## Task Teacher Guide

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### In This Task…

Students will analyze the pattern of a melting glacier.

### Intentionality…

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.

## Spark

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

Show students this video:

**What do you notice?****What do you wonder?**

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

Consider replaying the video here, but prompting students with the following:

**I’m going to play the video again. ****What will you be looking for when I do?**

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 a glacier.
- I notice a scale.
- I notice the glacier melting.
- I notice a the number of years across the screen.
- I notice it started at 0 years.
- I wonder how long it will take for the glacier to melt.
- I wonder if it will continue melting at the same rate.

### 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:

Assuming this pattern continues, how tall will the glacier be after 5 years?

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 reasonable height after 5 years. Students will likely leverage the rate of -3 feet per year. Give them a chance to discuss with a partner before sharing their answer with the larger group.

The intentionality behind this estimation prompt and the reveal that is to follow is to reinforce the iterative (multiplicative) approach, which can help set the stage for students to begin leveraging a rule (or equation) to determine the number of years it will take for the height to reach 0 feet.

### Estimation: Reveal

## Sense Making

### Crafting A Productive Struggle: Prompt

## During Moves

### While Students Are Productively Struggling…

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### Student Approach #1: Skip Counting Backwards in a Ratio Table

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### Student Approach #2: Difference and Quotative Division

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### Student Approach #3: Equation with Cancelling

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## Next Moves

### Consolidation: Making Connections

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### Reveal

### Reflect

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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## Explore The Entire Unit of Study

This Make Math Moments Task was designed to spark curiosity for a multi-day unit of study with built in purposeful practice, and extensions to elicit and emerge mathematical models and strategies.

Click the links at the top of this task to head to the other related lessons created for this unit of study.

### Consolidation Prompt #1

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### Consolidation Prompt #2

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### Consolidation Prompt #3

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**Download Editable/Printable Handout**

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