CPM Index Cards of Teaching Strategies

Several small teams can brainstorm at once with this idea by Pam Robbins. Divide the participants into teams of two or four. Topics or questions are written on large poster paper and either hung up around the room or placed one at each table. Teams gather and discuss the topic and make a decision about what to write on the chart. After two or three minutes the teams move on to the next topic--either the teams move physically if the charts are on the wall or the charts move physically from table to table. The teams read what the previous teams have written have a discussion, and then add to the list. This continues for as long as you have time. You do not have to have every team respond to every chart. Stop when you feel that the teams have exhausted most ideas. Then have a "gallery walk" where the teams can go around and read all of the charts. Some teachers have the problems posted on each poster but the students DO NOT write on the posters. This can be done at the end of the chapter with review problems. Even though the students can sit at their desks and work on the problem this gives them the opportunity to move around.

• Write a different problem/topic/question on large poster sheets hung on the walls or on each table. • Each team is given a different colored marker. • Each team goes to a different poster, discusses the topic and decides what to write. • Teams rotate to all of the posters, adding to what was written by previous teams (have a time limit). • When done, each team does a "gallery walk." • A large class discussion/debrief can then be held

• Have the participants write one thing that they really need help with in their classroom - management, homework, getting kids to work, etc. • The card gets passed around with the other participants offering suggestions on how to solve the problem. • Carousel: Station Rotation • Have one or two more stations than the number of student groups. • Place a sheet of review problems (4 - 6) at each station. (Good idea to use a sheet protector). • Have a blank answer sheet at each station for each team. (Good idea to have the exact number of spaces needed to answer the questions at each station. All of the spaces are in numerical order even though the team may not solve them in that order. This will make it easier to grade the papers, if you elect to do so.) • The students work the problems as a team. When they finish they turn in the station paper to the teacher and move to the next available station.

Purpose: Individual think-aloud Dyads can be used in many ways. The first day of school is an opportunity for students to get some of their excitement out. They pair up and have each person take their turn talking about "How it feels to be back in school." If students have concern about a math topic or test or project that is due, this would be a chance for the students each to be able to talk about it. Each person is given equal time to talk. The listener does not talk a dyad is not a conversation. Confidentiality is maintained. Maintain eye contact and good body language.

Purpose: Model an aspect of teamwork structured observation Many times in class there is a need to model a team activity for the whole class. Sometimes it is important to model team norms. A way to do this could be through a Fishbowl activity. This way the students can watch a team as they perform the task. The teacher can point out behaviors that are important to notice. Questions can be handed to the teacher or the team silently and answered when appropriate. • Used to model to whole class expected behaviors/norms. • One or two teams sit in the middle of the class and work on the math problem. • Rest of class stands near the team and observes or takes notes about how the team works questions that are asked, etc. • After five to ten minutes, the teams return to their own tables and work on the math problem.

Purpose: Elicit responses from each student to a prompt before discussion Develop a list of five or six sentence starters to use as "fortunes" for this activity. The sentence starters should be related to chapter topics or general ideas or norms that need to be discussed. The sentence starters will need to be copied, cut apart and one set of each of the sentence starters put into envelopes. Each table gets an envelope. The first person draws a piece of paper, reads it aloud and then makes one statement about it or responds to it appropriately (30 sec). After making his/her one statement, the next person rereads the statement and makes one statement or makes one comment about what the first person said. Continue the process. After each person has had his/her chance to speak, then the whole team can take part in a discussion if they still have issues to discuss. If needed, place a time limit on this open discussion. (You can tell how the discussion is going as you walk around.) The second person pulls a new sheet of paper out of the envelope and the process is repeated. Everyone will have a chance to begin the discussion by drawing a "fortune." You should model this activity the first time it is used. If you have a large team you may want to appoint a timekeeper and limit the "open" discussion to one minute. This activity also provides a good opportunity to model appropriate behavior in dealing with teams. Circulate and respond accordingly. For each of the "fortunes" of this activity, have a poster with the scenario written across the top already made. Have each team quickly put their best response/comment on a sticky note to be placed on the poster. Note: The focus of the Fortune Cookie activity is the discussion, so do not mention the posters ahead of time, nor make them a big, time-consuming activity. They should be used to wrap up the discussion. • Choose five or six questions and put them in an envelope. • Each team receives an envelope. • One person draws a question, and makes one statement about the topic, then passes it on. • The next person adds his or her own statement or responds to the previous statement. • When everyone has responded to the first statement, another person draws from the envelope and repeats the process.

Purpose: To share ideas with a presentation or poster or give feedback about other teams' presentations or posters This activity allows students to share ideas with or about posters or presentations. After the posters or presentations are displayed, students walk around the room in teams or individually quietly (Museum Walk) or talking (Gallery Walk) in their team. After students have posted their presentations either at their desks/tables or on the walls students walk around and look at/read the presentations giving feedback (if the teacher desires this). Otherwise they go around to see what the other teams are presenting. The Gallery Walk can be done in teams where the teams review the presentation, discuss it with their teammates and then write their comments on post it's to share with the team who prepared the presentation. Typically, they do something like 'two stars and a wish': Two things they really liked about the presentation and one thing that they feel the team could do to improve their poster/presentation. Sometimes the team leaves a representative with their presentation to answer questions. A Museum Walk is like a Gallery Walk except there is no talking. If feedback is to be given, it is done individually and on post-its or a sheet of paper left with the presentation. • Students post their presentations around the room. • Students, individually or in teams, walk around and look at the presentations. • Students give feedback.

Purpose: Share ideas This is an activity to use when getting people to share a lot of ideas or suggestions. An idea for adults could be to share ideas for correcting homework. For students you could ask the students to write three ideas for being successful in class. Record three ideas to share related to a certain topic on separate pieces of paper or index cards. Circulate and share ideas for every idea given they receive one in return and record them on a piece of paper - including the name of the "giver." Begin team sharing by inviting a volunteer to share one idea received and citing the "giver." The named person then continues the sharing process. • Record three ideas to share related to a certain topic. • Circulate and share ideas for every idea given they receive one in return and record these on a piece of paper - including the name of the "giver." • Begin team sharing by inviting a volunteer to share one idea received and citing the "giver." The named person then continues the sharing process.

Get One, • Record three ideas to share related to a certain topic. • Circulate and share ideas for every idea given they receive one in return and record these on a piece of paper - including the name of the author. • Begin group sharing by inviting a volunteer to share one idea received citing the author. The named person then continues the sharing process.

Purpose: Each student participates in constructing an answer/response A Hot Potato is a way to pre-assess or review multi-step problems. Every team needs one paper and one pencil or one paper and a different color of pencil for each team member. The first person writes down the first step, simplification, or answer while explaining his or her thinking out loud. The next person corrects the first person's work, if necessary, and then puts the next step down, while explaining their thinking out loud. The third team member corrects anything that is incorrect and then does their writing and explaining. And so on, until the problem is completed and checked. At the end you could have the students each sign off that they understand and agree with everything that was written down. • Every team has one sheet of paper and each student has a different colored pencil. • A problem is given to the team. • The first person writes the first step of the solution process, explaining aloud, and passes the paper on to the next person. • The second person makes any corrections and adds the next step, explaining aloud, and passes the paper on. • Process continues until the problem is competed.

Purpose: Individual accountability during teamwork Because individual accountability is so important, a Hot Seat is a good way to emphasize this. After the teams have been working on a set of problems, have one member from each team come to the front of the classroom to work individually. A problem (similar to the ones they have been working on) is put on the overhead with a two‑minute time limit. The team members left in their team work quietly together to solve the problem. The team member in the front works without talking, independently, on the same problem. At the end of two minutes, the teacher checks the solutions. Two points are awarded to each team if the individual member at the front gets it correct. One point is awarded to each team if the team gets the solution. Continue with a new team member going to the front. • One chair/desk per team is set up in the front of the room. • Using Numbered Heads, Person #1 from each team comes to the front of the room and sits. • Teacher gives everyone a problem to work on in a specified amount of time. • Teams can talk, but not the individuals in front. • Check individual and team answers award two points for correct individual answers and one point for correct team answers. • Person #2 from each team is up next and repeat. Huddle Purpose: Deliver information to teams collect information on team progress If you want to check on the progress of the teams give additional information or ask for a consensus on something to do with the problem everyone is working on, you could call a "huddle." Have one person from each team come to a meeting (at the front of the room or just outside the door). You give that person the information and they return to the team and share it. This strategy is a way to communicate with all the teams without having to call the whole class together. • One person from each team (teacher's choice) is called to the front of the room. • Teacher gives a piece of information, checks for understanding.... • Student goes back to team to share.

Purpose: Share ideas between teams If a team is stuck on a problem, one way to get unstuck is to send a spy to another team. The spy can walk up and listen (no talking allowed) to another team until they get ideas to help them continue with their problem. The spy then goes back and reports to their team. No one in the team that the spy visits should be distracted by, or talking to, the spy. • When the team is stuck, one student (i.e., the Resource Manager) can go around to another team and listen in. • No talking. • Student reports back to the team what was learned.

Purpose: Build understanding of a large quantity of information There are various ways to organize the jigsaw activity, but the central concept is that teams of people are assigned or select topics that they teach to others. The teams decide collectively how they are going to share what they know. One way to acquire knowledge from a large amount of material is to break it into smaller pieces. Each team of students becomes an expert for a part of the material and then shares their knowledge in their team. For example, if a large part of a reading assignment is broken into four parts, then each member of the team takes one part to become an expert on. Each team numbers off from one to four. All the ones become expert on the same material and discuss it in one section of the room. All the twos do the same with their part, as do the threes and fours. Then they return to their original teams and each shares their information. • Each study team member is assigned a different part of a task/topic. • Each member researches/learns about the task/topic (possibly with others with same topic). • Each member then presents the information to the others in his/her study team.

Purpose: Focus attention on questions and problem-solving process In a team of four students, two of them, A and B, are the "mathematicians" who vocalize their thinking as they work together on a problem. Solving the problem is not the main focus of the "mathematicians " rather v they concentrate on vocalizing their thoughts as they work toward a solution. Another person, C, listens to the "mathematicians" as they work and asks for clarification when needed. As an active listener, C seeks to understand the mathematicians' thinking. The fourth team member, D, silently observes A, B, and C, and records what happens. As a silent observer, D may only take notes about what goes on, and may not join in or interfere in any way. After five minutes, the work stops and the team processes what occurred for 10-15 minutes: First, C explains what A and B were talking about and doing then A and B respond to C's interpretation and lastly D shares notes and observations. After processing one round, roles are rotated among team members and the process starts again, with the new "mathematicians" selecting a new problem. The exercise continues until all team members have played and processed each role. • Students #1 and #2 work on a math problem aloud in their team. • Student #3 listens to the discussion and can ask clarifying math questions. • Student #4 only records what is discussed and verbalized (looks for attitudes) and does not talk. • After 15 minutes, work stops and student #4 shares notes and observations. • A variation is Students #1, #2, and #3 work and #4 observes and then shares.

Purpose: Silent reflection or idea summarizing A Math Chat is a silent way to do a reflection, summarize ideas, generate ideas, check on learning, develop projects and solve problems. Because it is done completely in silence, it gives students a change of pace and encourages thoughtful contemplation. Topics are posted around the room. These topics can reflect what was learned in the chapter or could be general topics about classroom behaviors or norms. Time varies according to need. • Have posters, with a topic on each one. • Each person has a writing utensil. • No talking. • People write something about the topic. • When it's done, it's done.

Purpose: Individual accountability during teamwork Numbered Heads is an effective strategy for keeping all students involved and accountable during teamwork. Students number off in their teams. Then they are given a problem to solve, a question to answer, or any task to complete. The team members work together making sure that each student in the team understands what they are doing, knows the answers, and can explain the team's work. While teams are working, you can use the numbers to randomly select students to whom you can ask questions about the work their team is doing. When the teams finish, use the numbers to randomly select students to share the team's answers, the processes used, or any other appropriate response. Students can signal responses, explain their ideas, hold up a paper for a quick check, etc. This is also a good way to assign team roles or have students pick up materials or turn in papers. For example, all the #3's can pick up the supplies for their team project. The #4's can report out. • Students number off in their study teams. • The team is given a problem to do. • When the team finishes, use random numbers (1 - 4) to ask questions or have team members share the solution process. • The numbers can also be used to assign roles.

Purpose: Check individual understanding with opportunity to ask questions Pairs Check is an effective strategy to use when students are practicing a new skill or procedure or to pre-assess a topic that will soon be taught. Within each team of four, students work in pairs to solve problems and then check their solutions with the other pair. Each pair has one paper and one pencil. Student #1 does the writing while student #2 does the explaining. If Student #1 does not understand part of the explanation, it is their responsibility to ask questions and not blindly write everything that Student #2 says. Then the paper and pencil are passed to student #2 and they reverse roles for the second problem. When the first two problems have been completed, each pair stops and checks with the other pair. If both pairs agree on the first two problems, have them circle the check mark and proceed to the next two problems. If they disagree, they review their work and figure out what went wrong. Once the students are familiar with the process of Pairs Check, they can set up their own work space or work directly from sets of problems in their text. • Each pair has one paper and pencil. • Student #1 writes what Student #2 explains. • Then roles are reversed for the second problem. • Then each pair checks their work with the other study team pair. • Continue on to the next pair of problems.

Purpose: Assess team interaction and communicate characteristics of effective teamwork. Teaching students to work effectively in study teams must be done explicitly and routinely. Even in classes that function well, teamwork can periodically break down. When a particular lesson is especially challenging, students may not realize that their best teamwork skills are required for success. To help with these struggles, teachers developed a structure known as a Participation Quiz. For more information on this strategy, go to the assessment part of the Teacher Version. • Pick a team worthy task. • Tell students which norm you are focusing on. • Show teams how you are keeping track (overhead, posters, chalkboard). • Record comments while students are working. • Debrief (do not need to record everything).

Have the students find proximity partners. They stand up, push their chair in, touch 2 tables/desks, three walls and a chair and find a partner, not from their team (or you can play music and have the students walk around until the music stops). Then whomever they are standing near is their proximity partner. They stand there and talk about the topic. When they are finished, they say thank you and return to their team.

Purpose: Individuals articulate understanding This is an activity that can be done at any time during the class period to check for understanding. At the beginning of the period, students could be asked to explain a concept or definition from the previous day or week. It would serve to remind them of what they have just learned. Or this might be a way to introduce the topic of the day by remembering some of the parts leading up to the concept that have been learned in previous units. If reciprocal teaching is used during the middle of class it can be used to check the comprehension of what is being learned in that day's lesson. This is also one way to summarize topics at the end of class. Have students seated in pairs facing the front of the room. One student is named Student A, the other Student B. After a small amount of material has been presented (teacher, video, reading, etc.) ask Student A to suppose that her Student B just arrived and missed the information presented. Student A's task is to teach the material to Student B. While Student A is teaching, listen to as many pairs as possible to make sure what they are teaching is correct and to identify questions and points of difficulty. As more information is presented, continue having the pairs teach, but reverse the roles each time. • In pairs, Person A pretends that Person B was absent and explains a concept. • Switch roles and continue.

Purpose: Check in with teacher at a specified point. Often the teacher will not want the students to go ahead and work on the next problems without having the opportunity to make sure the solution is correct in the first problem. It might be that the problems all build on one another and if the first problem is done incorrectly, it will affect the outcome of subsequent problems. Or it might be that there are many different problems that are unrelated, but the teacher wants to check each solution before the teams move on to the next type of problem. This is when a Red Light Green Light Strategy can be used. • The team works together on a problem or set of problems. • When they finish the problem, then they must stop. • The teacher verifies the work/answer with questions. • The team is then given permission to go to the next problem or set of problems.

Purpose: Present logical arguments written communication A Silent Debate is a great way to improve the writing/communication skills of students. It helps them to realize that it is important to be very clear with what they are saying and also learn how to present logical arguments. This is very similar to an oral debate except that it is silent. The students pair up and the teacher assigns one person to take the pro side and the other takes the con side. They do not get to choose. The pro goes first. Each pair has one paper and one pencil between them. A topic is given to the students. The pro writes it down and then makes a statement written communication A Silent Debate is a great way to improve the writing/communication skills of students. It helps them to realize that it is important to be very clear with what they are saying and also learn how to present logical arguments. This is very similar to an oral debate except that it is silent. The students pair up and the teacher assigns one person to take the pro side and the other takes the con side. They do not get to choose. The pro goes first. Each pair has one paper and one pencil between them. A topic is given to the students. The pro writes it down and then makes a statement in writing, in support of the topic. Then the con reads the statement and responds to the statement or makes a comment against the topic. This goes on, back and forth, until everyone has had three or four chances to respond. • Student pairs: One is assigned the "pro" position, and the other "con." • Each pair has one pencil and one sheet of paper. • A topic is given, and the student with the "pro" position goes first. • The "pro" student makes a supportive statement in writing. • The "con" student reads the statement and then writes a comment against the topic. • The process repeats three or four times.

Purpose: Share ideas (beyond study teams) When students are working on a Big Problem, sometimes it is well worth the time to have them share their ideas or hear other team's ideas without having a whole class discussion. One way to do this is through a Swapmeet. Part of the way through a problem, have two people from each team rotate to a new team. They can then share what they have been working on, what strategies they have tried and what questions they still have. After each pair shares with one team, they return to their original team. Then they share what was learned from other teams and continue to work. • When a team task is partially finished, one pair from each team rotates to the next team. • Pairs from the two teams share ideas, solutions, thinking... • Pairs return to their original teams and share what they learned.

Purpose: Team discussion and decision-making Teammates Consult is an effective strategy to use for problem solving and concept development situations. It allows the students an opportunity to think and discuss the problem before actually writing anything down. Students begin by putting all pencils and calculators in the center of the table. One student reads the problem or question to the team or each student reads it individually. Then they discuss the problem, making sure that each team member understands the information given and what they are asked to do. Possible strategies and answers are also discussed and explored. When each student in the team understands the problem and has a strategy for solving it, all the students pick up their pencils and write out their solution. It is best for the teacher to signal to the class when they may pick up their pencils. The teacher can determine when to do this by walking around the room, listening to the team discussions, and questioning team members. Students may then compare their work with others in their team or share it with the class. Team Roles or Numbered Heads can be used for determining who will read the problem, who will answer the questions, and who will share the solution with the class. Individual student papers can be collected for evaluation. • All pencils and calculators are set aside. • Students read the problem or question. • Give students individual think/work time. • Teams discuss the problem for clarity. • Possible strategies are shared. • Teacher gives okay for pencils to be picked up and written work to begin.

Purpose: Individual reflection prior to discussion Think Ink Pair Share was developed by Frank Lyman and his associates at the University of Maryland. It works well when students are involved in concept development or problem solving situations. The strategy emphasizes the importance of thinking about the situation before jumping to an answer. It gives students the opportunity to be creative and to explore different approaches. Students work with a partner. They begin by thinking about a question or problem without the use of a pencil or paper (about two minutes, depending on the difficulty of the problem). Then the teacher gives the signal that they may use their pencils. At this point they still may not talk to their partner. They decide what approach to use and write down their ideas, solutions, etc. Then after a period of time determined by the teacher, they pair up and share their thinking and work with their partner. When partners have finished sharing, you may want to have each pair share within their team or have students share with the whole class. • Teacher poses a question/problem. • Without pencils, students think for one or two minutes. • Students may then use pencil to begin working...without talking to their partner. • Students then share their thinking and results with their partner. • Pairs then may share with their team or the class.

Purpose: Individual reflection prior to discussion Think Ink Pair Share was developed by Frank Lyman and his associates at the University of Maryland. It works well when students are involved in concept development or problem solving situations. The strategy emphasizes the importance of thinking about the situation before jumping to an answer. It gives students the opportunity to be creative and to explore different approaches. Students work with a partner. They begin by thinking about a question or problem without the use of a pencil or paper (about two minutes, depending on the difficulty of the problem). Then the teacher gives the signal that they may use their pencils. At this point they still may not talk to their partner. They decide what approach to use and write down their ideas, solutions, etc. Then after a period of time determined by the teacher, they pair up and share their thinking and work with their partner. When partners have finished sharing, you may want to have each pair share within their team or have students share with the whole class. • Teacher poses a question/problem. • Without pencils, students think for one or two minutes. • Students may then use pencil to begin working...without talking to their partner. • Students then share their thinking and results with their partner. • Pairs then may share with their team or the class.

This excludes writing down, after the first think, what the student was asked to think about. This strategy could be used when beginning a Unit Summary. Have the students Think about what concepts were covered in the unit, then they Pair up and talk about their ideas in their group or with a partner. Finally the whole group Shares the ideas. This could also be used when introducing Diamond problems and doing Mental Math.

Purpose: To have students communicate mathematically The Traveling Salesman strategy has students in a team plan a presentation around a math problem or topic. It doesn't matter if the teams have the same problem or not. The students plan and practice the presentation with their team. Then one member (salesman) from each team rotates to another team to pitch their presentation. The team can ask the 'salesman' any clarifying questions. Then the 'salesman' rotates to the next team to present again. The salesman can be the same person for the sales pitch or a different team member can do the presentation each time there is a rotation. This works well in combination with Numbered Heads. The Number 1's all rotate the first time, the Number 2's the second time and so on. Or the teacher can always randomly (or on purpose) choose the 'salesman.' It might be the time to choose someone who does not speak up much or one who usually does not get actively involved in working with the team. There does not need to be a rotation to every single table. The purpose is to make sure that students have a chance to present. If time is limited, one rotation might be all that can be done. • Teacher assigns a topic/problem to each team. • Students solve the problem then plan a presentation. • One team member presents the mathematics to another team. • Repeat.

Purpose: Use movement while communicating mathematically Walk and Talk allows the student to move around, which is good for their brain cell growth, while talking about mathematics. Students are put in pairs, their choice or the teacher's, and take a walk around the classroom (or outside if possible) while they talk about some aspect of what they have been learning. They can summarize what they learned, clarify ideas, ask each other questions or come back with a question for the teacher. If there is not enough room to have the pairs walk around, another idea is to have the students find proximity partners. They stand up, push their chair in, touch 2 tables/desks, three walls and a chair (or you can play music and have the students walk around until the music stops). Then whomever they are standing near (should not be anyone from their team) is their proximity partner. They stand there and talk about the topic. When they are finished, they say thank you and return to their team. • Topic is presented. • Pairs walk around the classroom (or meet with a partner) discussing the topic.

Purpose: Elicit final reflective comment from each individual The Whiparound allows each person to have a final comment about a problem or lesson, or after a suggestion. Whiparounds work best with everyone sitting in a circle, but does not have to be set up that way. The teacher states a topic or question and the students make a brief comment about it. They could go in order around the circle or anyone could talk. Everyone does not have to make a comment, but they are encouraged to do so. • Basic Whip-Around • Topic or question is presented. • Students randomly have an opportunity to say something briefly about it. • Everyone does not have to comment but are encouraged to do so. • Another form of Whiparound I Have...., Who Has.... • Each student has one card with a problem and an answer to a different problem. • Student 1 asks, "Who has..." and states the problem. • The person with the solution says, "I have ...." and states the answer. • The responding student then poses her problem and the student with the answer on his card responds. • The process continues until all the questions and responses are given.