong linear correlation)
3. Continuous graph (water moved vertically through all the decimal ml and whole ml of water continuously as it rose)
4. Domain and Range (the realistic limits on number of marbles, domain, and height of the water range due to physical limitations)
5. Independent and Dependent variables (the height depended on how many marbles were in the cylinder)

The Rosetta Stone organizer helps students understand the connection between several different vocabulary words that all mean the same thing just different names when we discuss different types of representations such as algebraic rule, graph, and application (example:  constant rate of change and slope or initial amount and y-intercept).