## Task Teacher Guide

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### In This Task…

Students will determine the fraction of the driveway that has been cleared, and the fraction of the driveway still covered in snow.

### Intentionality…

In this task, students will observe a driveway being cleared of snow using a shovel. The shoveller will clear sections of the driveway and then retreat to his home to warm up, leaving a snow covered fraction of the driveway each time until the task is complete. Students will be asked to determine how much of the driveway has been cleared, and how much remains covered in snow.

Some of the * big ideas* that will likely emerge in this task include:

- Multiplication can be interpreted as “groups of” or “parts of”, where the first factor is the number of groups, and the second factor is the quota.
- Multiplication can be represented using an array or area model.
- A part of a whole unit can be expressed as a fraction.
- A fraction described the number of parts relative to a whole.
- The fractional unit (the denominator) communicates how the whole is partitioned (number of parts).
- Equivalent values can be represented by different fractional notation (for example, \(\frac{1}{4}\) is equal to \(\frac{3}{12}\))

## Spark

### 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 and/or leaving a screenshot from the video up 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 a house.
- I wonder where it is.
- I wonder who lives there.
- I notice snow on the driveway.
- I wonder how much snow that is.
- I notice the person has a shovel.
- I notice he shovels a part of the driveway.
- I wonder how long that took, is the video real time?
- I wonder how much of the driveway he has left.
- I wonder how long it will take him.

At this point, you can answer any wonders that you can cross off the list right away. For example:

- This is a driveway in Belle River, Ontario.
- The video was filmed on Saturday January 23rd, 2021.
- Snow started early in the morning and the forecast predicted about 3 cm of accumulation.
- The man who is shovelling is named Kyle.

### 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 much of the driveway did he shovel? How much is left?

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 fraction of the driveway that would be reasonable before determining a more precise answer. Consider asking students to think about an estimate that would be “too low” and an estimate that would be “too high” before asking for their best estimate in order to help them come up with a more reasonable estimate.

It can be helpful to encourage students to draw a model of their thinking by creating a rectangle and partitioning the driveway to show the fraction of the driveway that was shovelled and the fraction of the driveway that remains covered in snow.

Encourage students to share their estimates, however avoid sharing their justification just yet. We do not want to rob other students of their thinking.

**Facilitator Note: **

The prompt intentionally omitted the word “fraction”. You might hear students describing the amount of driveway using fractional language, decimal language or standard units of measure. All descriptions of the amount are welcome. This might be a great opportunity to discuss equivalence.

### Estimation: Partial Reveal & Update

Show students the following video:

You might consider having students estimate what fraction of the * remaining snow* was cleared in this second snow shovelling session and what fraction of the remaining snow remains.

After students share their estimates, you can reveal to them that * one third* of the remaining snow covered portion of the driveway was cleared in the second session and prompt them with this:

One third of the remaining snow covered portion of the driveway was cleared during the second snow shovelling session.

Based on your estimate of how much snow was cleared during the first shovelling session and knowing that one third of the remaining snow covered portion of the driveway was cleared during the second shovelling session…

What fraction of the whole driveway was cleared during the second shovelling session?

What fraction of the whole driveway is still covered in snow?

Give students some time to use their area models they have drawn to estimate the fraction of the driveway that was cleared during the first snow shovelling session and now partition the remaining snow covered portion of the driveway to represent removing one third of the remaining snow.

You might consider having students share their reasoning here through a mini-consolidation that is built off of student work samples that you carefully select and sequence.

## Sense Making

### Crafting A Productive Struggle:

Show students this short silent animation clip to reveal how much snow was cleared during the first session and how much snow was revealed during the second session:

Then, reiterate some of what was shared in the video by stating a storyline similar to the following.

**Prompt students by stating:**

One fourth of the driveway was cleared during the first shovelling session and one third of the remaining snow covered portion of the driveway was cleared during the second snow shovelling session.

What fraction of the whole driveway was cleared during the second shovelling session?

What fraction of the whole driveway is still covered in snow?

**Facilitator Note:**

Clarify, if needed, that you want students to determine the amount cleared in the second trip only (not the cumulative amount from both the first and second video). Be sure to remind students that they are not to use a calculator to determine the fraction of the driveway cleared during the second trip.

## During Moves

### While Students Are Productively Struggling….

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### Student Approach #1: Paper Folding

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### Student Approach #2: Area Model

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### Student Approach #3: Area Model with Equivalence

## Next Moves

### Consolidation: Making Connections

### Reveal

Show this video that reveals the fraction of the whole driveway that was cleared during the second shovelling session and how much of the whole driveway remains to be shovelled:

Or consider sharing this image of the final frame of the video here:

### Reflect

Students will complete the following consolidation prompts independently.

**Consolidation Prompt #1:**

**Consolidation Prompt #2:**

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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## Printable Handout

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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.

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

### Spark Image

### Estimation: Prompt

### More Information

### Update Your Estimates

*One third of the remaining snow covered portion of the driveway was cleared during the second snow shovelling session.*

*Based on your estimate of how much snow was cleared during the first shovelling session and knowing that one third of the remaining snow covered portion of the driveway was cleared during the second shovelling session…*

*What fraction of the whole driveway was cleared during the second shovelling session?*

*What fraction of the whole driveway is still covered in snow?*

### Crafting A Productive Struggle: Video

### Crafting A Productive Struggle: Prompt

*One fourth of the driveway was cleared during the first shovelling session and one third of the remaining snow covered portion of the driveway was cleared during the second snow shovelling session.*

*What fraction of the whole driveway was cleared during the second shovelling session?*

*What fraction of the whole driveway is still covered in snow?*

### Consolidation Prompt #1: Video

### Consolidation Prompt #1: Prompt

### Consolidation Prompt #1: Reveal Video

### Consolidation Prompt #1: Reveal Image

### Consolidation Prompt #2:

**Download Editable/Printable Handout**

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