1. Kubota-Zarivnij, 2010 BEFORE 5 to 10 minutes only Activating students’ mathematical knowledge and experience that directly relates to the mathematics in the lesson problem Includes student responses to a prompt/problem that is similar to previous work to highlight a few key ideas and/or strategies

2. Kubota-Zarivnij, 2010 DURING 15 to 20 minutes Understand the problem, Make a Plan, Carry Out the Plan Understand the problem - Ask, “What information from the problem will we use to make a plan to solve it? Explain.” Teacher records below the problem the information the students identify in a list. Students solve the problem in pairs or in small groups

3. Kubota-Zarivnij, 2010 AFTER (Consolidation) 20 to 25 minutes Teacher selects 2 or more solutions for class discussion and decides which solution to share first, second, third. Teacher organizes solutions to show math elaboration from one solution to the next, towards the lesson learning goal Students (Authors) explain and discuss their solutions with their friends Teacher mathematically annotates (math symbols, math terms, labelled diagrams, concise explanations) solutions to make mathematical ideas, strategies, models, and tools explicit to students for their learning

4. Kubota-Zarivnij, 2010 AFTER (Highlights/Summary) 5 minutes Teacher and students revisit key ideas, strategies, and models of representation from student solutions that relate to the lesson learning goal Teacher records in a list key ideas, strategies, and models of representation separately, so the students see how the mathematical details from their solutions relate explicitly to the lesson learning goal

5. Kubota-Zarivnij, 2010 AFTER (Practice) 5 to 10 minutes Teachers chooses 2 or 3 problems, similar to the lesson problem for students to solve individually (or in pairs as a scaffold). Problems are different by number (choice, size), problem contexts, or variation of unknown that needs to be solved Students are asked to use a strategy different from the one they used in the lesson to solve the practice problems

6. Kubota-Zarivnij, 2010 solutions Labels for Each Category (e.g., mathematical strategies, numeric equations) BEFORE Activation DURING AFTER - Consolidation (focused on knitting ideas together from one solution to another towards the learning goal) AFTER Highlights/ Summary - Key ideas, strategies in relation to aspects of solutions AFTER Practice -Similar problem to the lesson problem to be solved individually mathematical annotations - either on the board or on the student solutions to make explicit mathematical ideas, strategies, and tools and to show relationships between the solutions - “What information from the problem will we use to make a plan to solve the problem? Explain. Record the info In a list <problem or previous day solutions> Record 2 solutions to highlight math ideas BANSHO FRAMEWORK solutions