Planning a Lesson
The CMP teacher materials are organized around an instructional model that supports “inquiry-based” teaching. The Launch, Explore, and Summarize are described in more detail in the Philosophy, Instructional Model.
The teacher support materials contain a wealth of specific information to help you plan your lessons. Here we suggest some general ideas. Also, you may find the Planning Guide helpful. It provides a summary of questions to help a teacher think about the planning of and reflecting on the teaching of a lesson.
Begin by actually doing the Problem yourself. The learning process that your students will experience will become evident. You will be able to anticipate where students may struggle. You will discover how the Problem connects to prior learning as well as how it leads into the next Problem. The teacher’s role during a typical daily lesson is to facilitate student learning and to orchestrate the lesson. Within each phase of the lesson the teacher listens and poses questions to elicit student reasoning.
The students' role during a typical daily lesson is to explore a concept or skill with a problem-solving mindset. Within each phase of the lesson students listen to each other’s ideas and pose clarifying questions to each other. This exchange deepens their understanding of a concept or skill. Students actively share their problem-solving strategies and conclusions. See also Communicating to Learn. Recording their reasoning and conclusions is a key element of students being able to share the ownership of their learning with others. Creating a visual display of learning will occur regularly in each Investigation.
The Launch ensures that all students have access to the context and content to explore that lesson's Big Idea concept or skill. Connecting to prior knowledge and encouraging students to delve into the task without giving away too much of the Problem is the challenge.
A new component of CMP3 is the Focus Question, which is designed for the teacher’s use as a guide to monitor students’ progress during class. Occasionally, some teachers have posed the question to the whole class during the Launch as a challenge or advance organizer, or during the Explore as a way of deciding if it is time to summarize. Students should be able to respond to the question during the Summarize. The students’ role is to garner enough information to answer the questions in the mathematical task. Some teachers post the Focus Question in place of the lesson objective.
Some Problems have a “boxed-Launch” question before the Problem, which offers a choice for opening up the Problem task for students. For more information on this feature, visit Organization in Student Materials.
Questions to consider when planning the Launch
- How does this problem connect to previous mathematics my students have studied in this investigation or unit?
- What other prior knowledge do my students need to call upon?
- What do the students need to know to understand the story and the challenge of the Problem?
- What advantages or difficulties can I foresee?
- How will I launch this Problem to ensure that all students have access to begin the task?
- How can I make it personal to them?
- How can I keep from giving away too much of the Problem?
The purpose of the Explore phase of the lesson is for students to explore a rich Problem, which will enable them to analyze and generalize a concept or skill. Students may tackle the mathematical task individually, with a partner, with a small group, or sometimes as a whole class, depending on the challenge and format of the Problem. The students'' role during the Explore phase is to delve into the Problem. When appropriate, students should collaborate with their peers to make sense of what the questions are asking and to make a visual display of their learning for others to consider during the Summarize.
The teacher's role during this phase is to plan for the Summarize phase and provide for individual needs. To do this, the teacher must observe and listen to the students at work. The teacher will pose questions to support struggling students, taking care to follow the students’ thinking rather than the teacher’s pathway of reasoning. The teacher will pose questions to push the thinking of those students who quickly complete the task and demonstrate that they are ready to be challenged further. Consideration must be given to when to end the Explore. It is not always necessary for all students to complete all parts of the problem. Assessing the level of sophistication students can achieve in answering the Focus question can guide when to end the Explore. Also, the teacher needs to decide the opening question for the Summarize. A teacher must plan which students’ reasoning and conclusions, and which sequence, will provide a stimulating discourse on the mathematics.
Question to consider when planning the Explore
- Will I organize the students to explore this Problem individually, as pairs, or as small groups? Or can they organize themselves to best engage the task?
- What materials should be made available for students?
- Will students display their learning in individual papers, on chart paper, on construction paper, or by oral presentation?
- What are different strategies I anticipate them using?
- What Mathematical Practices do I anticipate students using?
- What kinds of questions can I pose to prompt their thinking if the level of frustration is high?
- What kinds of questions can I pose to make them probe further into the Problem if the initial question is answered?
- What kinds of questions can I pose to encourage student-to-student conversation about their thinking, reasoning and learning?
- What kinds of strategies will I be looking for to facilitate the summary, and how will I sequence them to stimulate a productive summary?
- How will the Focus Question help to decide when it is time to end the Explore?
The purpose of the Summarize phase of the lesson is to orchestrate whole-group student discourse about discoveries students made during the Explore phase of the lesson. It is during the Summarize that the teacher guides the students to reach the mathematical goals of the Problem and to connect their new understanding to prior mathematical goals and Problems in the Unit. Student conjectures and conclusions are shared and considered by their peers. Conclusions are solidified and sometimes questions are posed for further exploration in future lessons. The teacher begins by posing an opening question that will get the conversation started. After that, the students should lead the Summarize by presenting their conjectures and conclusions with mathematically sound justification.
The teacher and students ask clarifying questions. Students draw conclusions addressing the mathematical goals of the lesson. Answering the Focus Question can help guide the Summarize.
Questions to consider when planning the Summarize
- How can I help the students make sense of and appreciate the variety of mathematical strategies that may occur?
- How can I orchestrate the discussion so students lead the summary of their thinking in the Problem?
- What mathematics and processes need to be drawn out?
- How will these ideas be recorded?
- Which ideas need to be made visible and displayed for future reference?
- What needs to be emphasized?
- What ideas do not need closure at this time?
- What do we need to generalize?
- How can we go beyond? What new questions might arise?
- What will I do to follow up, practice, or apply the ideas after the Summarize?
At the end of each lesson it is productive to take note of student understandings:
- What evidence do I have of what my students learned about the Focus Question?
- What revelations occurred? What struggles did students have?
- How does this affect my instructional decisions for the next lesson? For the next time I teach this Problem?
- Where will I revisit or enhance the understanding of these ideas in the next Problem, Investigation, or Unit?