## SOWING SEEDS [DAY 3]

### Whole Number Partitive and Quotative Division (1 & 2-Digit)

Introduction to partitive and quotative division. This unit is designed to support students in understanding the two types of division and should be considered before exploring all other division units.

## Intentionality & Unit Overview

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Students will determine the number of pots needed based on the known rate of peas/pot.

## Intentionalityâ€¦

In this task, students will determine the total number of pots needed based on the total number of peas (the quota) and the identified number of peas per pot. In this quotative context, the students will leverage skip counting as a strategy to determine the total number of pots needed.

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

• There are two types of division;
• Quotative division is when the total quota is known (the dividend), and the number per group or the rate (the divisor) is known;
• Quotative division reveals the number of copies or iterations of a rate that can be derived from the overall quota (the dividend);
• In quotative division, the dividend and the divisor have the same unit;
• The dividend and the divisor of any division sentence represent a ratio;
• In a quotative context, the ratio is a multiplicative comparison;
• 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 Ã· 5 = 45 Ã· 5 + 40 Ã· 5 = 9 + 8 = 17).
The remainder can be divided by the dividend resulting in a fraction in both partitive and quotative division contexts, unless the unit is discrete and cannot be partitioned (for example, a marble or a person).

## What Do You Notice? What Do You Wonder?

Show students the following video:

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 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 another package of pea seeds.
• There are instructions in English and French on the back.
• I wonder how many seeds there are?
• It looked like 8 seeds were planted in the pot.
• How many pea seeds do you think theyâ€™ll be using?
• And many more.

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

• This is a different package of pea seeds than we saw the other day.
• Yes, there were 8 seeds planted in the pot.
• I also wonder how many seeds there are. I wonder if we could estimate how many? (consider allowing students to share their estimates).
• And feel free to add other details that will not rob the thinking of students later in the lesson.

## Crafting A Productive Struggle: Prompt

Prompt students by stating:

Based on the planting recommendations, there is enough space to plant 8 peas in each pot. If each pot will have 8 peas, how many pots are needed to plant all 96 peas in this package?

Be sure to remind students that they are not to use a calculator to determine the number pots as using that tool will rob them of this mathematical experience. Students should use a mathematical model in order to communicate their thinking.

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## While Students Are Productively Struggling…

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## Student Approach #1: Concrete Set Model and Skip-Counting

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## Student Approach #2: Array Using Repeated Addition

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## Student Approach #3: Open-Array Using Partial-Products and Revealing Partial-Quotients

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## Reveal

After you have taken the time to consolidate using student approaches, you can share the reveal video to show what really happened:

Here is a screenshot of the final frame you might choose to share as well:

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## Consolidation

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## Reflect and Consolidation Prompts

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

### 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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## Educator Discussion Area

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