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Take some time to look over each of the engagement strategies and like the ones that you've used. Feel free to comment on them as well if there is a strategy you would like to learn more about or have context on.

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The jigsaw technique can be a useful, well-structured template for carrying out effective in-class group work when there are multiple activities or examples you want to divide and conquer. The class is divided into several teams, with each team preparing separate but related assignments. When all team members are prepared, the class is re-divided into mixed groups, with one member from each team in each group. Each person in the group teaches the rest of the group what he/she knows, and the group then tackles an assignment together that pulls all of the pieces together to form the full picture (hence the name "jigsaw").

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In groups, students take turns sharing their ideas or solution.

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Each corner of the room or each side of the room is designated with a letter. Show a question on the board with four (or two) answer choices, each matching with a designated letter. Give students time to think and then have everyone move to their corner or side at one time. Allow time to share at their letter and then also as a whole class.

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• Round One:
Each member completes step one (or problem 1). Pass clockwise when all finished.
• Round Two:
Check round one. Praise or Coach.
Complete step two (or problem 2). Pass clockwise when all finished.
• Round Three:
Check round two. Praise or Coach.
Complete step three (or problem 3). Pass clockwise when all finished.
• Round Four:
Check round three (or problem 4). Praise or Coach.
Complete step four. Pass clockwise when finished.

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• Students move to pairs and assign A or B to each partner.
• Teacher announces a topic or shows a problem and states how long each student will have to share.
• Teacher provides think time for all students.
• In pairs, Partner A shares their response or start of the solution and Partner B only listens.
• Teacher announces time to switch.
• Partner B responds by adding on to the solution, making a correction, providing another method, or recapping while Partner A only listens.
• Pairs switch roles for the next problem.

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Provide sentence stems to help build classroom discourse. Sentence stems can be used with a partner, small group, or whole group.

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(1) You will need numerous questions on your content (boardwork questions, worksheets, or even straight out of a textbook).
(2) One student from a pair begins by saying out loud how they would solve the problem given in a step by step manner as their partner writes down the process.
(3) If the student solving the problem is unsure, their partner can coach them.
(4) Roles are then reversed for the next problem.
(5) The structure ends either when all questions have been completed or when the teacher calls time.

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Students express their understanding of a solution or topic with a 0-5 scale (fist to five fingers).

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One student from each group is the designated spy. Option 1: Students can send their spy out to look at what other groups are doing as need. Option 2: The teacher can announce "Send out your spies" and all spies can move around the classroom observing other groups. With both options, the spies are responsible to report back to their home group.

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Option 1: A paper is divided in four quadrants with a circle in the center and number in the circle. Each quadrant has a different problem to solve. The SUM of the answers to the four problems will be the number in the center of the circle. So students know if they didn't get that sum, then one (or more) of their solutions is incorrect and they must work together to fix it.
Option 2: Each group has a piece of poster or butcher paper and divides it into four quadrants. Each quadrant should be titled with a representation type (e.g. table, graph, bar model, double number line, verbal, algebraic, etc.) Each student is assigned an expression or equation and sits in front of one of the quadrants. Each student models their expression or equation with the representation of their quadrant. Then the students rotate to complete each representation with their expression or equation.

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While students are working with their group, only group questions are allowed. If an individual has a questions, they ask their group first. If no one in the group can answer, it becomes a group questions and they can ask the teacher. To enforce this, when the teacher approaches a group, any person in the group should be able to state the question.

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One person from each group rotates to a new group. For example, if each student in a group of 4 is numbered 1-4, the teacher might say, "All of the 1s rotate one table to the left."

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Students have an opportunity to think on their own first, then share their thoughts with a partner, and then share out with the class.

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Mini whiteboards can be used individually, in pairs, or in small groups. They can be used to check for understanding and also to show work using other strategies like Sage and Scribe.

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• Students can each create a flashcard or choose one from a preexisting set
• Teacher announces Stand Up, Hand Up, Pair Up
• In pairs, Partner A shows the front of their card and quizzes Partner B. Partner B answers the question and Partner A confirms or coaches.
• Partners switch roles so Partner B quizzes Partner A.
• Partners trade cards and find new partners.

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Each student in the group is assigned a role. Some examples are: Leader, recorder, speaker, materials, spy, mayor, reporter, or super hero. These roles should change frequently so that all students have opportunities to take on different roles. This helps with individual responsibility and collaboration.

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Provide the answer before students begin working on the problem so that the focus of the discussion is on the strategy and not the answer.

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Option 1: A paper is divided in four quadrants with a circle in the center and number in the circle. Each quadrant has a different problem to solve. The SUM of the answers to the four problems will be the number in the center of the circle. So students know if they didn't get that sum, then one (or more) of their solutions is incorrect and they must work together to fix it.
Option 2: Each group has a piece of poster or butcher paper and divides it into four quadrants. Each quadrant should be titled with a representation type (e.g. table, graph, bar model, double number line, verbal, algebraic, etc.) Each student is assigned an expression or equation and sits in front of one of the quadrants. Each student models their expression or equation with the representation of their quadrant. Then the students rotate to complete each representation with their expression or equation.

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1. Student 1 and 2 work on a math problem aloud in their team.
2. Student 3 listens to the discussion and can ask clarifying math questions
3. Student 4 only records what is discussed and verbalized (looks for attitude) and may not talk.
4. After 15 minutes, work stops and student #4 shares notes and observations

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Ask students what they notice and what they wonder when presenting them with an image, a problem, a video, etc.

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We know we want students to ask each other questions, but this isn't necessarily a skill that all students have. By providing questions and question stems, we can build students understanding of effective questions to ask each other and how they can use questions to collaborate.

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Plan questions in advance to…
-help students share their ideas, make connections, problem solve, and relect on their work.
-guide, clarify, deepen, and check student understanding.

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Talking Chips are manipulatives (e.g., counters, paper tokens, etc.) given to students during small group discussions. Each time a student wants to speak, they “spend” a chip by placing their chip in the center of the group's table. When a student no longer has chips, he or she must wait to speak until all other students have used up their chips too.

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Fishbowl conversation is a form of dialogue that can be used when discussing topics or solutions within large groups. Fishbowls involve a small group of people seated in a circle and having a conversation (fish). They are surrounded by a larger group of observers, seated in an outer circle (bowl). The facilitator or subject matter expert gives a short input of 5-10 minutes which sets out the general outline of the discussion and after that the inner circle starts to discuss. The outer circle usually listens and observes. Whenever someone wants to participate and move to the inner circle, a participant from the fishbowl must free a chair and move to the outer circle. Alternatively, you can have groups rotate into the fishbowl and take turns demonstrating problem solving.

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Numbers Talks are a short exercise that help students practice mental math and see a variety of strategies.

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Place different problems around the room and have students rotate to complete them all. This can also be used as a larger group version or simultaneous round table where groups of students are each completing the next part of the task at each station. (See video example).

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Many of us know about wait time. After we ask a question, we should wait several seconds before calling on anyone so all students have an opportunity to process, but there's another type of wait time that many teachers miss out on. It's wait time II, and it's giving wait time after a student speaks. This allows other students to process and respond to each other. It encourages student-to-student discourse.

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Option 1: Before students pick up their pencils, they talk with their partner or group about what they know about the problem and possible strategies for solving. Option 2: Give students independent writing time to start the problem (and set a timer for a minute or two) letting students know that when the timer goes off they are going to put their pencils down and talk to their group about how they started.

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● Students find three classmates to agree with all of their answers. The goal is to have 100% correct on the assignment.
● Give students about 10 minutes.
● When a student finds a person who agrees, they should have them sign their assignment (complete signature).
● If a classmate disagrees with one or more of a student’s answers, they may choose not to sign and must then try to find others who agree, OR, they may listen to each other explain their thinking, and either student may change answer(s). If all answers are now the same, they sign each other’s work.
● (This step can be skipped until the class gets the jist of the activity). If a student changes one of their answers after someone else has already signed their work, it is their responsibility to find that person and explain the change you made. They may cross their name off the work, or change their answer to match.
● Students should sit down once they have three signatures, or when they hear the timer.
● Students should be ready to explain:
○ why and how they convinced someone to change an answer (or)
○ why they changed an answer (or)
○ one of your methods for solving a problem

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Numbers Talks are a short exercise that help students practice mental math and see a variety of strategies.

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If a student is unable to answer a question or answers in correctly, allow for other students to answer, but then return to the original student to have them summarize the answer. This should be used consistently so students understand that the expectation is for everyone to participant and leave with understanding. It is okay for them not to know at first, but it is an opportunity to learn.

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In small groups, each student is given a number 1-3 or 1-4. After students have had time to discuss or work on a problem, the teacher calls one of the numbers to share out for their group. Students know that each of their group members must be well prepared to share out.

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TAPPS (Think Aloud Pair Problem Solving)

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TAPPS (Think Aloud Pair Problem Solving)

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1. The class is divided into pairs and informed of the rules for each of their roles:
A. Problem solvers: students talk aloud while solving a problem explaining their reasoning and
process as they go through the problem.
B. Listeners: students engage the problem solvers and ask them to think aloud asking for
clarification as needed.
2. The teacher poses a problem for each group of students or for the class as a whole.
3. Students work in pairs and alternate roles as stated above to solve the first problem.
4. The teacher calls time and asks each listener to state the answer to the problem and a short
version of the process the problem solver used.
5. The teacher can repeat the process and reverse the roles.

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Digital activities powered by Desmos. Use a pre-created activity or build your own. You can even take a lesson and turn it into a Desmos activity.

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1. This is a way to structure pair work on mastery-oriented worksheets.
2. Students work in teams of four with two sets of partners.
3. The worksheet is set up with problems presented in pairs.
4. The first person in each partnership does the first problem with the pair partner serving as coach, and offering praise as appropriate. (Rally Coach)
5. After the first problem is done, partners change roles.
6. After each pair of problems, teams of four can check each other’s work and, if they agree, give a team cheer or handshake. (Pairs check)

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Ask students to make a prediction about the problem before starting it. If it's a numerical answer, ask them to guess numbers that are definitely too low and definitely too high. Ask them what solutions would be unreasonable.

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This is a strategy for when students are going to be working in pairs. Students stand up and put their hand up in their air (like they're ready for a high-five). Students pair up with someone who also has their hand up. This also works well when students are rotating partners because it lets others know they are ready for their next partner.

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Index Cards are great for students!  It gives them the opportunity to write down the word and then give their own explanation of the word or process.  The student is asked to keep the cards in a pocket in their journal.  They can reference it at anytime.

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"Effective teaching of mathematics engages students in making connections among
mathematical representations to deepen understanding of mathematics concepts
and procedures and as tools for problem solving." - Principles to Action, NCTM. Through questioning and task selection we can have an impact on how students use and connect various representations.

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Turn and talk. or Think Pair Share. When a topic of discussion is at hand, students are allowed to discuss and learn different methods of how to approach the problem for resolution.

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I love whiteboard.fi. It allows me to see what all my students are doing in real time. It allows me to intervene with a student immediately. It allows me to model the question and I can see them working with me at the same time.

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My students love to use whiteboards in class whether individually or in groups. They are eager to write and display their work to me and others it is definitely a sense of pride as to what the student can do. It allows the teacher to take a quick assessment of who is on track or struggling with the concept.