## INVASIVE SPECIES [DAY 3]

### EXPONENTIAL GROWTH & DECAY

Through the context of invasive species growth and the use of patterning, students will analyze the relationship between the size and unit of an exponent and the value of a power.

## Intentionality & Unit Overview

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Students will investigate the pattern of decay of the Giant Hogweed as the gardner tries to eradicate the invasive species from her garden.

## Intentionalityâ€¦

In this task, students will analyze the decay of the Giant Hogweed plant, an invasive species. They will record the data, determine the pattern rule, and make predictions about the pattern. Some of the big ideas that may emerge in this task include:Â

• Patterns can be extended because they are repetitive by nature.
• Pattern rules are generalizations about a pattern, and they can be described in words.
• One common use of patterns is predicting future events.
• A pattern can be extended to make a prediction.Â
• For far predictions, calculations are required for efficiency.Â
• An expression that represents repeated multiplication of the same factor is called a power.
• Exponential growth is a pattern of data that shows greater increases with passing time.
• Exponential growth is a pattern that increases at a rate proportional to its current value.
• Exponential decay is a pattern that decreases at a rate proportional to its current value.
• Exponential growth is a pattern of data that shows greater increases with passing time.
• Exponential decay occurs when the base is greater than 0 and less than 1.Â
• In a power, the base number is defined as a number which is multiplied by itself.Â
• Â In a power, the exponent represents the number of times the base number is multiplied.
• Graphical representations of exponential growth appear as a curved line.

## What Do You Notice? What Do You Wonder?

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## Crafting A Productive Struggle: Prompt

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## While Students Are Productively Struggling…

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## Student Approach #1: Multiplying by one-half in a table

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## Student Approach #2: Relationship between x and y

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## Reveal

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## Consolidation

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## Reflect and Consolidation Prompts

Provide students an opportunity to reflect on their learning by offering these consolidation prompts to be completed independently.

### Consolidation Prompt #1:

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### Consolidation Prompt #2:

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We suggest collecting this reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.

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## Educator Discussion Area

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