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…
n 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:
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:
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.

- 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.
- 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:
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.
How much of the driveway did he shovel? How much is left?


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:
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.
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?

During Moves
While Students Are Productively Struggling....
Monitor student thinking by circulating around the room and listening to the mathematical discourse. Select and sequence some of the student solution strategies and ask a student from the selected groups to share with the class from:
- most accessible to least accessible solution strategies and representations;
- most common/frequent to least common/frequent strategies and representations; or,
- choose another approach to selecting and sequencing student work.
- Paper folding.
- Using an area model
- Using a bar model
- Using equivalence
- Using common denominators
- Using a symbolic representation.
Student Approach #1: Paper Folding

Student Approach #2: Area Model

Student Approach #3: Area Model with Equivalence

Next Moves
Consolidation: Making Connections
Leverage a few student models to consolidate this task. Consider sequencing them from most accessible to least accessible.
Ultimately, we have designed these prompts to allow students to bump into multiplication of fractions using the area model. By partitioning a whole driveway into fourths, then partitioning into thirds, we can use the area model to visualize that the driveway has been partitioned into twelfths and counting how many twelfths were shovelled in the second session as well as how many twelfths of the driveway is still covered in snow becomes more natural.
Here’s a screenshot highlighting the driveway partitioned into fourths horizontally, then thirds vertically to reveal twelve equal parts:
Help students realize that he actually shovelled the same fraction of the driveway in the first and second video by asking purposeful questions. The following silent solution video may be helpful for students to “see” the equivalence by moving the parts and showing they “fit”:
After you have had an opportunity to make connections between some of the student solutions and the equivalence, land on the following question:

What operation was used to determine the fraction of the driveway shovelled on the second trip? How could we represent this context as an equation?Although students tackled this task through reasoning and visual representations, now is your opportunity to explain the context using mathematical language.
\(\frac{1}{3} \times \frac{3}{4} = \frac{3}{12} (or \frac{1}{4} \))In today’s context we can articulate the mathematical situation as finding one third of one-fourth. Or one-third part/group of the three-fourths of the driveway still covered in snow. You can view this silent solution video to help you plan how you can select, sequence and connect student representations to reveal this multiplication of fractions.
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:
Show the following clip and verbally explain what is happening in the video to set them up for your consolidation prompt.
Explain the Consolidation Prompt Video with a script similar to this one:
As an additional opportunity for students to reflect, you could ask them this second Consolidation Prompt.
When students are finished solving the first prompt, you can share the following reveal video. Note that this might be the next day if you used the consolidation prompt as a ticket out the door to check for understanding.
Here is a screenshot of the final frame:
Consolidation Prompt #2:
As we know, 6 twelfths of the driveway (or one half) was still covered in snow. During the 3rd shovelling session, 2 thirds of the remaining snow covered portion of the driveway was cleared. What fraction of the driveway was cleared during the third shovelling session? What fraction of the driveway remains covered in snow? Write an equation to represent the fraction of the driveway shovelled on the third trip.


What did you notice about all three trips to the driveway? How was the amount of snow shovelled the same? How was it different?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 and Downloads
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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
What fraction of the driveway was cleared during the third shovelling session? What fraction of the driveway remains covered in snow?
Write an equation to represent the fraction of the driveway shovelled on the third trip.
Consolidation Prompt #1: Reveal Video
Consolidation Prompt #1: Reveal Image
Consolidation Prompt #2:
What did you notice about all three trips to the driveway?
How was the amount of snow shovelled the same?
How was it different?