Students will determine the number of tanks of water needed to flood a backyard skating rink.

In this task, students will observe a tank of water being drained as the contents are used to flood an outdoor skating rink. Students will be asked to divide the ratio through partitive division in order to determine the number of tanks of water per rink.

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 or through fair sharing.

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 tank of liquid, maybe water.
• I notice a rectangle.
• I notice that as the tank empties, the rectangle fills.
• I wonder what they are filling.
• I wonder if the tank and the rectangle have the same amount of water.
• I wonder how many tanks of water it will take to fill the rectangle.

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

• This is a tank of water
• The water is being used to flood (or resurface) a backyard skating rink. 
• If students are not familiar with “flooding” a rink, share the Spark video from Day 3 of Shovelling the Driveway

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 rink will a full water tank flood?

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 number of tanks 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.

Prompt students by stating:

If four-fifths of a tank of water was used to flood two-thirds of a rink, how much of the rink will a full water tank flood?

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

Consider offering students this extension prompt to build on this context and possibly promote leveraging a linear model like a double bar model or double number line.

If four-fifths of a tank of water was used to flood two-thirds of a rink, how many tanks are needed to flood the whole rink?

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After consolidating using student approaches and solution strategies to make connections, you can share the following reveal video highlighting how much of a rink can be flooded with one full tank:

Consider leaving up the final frame from the reveal video here:

You can share the following reveal video highlighting how many tanks are required to flood a full rink:

Consider leaving up the final frame from the second reveal video here:

Students will complete the following task and reflection 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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