Pre-Modeling activity helps students understand what a residual means in relation to a data set and a graph. A linear model is used here because students are familiar with linear associations and predictions. Data sets are carefully selected by teacher to help students understand that more than just a correlation coefficient is needed to find the best model for a data set.
1A,2A: The lesson focuses on the depth of course-level cluster(s), course-level content standard(s) or part(s) thereof. The teacher makes the mathematics of the lesson explicit by using explanations, representations, and/or examples.
1C: The lesson
intentionally targets the aspect(s) of rigor (conceptual understanding,
procedural skill and fluency, application) called for by the standard(s)
being addressed. Pre- Modeling activity helps students understand
what a residual means in relation to a data set and a graph.
3A: The teacher poses high quality questions and problems that prompt students to share their developing thinking about the content of the lesson. Teacher connects her introductory real life example to what students worked on in the pre- modeling activity.
1A, 3E, 3F: Students use precise mathematical language in their explanations and discussions. Teacher is modeling process to find a residual plot for the linear model using appropriate tools for putting the regression equation in y = and appropriate mathematical terms like diagnostics, residual values, and correlation coefficient . Students are helping each other when needed on steps (procedural skill).
1C, 2C, 3A: This part of the lesson is a good example of whole class discussion of uncertainty that linear model is correct. Students suggest two different answers and teacher asks entire class for support for either answer.
1B, 2C, 3F: Student question brings prior knowledge: the idea that the r value can be an indicator for a best fit curve. Teacher uses student question to confirm student understanding and review for entire class.
3D: Great discussion between 2 students about regression equation. Female student understands what the regression curve should look like and helps the male student find out what he is doing wrong.
1C, 2D: The teacher deliberately checks for understanding throughout the lesson and adapts the lesson to meet the condition of the students learning. Two different groups have the same misconceptions and teacher's questions help them understand the correct reason they are choosing their answer.
3G: Teacher questioning helps student revise their reasons for choosing a particular model.
2E: Teacher leads summary with questioning about r values and residual plot. Students add to this discussion to help summarize the activity.
1C, 3A: Students practice finding best model in groups and discuss procedural skill steps. (teacher refers to steps on green sheet).
1B, 3B: Students are computing r values as they practice finding models. Discussion about negative r and positive r and what that means. Also, students are not corrected as they find their errors as they practice a different scenario.