Algebraic Thinking and Proportional Reasoning, Day 3 (7/19/17)

We started the day by using the Jigsaw strategy to review the homework. Each table worked together to be an expert in one part of the homework problems, then we shifted around so that each group had an expert in one problem present, and the groups shared.

Next, participants worked through the Currency Exchange problem. This is another proportional relationship, but we’re extending our thinking to the more general class of linear relationships now. One particular challenge was writing the equation relating D (price in dollars) to E (price in Euros). Many people make the “reversal error,” in which they (incorrectly) translate the statement “$1.00 is worth €0.90” to “D = 0.9 E”.

After lunch, we did the Currency Exchange with a fee. We described how to represent this situation with an equation, or with a graph. We noticed that when we graphed the original currency exchange equation on the same axes as the currency exchange with a fee, the lines were parallel. We compared the equations and related this to the slope of the graphs.

Some notes from the Pedagogy discussions today:

Practice Math  Talk moves Examples
Make sense of problems and persevere in solving them.

 

Wait time If you’re finished show another way to solve and compare your answers

 

Look for and express regularity in repeated reasoning.

 

Repeating Using a prior explanation from another student to solve a similar problem with different numbers

Extending the structure of a problem (solving an equation—word problem)

Reasoning Can you model your solution in a different way?
Model with mathematics Turn and Talk Modeling equivalent fractions with manipulatives (each group uses different manipulatives)
Look for and make use of structure.

 

Reasoning How is your comparison different from your partner’s?  Can you explain?
Construct viable arguments and critique the reasoning of others.

 

Reasoning Did anyone use a different strategy to solve the problem or same strategy with a different answer?
Attend to precision.

 

Revising Would you like to revise your writing/thinking using specific math vocabulary
Adding On Clarify or add more detail

Convert units—explain or rounding in context to the problem

Homework:

Math: Read Block 3, p. 11 – 12.

Pedagogy: Read Message 12: “Upside Down Teaching”. Think about a task at your grade level that you can “turn upside down”

If you have extra time: For pleasure read “13 Rules that Expire” article.

Bring your curricular materials tomorrow!

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