Students will analyze the migration of two flocks of ducks in Canada. Through this context, students will explore and extend growing linear patterns with and without an initial value.

In this task, students will analyze and make predictions about the migration of two flocks of ducks. Students will extend both patterns to determine which flock flew the greatest distance after twelve hours of observation. 

• 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.
• 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. 
• 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 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 it’s a line graph.
• I notice there are no labels.
• I notice there are two lines.
• I notice one line starts at 0 and the other line starts at 20.
• I wonder if these are birds migrating.
• I wonder why one started at 0 and the other did not.
• I wonder when they will cross.

I notice one line is steeper than the other.

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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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Consolidation Prompt #3:

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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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