Students will determine the number of bottles of juice stocked on a grocery store shelf.

In this task, students will determine the total number of bottles of orange juice on the shelf. The organization of the cases in rows and columns will serve to emerge the array model as a tool for thinking. The associative, distributive and commutative properties of multiplication can be explored through this context and model. Some of the big ideas that may emerge through this task include:

• Multiplication can involve determining the total quantity given the number of equal groups and the size of each group;
• The order of the numbers in a multiplication sentence does not matter due to the commutative property;
• The strategy of doubling and halving is possible due to the associative property of multiplication;
• The distributive property of multiplication supports the strategy of partial products (where one or both factors can be decomposed over addition or over subtraction).

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 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 case of juice.
• I notice it is orange juice.
• I notice there are 24 bottles of juice.
• I notice it is a 4 by 6 array.
• I wonder how much the case costs.
• I wonder if this juice is from a store.
• I wonder how many cases there are.
• I wonder how big the bottles are.
• I wonder who the juice is for.

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

• This case of orange juice is sold at the local grocery store.
• There are 24 bottles in a case.
• Each bottle has 10 oz of juice.
• The cost is $21.95 before tax.

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

The grocery store clerk is going to stock 4 of these cases of orange juice on a shelf. How might he go about organizing the cases?
Consider all the possibilities for organizing the cases on a shelf in the store.

We can now ask students to predict how the grocery store clerk will organize the four cases. As you are observing the students draw various diagrams, ask them whether or not they can describe their diagram with one or more multiplication sentences.

Ask a few students to share their diagrams. How they believe the cases will be stocked on the shelf.
Show the following video of possible solutions:

Student prompt:

Determine the total number of bottles of orange juice in 4 cases of orange juice. Justify your thinking.

Be sure to remind students that they are not to use a calculator to determine the number of bottles 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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Show students the following reveal video:

Or consider sharing the final screenshot of the video:

Answer: 96 bottles of orange juice.

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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