Students will determine the number of bags of salt needed to de-ice one whole driveway.

In this task, students will observe a driveway being salted using one bag of salt. The shoveller will salt a fraction of the driveway, and in doing so, use a fraction of a bag. Students are then asked to determine how many bags of salt will be needed to de-ice the entire driveway given this information.

Some of the big ideas that may emerge through this task include:

• Partitive division is one of the two types of division;
• When dividing partitively, the dividend and the divisor often (not always) have two distinct units;
• The resulting quotient has a compound unit (quantity of dividend per one unit of divisor);
• The dividend and the divisor are a ratio before the division is performed;
• The quotient in a partitive division problem is a rate; and,
• The quotient can be revealed through scaling the ratio in tandem to one whole of the divisor.

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 wonders 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 a bag in his hand.
• I wonder what is in the bag.
• I notice that he is shaking the content of the bag onto the driveway.
• I notice that he is using salt.
• I wonder if he will cover the whole driveway.
• I wonder why he is doing that.
• I wonder if he will use the whole bag.
• 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.
• He is salting the driveway.
• People salt their driveway to de-ice them so that they are not slippery.

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

About how much of the driveway did he salt?

About how much of the bag of salt did he use?

Make an estimate.

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 and the bag 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. 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 and the bag 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.

Share the following image with students revealing that one-third of the driveway has been salted:

Follow up with another short clip showing that he used one-fourth of the bag of salt:

Here’s a screenshot to summarize the fraction of the driveway that was salted and the fraction of the bag of salt that was used:

Celebrate student estimates that were very close to the actual fraction of the driveway and fraction of the bag used via a routine of your choice as we head into the sense making portion of this lesson.

Prompt students by stating:

About 1 fourth of the bag was used to salt 1 third of the driveway.

How many bags will he need to salt the whole driveway?

Students should reason through this prompt without the use of a calculator. Visual or concrete representations should be encouraged.

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Share the following reveal video:

You might also share the following screenshot of the final frame of the video:

Students will complete the following independently without the use of a calculator.

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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