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INVASIVE SPECIES

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

Spark Curiosity

Fuel Sensemaking

During Moves

Student Approaches

Consolidation

Reflect and Consolidation Prompts

Resources & Downloads

Educator Discussion Area

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PRESENTATION MODE

Intentionality & Unit Overview

Length of Unit: 5 Days

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DAY 1
DAY 2
DAY 3
DAY 4
DAY 5

Students will investigate the pattern of growth of an invasive plant, the Giant Hogweed, that continues to grow at an exponential rate.

In this task, students will analyze the growth 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: 

  • 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. 
  • For far predictions, calculations are required for efficiency. 
  • Exponential growth is a pattern of data that shows greater increases with passing time.
  • In a power, the base number is defined as a number which is multiplied by itself. 
  • In a power, the exponent represents the number of times the base number is multiplied.
  • When a pattern is growing exponentially, the variable representing time is the exponent. 
  • Graphical representations of exponential growth appear as a curved line.

Spark Curiosity

What Do You Notice? What Do You Wonder?

Show students the following video:

Then, ask students:

What do you notice?
What do you wonder?

Give students 60 seconds (or more) to do a rapid write on a piece of paper.

Replaying the video can be helpful here.

Then, ask students to share with their neighbours for another 60 seconds.

Finally, allow students to share with the entire group. Be sure to write down these noticings and wonderings on the blackboard/whiteboard, chart paper, or some other means to ensure students know that their voice is acknowledged and appreciated.

Some of the noticing and wondering that may come up includes:

  • I notice dirt or the ground, maybe a garden.
  • I notice on week 0, there was one plant.
  • I notice on week 1, there are three plants.
  • I notice on week 2, there are 9 plants. 
  • I wonder how many plants there will be on week 3.
  • I wonder if there will be six more plants every time. 
  • I wonder if the growth is the same every week.

Estimation: Prompt

After we have heard students and demonstrated that we value their voice, we can land on the first question we will challenge them with:

How many weeds will appear in the garden on week 3?

Sharing the video a second time could be helpful.

We can now ask students to make an estimate (not a guess) as we want them to be as strategic as they can possibly be. This will force them to determine a number of weeds through reasoning. Give them a chance to discuss with a partner before sharing their answer with the larger group. Some students may view this pattern as linear, add six, while others may recognize that each weed is being replaced by an additional three weeds every week.

Estimation: Reveal

Show students the following video.

Here is a screenshot of the final frame of the video.

Fuel Sense-making

Crafting A Productive Struggle: Prompt

Giant hogweed is an extremely invasive species that originated from Asia and Eastern Europe. An invasive species is an organism that is not native to an ecosystem and causes harm to the environment. The weed has taken over this patch of garden.

If the gardener does not intervene, predict how many Giant hogweeds she will find in her garden in 5 weeks. Justify your answer.

A screenshot of the final frame in the Struggle Prompt Video can be found below:

 

During Moves

While Students Are Productively Struggling…

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Student Approaches

Student Approach #1: Counting in a Pictorial Model

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Student Approach #2: Tree Diagram

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Student Approach #3: General Term

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Next Moves

Reveal

Show students the following reveal video:

Here is a screenshot of the final frame of the video:

 

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.

Resources & Downloads

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Educator Discussion Area

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