Interpreting Multiplication & Division

The teacher began the lesson on the rug and they did some examples together.  Then, they each got a chance to discuss their thinking and how they did their work and she got three examples from students.  Students asked questions to the teachers and she explained what the student did if they had questions.  She did this and allowed students to think; she did not give them precisely how to get the answer.

During the discussion, the teacher asked questions such as "How could you solve the problem without writing anything down?".  Something she did to focus on understanding was asking one student what she did first, then asked students if they agreed.  Then she asked the same student what she did next and to tell her about why she did what she did.  Then the teacher explained what the student said.  She asked students questions to allow them to discuss the answer and how they got the answer rather than telling them exactly how to get to the desired answer.  She gave them prompts to think about and discuss with one another or think to themselves.

After the discussion about how they got the answer of the mental math question was complete, she had them each pick a card with a math problem on it and students did their problem using manipulatives.  While they are gathering understanding on the problem they are given, she gives students a formative assessment by asking questions on the process they are using.  She checks to see the understanding they have gotten so far and if they are struggling, she asks them to read the question over a few times and see what they are looking for in the problem.

After they all answer their questions, she has them come back to the rug and they discuss the answers to their problem.  They have a chart with answers to their problems and they get to look at the chart and identify their answer.  Students find the other people who had the same problem and they discuss their understanding of the problem and whether they agree or disagree with what the question is asking/ the answer they got.  During this time, students have to come to an agreement on the problem they were asked.

During their time on the rug, she asked if students agreed or disagreed with what their peers said and asked if they had any other answers- and this is showing math practice of critiquing.  They also did this at the end when they were in groups with people who had the same question.  They asked one another the process they used to get the answer and if they all got the same answer.  She also used the math practice of modeling when she wrote on the sheet of paper and used MP4.  Students were able to model with manipulative tools and showed modeling this way.  During the lecture part, she showed them how she wanted them to create the problems and show their thinking on paper.  However, students were solving the problem without paper and used only manipulative tools.  Students showed one another the way they got their answer using the manipulative tools, so they modeled their thinking for one another.