Guide: Classroom Routines

Introduced in Lesson 1.1

Popularized by Annie Fetter’s NCTM Ignite Talk in 2011, Notice & Wonder is an incredibly flexible routine that can be implemented in nearly any content or context. Based on a stimulus (e.g. an image, graph, or statement), students begin by noticing: they make statements about what they observe. Then they wonder: they ask questions about the stimulus. 

Implementation

• Routine: (10 minutes)

  • Students see an image and write down statements (noticings) and questions (wonderings) about it. (30 - 60 seconds)

  • Students discuss their noticings and wonderings with a partner or small group. (1 - 2 minutes)

  • Students share their noticings out loud and the teacher records them for all to see. (1 - 2 minutes)

  • Students share their wonderings out loud while the teacher again records them for all to see. (1 - 2 minutes)

  • The teacher launches a discussion based on the student provided statements and questions that are most relevant to the lesson. (3 - 6 minutes)

• The prompt is a scenario - that is, an image, graph or statement - that does not include a question. This guarantees that all students can engage with the prompt, and it diverts those who would race to answer a question ( because it doesn't have one!).

• Students use a T chart (a two-column list) to list statements and questions about the prompt. Students should take the time to realize whether their comment is a noticing (statement) or wondering (question). T charts are provided on the lesson handouts.

Modifications

• Slow reveal graph

  • As a prompt for the Notice & Wonder, an incomplete graph is provided, with titles, axis labels, and/or even scales removed. 

  • The incomplete graph gets students thinking about the data or behavior of the graph before being influenced by the context or jumping to conclusions based on prior knowledge.

  • Gradually, the missing information is introduced to the graph, bit by bit. Each introduction of additional information comes with another short stage of noticing and wondering. 

  • While partner conversations can occur at any point(s) along the way, the whole group share out and conversation is reserved for the final stage.

  • In this course, an incomplete graph is sometimes presented during the Lesson Starter. Its complete version is then presented during the main lesson or the Discussion Question. Although separated by other lesson content, revisiting the graph provides closure to lingering discussion from the Lesson Starter. During the Lesson Starter, teachers should be careful to avoid oversharing information during the initial implementation.

For more detailed information and examples related to Notice & Wonder, check out OER Commons.

Introduced in Lesson 1.2

Ten-minute talks give students the opportunity to think about a prompt in any way that makes sense to them. This gives teachers valuable insight to what students know and are able to do. The simplest framing of a ten-minute talk is “tell me everything you can about what you see.”

Implementation

• Routine: (10 minutes)

  • Students independently jot down everything that they know or can conclude from the prompt (using their handout or an individual whiteboard) (2 minutes)

  • Students discuss their responses with a partner, taking turns sharing their ideas (1 - 2 minutes)

  • Whole group discussion focuses on connecting new responses to previous ideas shared (6 - 7 minutes)

• While the prompt can be almost any graph, image, table, or statement, ten-minute talks are most effective when there are many ways that students can respond.

  • A math problem with one answer or only one way to solve it is generally not used with this routine.

  • The prompt can likely be represented many ways or has a variety of characteristics that students can identify

• Ten-minute talks generally do not include a specific question. They may, however, ask students to write or create something that demonstrates their understanding. (e.g. Lesson 3.3)

• Ten-minute talks provide teachers with formative opportunities to assess students’ knowledge of a topic.

  • As an opening to assess prior knowledge about content or a context.

  • As a review activity to assess student learning of a topic already addressed.

Modifications

• Timing

  • Ten-minute talks in this course need not use the full ten minutes. Using the identified routine is recommended but some of the prompts may not require as much time as the routine calls for.

  • The goals of this routine are student conversation and formative assessment by the teacher. If these goals can be met in less than ten minutes, adjusting proportionally is suggested. For example, rather than 2-2-6 minutes as the structure, 1-1-3 may be sufficient.

For more detailed information and examples related to ten-minute talks, check out OER Commons.

Introduced in Lesson 2.2

Students compare and contrast graphs, images, equations, statements, and/or some combination of items. The most common version of this routine involves comparing and contrasting just two items, but our course often challenges students to compare and contrast more than two items at a time. When considering more than two items, students can group items that are the same or different in multiple ways. 

Implementation

• Routine: (10 minutes)

  • Given two or more expressions, images, or graphs, students identify similarities/differences and record them in a T chart provided in the lesson handout. (30 - 60 seconds)

  • Students discuss their similarities and differences with a partner or small group. (1 - 2 minutes)

  • Students share their similarities and differences out loud and the teacher records them for all to see. (1 - 2 minutes)

  • The teacher launches a discussion based on the similarities and differences most relevant to the lesson. (3 - 6 minutes)

• When there are more than two items, students should work in parallel, offering how groupings of two or more items are similar or different to another grouping

Modifications

• Math Debate - Same or Different can be the basis for a class debate about a topic. For a Same or Different that has one main characteristic for consideration, students can be given time to think about that characteristic and can then choose their ‘side.’ The whole group or small groups can then debate (discuss) their perspectives and reasoning for how those items are the same or different.

For more detailed information and examples related to Same or Different, check out this resource. Many of the resources found on the internet about Same or Different (also listed as Same and Different) focus on K-5 students. However, we’ve found that this routine also provides high school students with a powerful way to examine and discuss two or more ideas, especially as a way to launch into the main portion of the lesson.

Introduced in Lesson 2.3

In a Which One Doesn’t Belong? (WODB), students are asked to look at four items (some combination of images, expressions, graphs, etc.) and decide which one doesn’t belong with the others (and justify their choice). The unique feature of this routine is that, depending on students’ perspective and criteria, they could make a case that every item doesn’t belong in one way or another. Students engage in a rich discussion about the reasoning for their different choices, which can often motivate the lesson’s real-world context, mathematical concepts, or both.

Implementation

• Routine: (10 minutes)

  • Students independently examine the two-by-two frame to decide which of the four representations doesn’t belong and determine a reason for their choice. (1 - 2 minutes)

  • Students take turns sharing their choice and reasoning with a partner. (1 - 2 minutes)

  • Whole class discussion addresses all four options, with multiple reasons voiced for each. (3 - 5 minutes)

  • Reflection (whole group or partner):What choice or reasoning was a surprise to you? Why?  (2 - 3 minutes)

• Students can indicate that they have a response ready using a pre-determined signal so that the teacher can move on to partner sharing when all are ready (using more or less time as needed).

  • One common signal is to  have all students begin with a fist to their chest. When they have an answer, they give a thumbs up. 

  • Students should be encouraged to keep searching for solutions until time is called. Using the above signalling method, they can indicate a second answer by raising their index finger, and then a third finger, etc.

• Students may benefit from being given sentence frames, like these:

  • “___ doesn’t belong because _____________”

  • I chose _____ because it is the only one ________________________.

Modifications

• Four corners

  • Another way to discuss and share out thinking for WODB is to have students go to a corner of the room that indicates which item they feel doesn’t belong. Then, students in the same corner discuss their reasons for their same choice. For the whole group discussion, each corner shares their choice and several reasons for it, before reflecting within that group about what the other corners reported.

• Creating a rule

  • Another sentence frame that challenges student thinking even more is “Three have (this characteristic), but ___ doesn’t so it doesn’t belong. In doing this, students create a rule that can define sets of 3 and test their rule against counterexamples. This can lift the cognitive load of the routine. 

For more detailed information and examples related to WODB, check out OER Commons.