We began today discussing our charts for the bus stop problem.  We talked about the benefit of titles, noting slope, noting “not drawn to scale”, pictures, color coding and whether or not scales on the x and y axes were helpful or not.  The graphs were amazing and I was so impressed with the process all the groups went through in drawing them.

We then discussed the idea of piece-wise functions and their use and moved into Standard 2 of CCSSM and watched a video of what this standard could look like in a 5th/6th classroom.

Charles picked up with Unit 3  material and reviewed the ideas of linear and proportional.  We had some good discussion about the exchange rate and how it works with rounding.  There as a question about when topics like this are handled in school.  Unit rates are in 6th grade and it builds to proportional statements in 7th grade.  One of the issues is using 10/9 or 1.11 and which is the numerator and which is the denominator.  There was also discussion about having students learn how to express ideas mathematically like “five plus seven” is 5+7.  Also we can talk about conversions younger grades discussed converting cups vs. ounces and understanding that both are valid representations of an amount and how we talk about how to decide on a scale when graphing. These are important building blocks to get to what they will be learning later on and we can use these ideas to connect to what they already know.   We also discussed the benefit of younger grade teachers seeing what types of skills seem to be stumbling blocks later on in order to inform their teaching of these concepts.  I was so excited by these questions and how participants were trying to think through problems like this that their age students could relate to.

Marina began talking about what makes a relationship linear and what makes it proportional.  We also talked about the equation of a line.

We ended the day by talking about Standard #3 and then discussed the concept of funneling and focusing questions.  We than moved into a questioning activity to practice the use of effective questions.  We will follow up with this in our homework tonight.

Homework:

Math p. 3.16 #8, 10, 11, 12   Also determine why ax + by + c = 0 is more versatile than y = mx + b.

Pedagogy Read P to A 37, 39-40  Listen to your audio recording or think about the questions you asked in our activity.  Using pages 37, 39-40 to examine the questions you asked while playing teacher and respond to these prompts:

1.  Were your questions funneling or focusing
2. How might you change it now?
3. What type of questions might be more productive for eliciting student thinking?  Write a few new questions – refer to pgs 36-37.

Percolating assignments:  When it is “ok” to use funneling questions.