As a way to start off and frame our conversation about the observation of our lesson, we looked at the student work and discussed the following questions:
 What methods did the students use? Do all the methods work?
 How well is each group able to explain their thinking?
 What are the strengths of each method? How could each be improved?

Strengths 
Improvements 
Nicole and Michael

 multiplicative reasoning
 trying to find equivalent fractions to compare – common denominator to compare numerators
 didn’t multiply the denominators to find the common denominator but had a more efficient method 
 number sense – recognized that doubling 35 (the total students in the other class) would give them 70 which they could also reach if they multiplied the 10 (the total of Josh's class) by 7
 used part to whole fractions
 now that the denominators are the same, we can compare. Our class would… By 9
 good vocabulary usage
 made their own problem… (determining the other class is more right thumbed)

 More proof on the paper – demonstrating the connection between common denominator and what it means in terms of the proportional reasoning – once they view as a fraction, are they demonstrating a proportional reasoning and equal grouping
 “if our classes were the same size, we would have more…” – evidence on the page
 Michael's understanding of manipulating fractions carried this group  he was unable to explain to Nicole why it was necessary to have equal groups when making the comparison
 One student's understanding dominated this group's solution method

Kenny and Jaquille

 reduced/scaled down the 20/35 to 4/7

 they were stuck on the bowtie method – they said, “That is how you find the answer here” – they were using a method that they didn’t understand why it worked and it didn’t really fit the situation

Kendra and Joseph

 we like the way they wrote out the part part whole with bracket
 Found the percent
 Stopped at .57 because they knew that was enough to compare with .70

 This group was not sure why they used percents

Some Goals for the Revision (based on our observation and analysis of student work) 
 We want there to be less of an emphasis on fractions

 We want students to use a wider range of methods

 We want to encourage using a chart to work on the opportunity

 We want to develop student presentations of their work

 We want to the lesson to give more explicit directions for how the teacher should use the board

 Collect both the posters (newsprint) and the student's work

Some Questions 
 What does it mean to be more or less leftthumbed?
 "If we have the same number of people in our class, more of them would be leftthumbed"
 Should we use words like "Relative amount", "magnitude", "scale", "proportional", "dominant", "majority", "relative to the whole"
 In step two – "for every 10, there are 7 people who are leftthumbed"

 Do we want to use academic vocabulary?
 Maybe, but at the end – have students develop the idea and then add the vocabulary (for example, you can do the rice/water opportunity and then talk about the word "proportional" to explain rice that is neither too mushy or too hard)
 We want them to struggle with the math, but also the vocabulary
 If someone knows there is a MATHy word for it, they are likely to think there is one way to solve it
 Is it important to focus on the semantics of how we word things in the lesson planning?

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