Notice and Wonder

Routine: Students are presented with an image and asked to describe things that they notice, then to describe questions that come to mind when looking at the image. Students may share with partners, using a rally robin structure where they take turns sharing one notice or one wonder. Ideas can then be shared witht the whole class.

Notice & Wonder Math Routine: Third GradeInstructional coach Kristin Gray uses a numberless word problem with a group of third graders, asking them to make sense of a context before solving. She records the ideas that students notice and wonder and uses talk moves to encourage student discourse.

When students have had practice with the Notice and Wonder routine using images, they can apply this same strategy to practical problems. Present a word problem to the students, but do not share the question from the problem. Have students read the practical problem situation and complete the notice and wonder routine.

Noticing and wondering is a tool to help students:

Understand the story, the quantities, and the relationships in the problem.
Understand what the problem is asking and what the answer will look like.
Have some ideas to begin to solve the problem.

This means that at the end of a noticing and wondering sessions, students should be able to:

Tell the story of the problem in their own words.
Give a reasonable estimate or high and low boundaries for the answer.
Work independently on carrying out steps or generating more data toward solving the problem.
And noticing and wondering is a skill students can get better at. That’s why it’s important to look back over your noticings and wonderings and ask, “Are we getting better?” After solving a problem, ask:
Which noticings and wonderings were really important to us?
Were there noticings and wonderings we didn’t really use?
How do we come up with noticings and wonderings that are mathematical? What makes them mathematical? Did we get stuck because we’d missed something? Why did we miss it? What could we do differently next time?

After noticing and wondering several times, ask:

Are there types of noticings and wonderings that are important? That we often miss?
Are we generating more noticings and wonderings each time? Are they getting more useful?
How do we go from noticings and wonderings to solution paths?