Students will analyze the pattern of a melting glacier and rising water level.  

In this task, students will analyze and make predictions about a melting glacier over time. They will determine the initial value and the rate for the pattern. They will extend the pattern, describe the pattern rule in words, and make predictions. Some of the big ideas that may emerge in this unit 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 linear patterns is predicting future events.
• A pattern can be extended to make a prediction. 
• For far predictions, calculations are required for efficiency. 
• In a growing pattern, the values increase and the rate is positive. 
• In a shrinking pattern, the values decrease and the rate is negative. 
• In a linear pattern, the values increase at the same rate.
• The rate can be determined by finding the difference between the value of two terms through subtraction.
• The order in which integers are written in a subtraction statement matters because the commutative property does not hold true.
• Constant difference refers to the idea that the difference between two numbers does not change after adding or subtracting the same quantity to both numbers. 
• The initial value in a linear pattern is the constant.
• When the initial value is not zero, the relationship between the two variables is not proportional. 
• Graphical representations of linear growing patterns appear as straight lines.
• The initial value in a linear pattern is the constant.
• When the initial value is not zero, the relationship between the two variables is not proportional.

Show students this 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 water.
• I notice the water is rising. 
• I notice a scale.
• I wonder where this water is.
• I wonder if it always increases by the same amount.
• I notice years. 
• I notice at year 0, it is at -5 feet.

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

Assuming this pattern continues, when will the water reach zero, or sea level?

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 year that would be reasonable to reach zero feet. Students will likely leverage the rate of 2 feet per year. They will likely determine that it will take between  2 and 3 years to reach zero feet. Precisely, 2 ½ years assuming the pattern continues at the same rate. . 

Give them a chance to discuss with a partner before sharing their answer with the larger group.

Show students the following video.

Share the following prompt:

The rate at which the water is rising is creating a pattern revealing a relationship between years and height of the water – relative to sea level (0 feet).

Determine the initial value and the rate for this pattern. Determine the height of the water level in feet after 8 years. Justify your answer.

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Show students the following reveal video:

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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