Students will investigate the Maid of the Mist boat tour attraction in Niagara Falls. Knowing the total number of passengers that the company would like to host at any given time, and due to newly implemented restrictions on the total number of passengers per boat, students will determine the number of boats that need to be added to the current fleet.

In this task, students will determine the total number of boats that the Maid of the Mist Company should purchase using quotative division in order to continue offering rides to the same number of passengers, given newly imposed restrictions on the number of passengers per boat.

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

• Multiplication and division are related.
• There are two types of division.
• Partitive division reveals a rate.
• Quotative (or measured) division reveals the numbers of parts when the rate is known.
• The dividend from any division sentence can be decomposed into smaller parts to allow for friendlier division by the divisor. This strategy is known as partial quotients. (i.e.: 85 ÷ 5 = 45 ÷ 5 + 40 ÷ 5 = 9 + 8 = 17)
• Percents and fractions are related.
• A percent of a quantity can be found through partitioning.
  Benchmark percent can be used to determine less friendly percent of a given quantity.
• Multiplying by a percent is the same as multiplying by an equivalent fraction.

Show students the following video:

Consider leaving a still frame of the video up and 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.

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 include:

• I notice a waterfall.
• I notice a boat.
• I notice a lot of water.
• It is misty.
• I wonder where this is?
• I wonder how much it cost to ride the boat?
• I wonder how many people are on the boat?

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

• This is in Niagara Falls, Ontario; the same location that the Sky Wheel Ferris Wheel is located.
• The boat is a “tour boat” called The Maid of the Mist.
• The cost is $19.25 for adults and $11.50 for children.
• The most recent boat, the Maid of the Mist VI, was launched in 1993, and can carry 600 passengers.
  There are currently two boats in operation, Maid of the Mist V and VI.

Now that students have been given an opportunity to share what they’ve noticed and wondered, we can now verbally share the following context to help set them up for their productive struggle.

Tell students a story including the following information:

With two boats in operation, the Maid of the Mist Company is able to carry 1 200 passengers at one time (600 passengers per boat). New safety restrictions have been put into place restricting boat tour companies to only carry 40% of their regular capacity.

If the Maid of the Mist Company wants to continue carrying 1 200 passengers, how many boats will they need to have operating at one time if only 40% of the regular capacity can now be onboard?

As usual, we do not want students using a calculator to determine the total number of boats.

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Once students have shared their thinking and you have connected student solution strategies and representations, you can share the following silent solution reveal animation:

You might also consider sharing a screenshot of the last frame of the video:

Provide students an opportunity to reflect on their learning by offering this consolidation prompt to be completed independently.

Consolidation Prompt:

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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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