## Task Teacher Guide

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### In This Task…

Students will determine how many hours it will take to move 1 260 passengers in a single day of operation.

### Intentionality…

Students will explore context which includes two * quotative division* contexts. First, they will determine the total number of trips needed to take 1 260 passengers in a single day.

They will know the total number of passengers and the numbers of passengers per trip (a rate). They will determine the number of trips (or parts). They will use this information to solve a second quotative division probably. How many hours will it take to make that number of trips.

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

- Multiplication and division are related.
- There are two types of division.
- 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). **Partial products**, made possible by the**distributive property**, allows one or both of the factors to be decomposed in order to simplify a multiplication sentence.

## 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 body of water.
- I wonder where it is.
- I notice some large cables.
- I notice something suspended on the cable.
- I notice that it is yellow and red.
- I wonder where they are going.
- I wonder if there are people on the ride.
- I wonder how many people.
- I wonder how long it takes to get across.
- I wonder what is on the other side.

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

- This Whirlpool Aero Car is in Niagara Falls, Ontario, Canada;
- The cable car is located in Niagara Falls, Ontario that transports passengers over a section of the Niagara River referred to as the Niagara Whirlpool.
- The system was designed by Spanish engineer Leonardo Torres Quevedo and has been upgraded several times since 1916 (in 1961, 1967 and 1984).
- The system uses one car that carries 35 standing passengers over a one-kilometre trip.
- The cost is $16.50/adult and $10.75/student.

### 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 long does it take to travel to the other side and back (one roundtrip)?

Make an estimate.

You might choose to share this short clip giving them a perspective of how fast the Aero Car moves.

Share the following animation and prompt students to **update their estimates**:

Consider leaving the following screenshot of the final frame of the animation up for students to see.

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 use relative thinking and proportional reasoning based on the information that has been shared.

Consider asking students to think about a length of time that would be “too low” and a length of time 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.

### While Students Are Estimating

Listen and observe as students work to make their estimates. Are students using spatial and proportional reasoning?

Are they using fractional and multiplicative language to describe the distance travelled by the car in the video relative to the entire trip? Are they considering the ratio that exists – distance travelled: time, and using appropriate units and mathematical language?

### Estimation: Reveal

Consider sharing this video of the Aero Car travelling one-way across the Whirlpool in 300 seconds (600 seconds round-trip):

You might consider sharing this animated video of the Aero Car travelling round-trip:

A screenshot you might consider sharing as well:

**Answer: **600 seconds round-trip.

Celebrate student estimates that were very close to the actual number of riders using a routine of your choice as we head into the **sense making **portion of this lesson.

## Sense Making

### Crafting A Productive Struggle:

Share that in a single day of operation, **1 260 passengers rode the Whirlpool Aero Car**, with each ride at maximum capacity of **35 passengers**.

**Prompt students by stating:**

How many hours was the Whirlpool in operation today to accommodate 1 260 passengers?

Be sure to remind students that they are not to use a calculator to determine the total length of time.

As a reminder, it took **600 seconds** or **10 minutes** for 1 round-trip ride on the Whirlpool Aero Car. You may choose to withhold this information to allow students to independently pull this information from their prior work before doing this thinking for them by giving the information to them.

## During Moves

### While Students Are Productively Struggling:

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### Student Approach #1: Array with Partial Products Over Addition & Subtraction

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### Student Approach #2: Repeated Subtraction on a Number Line

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### Student Approach #3: Partial Products Over Addition in an Open-Array

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## Next Moves

### Consolidation: Making Connections

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### Reveal

Once the lesson has been consolidated emerging the big ideas that multiplication and division are related including their helpful strategies of partial products and partial quotients in this quotative division context, you can share the following reveal video:

You might also consider sharing the following reveal image:

### Reflect

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.

You might choose to simply open the printable PDF handout to display on your display or download and print for students.

**Download Editable/Printable Handout**

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## Resources and Downloads

### Oh No! You Must Be Logged In!

Download a printable lesson plan, video/images, and presentation slides in Keynote and PowerPoint format to make the experience as smooth as possible by **becoming a member of the Make Math Moments Academy**.

## Lesson Tip Sheet

Download the lesson plan in PDF format so you can keep it handy and share with colleagues.

## Videos & Images

Download the videos, images, and related media files to your computer to avoid streaming.

## Keynote Slides

Download in Apple Keynote format to avoid streaming video and run the lesson smoothly.

## PowerPoint Slides

Download in Microsoft PowerPoint format to avoid streaming video and run the lesson smoothly.

## Printable Handout

Download/Edit the handout so you can keep it handy and share with colleagues.

## 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.

### Consolidation Prompt:

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**Download Editable/Printable Handout**

Become a member to access purposeful practice to display via your projector/TV, download the PDF to upload to your LMS and/or print for students to have a physical copy