# Algebraic Thinking and Proportional Reasoning Day #1 (August 7, 2017)

We began with a burning question from last week connecting scale factor and unit rate in solving proportions.

We also discussed the norms we are trying to establish in the workshop which included – everyone being heard, no fear of making errors, and respect for each others’ ideas.

Because of a glitch in the materials we then moved into discussing the first two standards for the common core and an explanation of these was found in the website:  https://www.scholastic.com/teachers/blog-posts/meghan-everette/guide-8-mathematical-practice-standards/

There are also some good videos of what the standards could look like found at:  http://www.insidemathematics.org/common-core-resources/mathematical-practice-standards/standard-2-reason-abstractly-quantitatively

Charles then led us into Block 1 with the sliding snail question.  We realized we could use a piece-wise function to express the height at any integer time value.

There was discussion about the value of generic rules for expressing even and odd numbers.  We expressed an even number as 2n and an odd number as either 2n + 1  or 2n – 1.

We had some good discussion about whether a remainder is negative or positive when dividing a negative number by a positive.   We found that thinking of it as positive made the problem of comparing 3/4 and (-24/4) and (27/4).

We talked about graphing the walk to the bus stop and showed that the steepness of the line can show the speed of my travel.

HW for tonight:

Charles recommended the going further problems on page 9.

For pedagogy

• Read Principle’s to Action pp 35-41 and 53-57
• In your notebook write a response to two prompts:
• In questioning in small groups of students working on a problem, a teacher noticed that when she asked a “focusing” question, the students continued to look at their work and continued to engage in their own dialogue. When she asked a “funneling” question, the students looked up at the teacher. Comment on these observations.
• Look at Maddie’s work and Gabe’s work, shown in figure 22 on page 55. How could Ms. Lewis leverage the student’s representations to develop Maddie’s understanding of the problem?