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 about 30-60 seconds to do a rapid write on a piece of paper or silent individual think time.

Replaying the video can be helpful here if appropriate. 

Then, ask students to pair share with their neighbours for another 60 seconds.

Finally, allow students to individually share with the entire group. Be sure to write down these noticings and wonderings on the blackboard/whiteboard, chart paper, or some other way that is visible to all. This helps students to see the thinking of their classmates and  ensures each student that their voice is acknowledged and appreciated. Adding student names or initials next to their notice/wonder is one way to acknowledge their participation and can motivate others to join in.

Some noticings and wonderings that may come up:

• I noticed he baked sugar cookies. 
• He must have taken a sheet out of the oven because then he was putting the cookies into boxes. 
• Does Calvin make more than one kind of cookie?
• I wonder if he took more than one sheet out of the oven this time?
• The boxes look the same, so I think there must still be 10 cookies in each box.
• I wonder how many cookies he made in this batch.
• This time there were 5 extras.
• How many boxes did he fill?
• And many more.

At this point, you can answer any noticings and wonderings that you can cross off the list right away. Things like “Does Calvin make more than one kind of cookie?” (yes) can be addressed right away to show students that we are indeed listening to their contributions and that we value student voice. 

Estimation: Prompt

After we have heard students and demonstrated that we value their voice, we can land on today’s question. Acknowledging that the question came from students underscores their identities as thinking mathematicians who are  making sense of problems.

How many sugar cookies are in this batch?

Follow up that question with:

How could you convince someone that the quantity you come up with for your estimation is correct?

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 think about place value (boxes and extras). The number of boxes isn’t clear which means they will also need to consider how many cookies could reasonably fit on a sheet. Before collecting student estimates,  students can share their estimates in small groups along with a justification for the reasonableness of their prediction.

Consider asking students to think about a number that would be “too low” and a number that would be “too high” before asking for their best estimate in order to help them come up with a more reasonable estimate.

While Students are Estimating: 

Monitor student thinking by circulating around the room and listening to the mathematical discourse. You may identify some students whose thinking would be valuable to share when the group’s estimates are collected.

Encourage students to use precise mathematical language (including tens, ones, extras, groups of ten, greater than, less than, more, less, half, higher than, lower than) to articulate their defense of their estimate. As well, now may be a good time to build up the vocabulary of this context: batch, baking sheet, box, tray.

Similar to collecting their noticings and wonderings, collect students’ range of estimates and/or best estimates along with initials or names. Having some students share justifications is an opportunity for rich, mathematical discourse.

At the end of this task, during The Reveal, revisit the estimates to see how accurate students were and to reflect on the assumptions they held and justifications they argued.