Adding Numbers in Multiple Ways (Frakes)

2A, 3C: The teacher allows multiple students to share their thinking about how the same strategies learned to add two numbers can be used to add four numbers.  Each explanation is accepted and revoiced by the teacher to develop a shared understanding; the teacher also uses a visual model to support the part + part = whole comments.  In addition, students are invited to come up to the front and use different representations to solve the equation: base-10 blocks, open number line, and mental math with compensation.  As each student comes up, he/she is asked to share mathematical thinking with the whole group, and the rest of the students are invited to agree/disagree.

As students do work in front of the class, they explain their mathematical thinking. This is a consistent expectation for every student, and the students freely elaborate on their thinking, often without prompting from the teacher. 

1B: The teacher prompts students to brainstorm all of the different mental strategies ("number strings strategies") and math tools they've learned and explored to help them add two numbers, and she asks students to form an opinion about whether or not these tools and strategies would be useful with the new skill of adding four numbers.  Students articulate their thinking to the class, making explicit connections to what they know about addition and what it means to add numbers.

2B, 3D: The teacher allows students to work with peers as they explore the math in the lesson.  This partner format creates the conditions for students to discuss their thinking and ask questions as needed.  Although some students choose to work individually, the teacher notes that "it's hard to have really good math conversations with yourself" to encourage partner work as the preferred option.  Students' math-focused conversations can be heard throughout the partner work time.

The teacher has structured the lesson to allow students to work with partners for more than 20 uninterrupted minutes.  Students have sufficient time to engage in the grade-level task and generate multiple solution strategies.

2C: During partner time, the teacher purposefully identified a variety of representations and solution methods to share on the document camera, including place value drawings, open number lines, decomposing, and compensating ("number strings strategies").  Selected students shared their work, explaining their thinking and making revisions as needed.  The teacher asked guiding questions and prompted the rest of the students to indicate any connections, in order to help all students strengthen their understanding.