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 noticed a kitchen counter.
• I notice a bag.
• I notice that it says “Ultra DishPods”.
• I wonder what it is.
• I wonder if it is dishwasher detergent.
• I wonder how much it costs.
• I wonder how many are in each bag.
• I notice it says “Pro” and “Deep Clean” on it.

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

• This is a bag of Ultra DishPods dishwasher detergent.
• It was purchased at the Grocery Store.
• The cost for this bag is $25.00

Estimation: Prompt

After we have heard students and demonstrated that we value their voice, we can share the following video which will reveal one of the first wonders we will challenge them to think through:

Verbalize the following prompt for students:

How many dishwasher detergent pods are in this bag?

How do you think they might be organized?

Make an estimate.

We can now ask students to draw a diagram of the dishwasher pods viewed from the front, side and top of the bag. Encourage them to actually identify the dishwasher pods pictorially, concretely or even using hand gestures to represent how they would be arranged in their columns and rows. Encourage students to engage in a conversation about how many dishwasher pods they would see from the top of the bag, and how they know.

Estimation: Partial Reveal

Share the following screenshot to allow students to update their original estimates.

How does this change their original estimates?

Consider sharing another perspective of a single 5 pod by 4 pod “layer” of 20 pods.

Encourage students to update their estimate based on this new information and share out their updated estimates based on their assumptions of how many “layers” of 20 pods are in this bag. Estimates between 80 and 160 are likely, however some students might notice a “shadow” less than halfway up the bag which might lead them to have estimates more in the 80 to 100 range.

Encourage students to explain their reasoning and take this opportunity to highlight the “array” that is formed for the base of this rectangular prism and how multiplying (or repeatedly adding) by the number of “layers” of that base will result in the total number of pods (i.e.: a conceptual algorithm for finding the volume of a rectangular prism).

Now you can confirm for students how many layers are in the bag of dishwasher pods:

If the pods in this bag are stacked 5 pods high, how many dishwasher pods are in this bag?

Estimation: Reveal

Show students the following reveal video and celebrate close estimates and their reasoning:

Here is a screenshot of the final frame that you might consider leaving up for students: