[bcohen]

Bill,

Are the included forms, x + p = q and px = q, intended to limit work in this grade to solving one-step equations? 

How about with a variable on both sides?  (ex., 3p+6=4p)

Thanks,

Brian

[bcohen]

Thanks, Duane.  I’m glad I’m not the only one who sees some tension between some of these standards.  Some of this was helpful, but I’m still struggling with making determinations for what should be taught/assessed when.  In this comment Bill frames the tension that I see:  “…On the one hand, there is no explicit requirement to use parentheses until Grade 5.  On the other hand, there’s a footnote on 3.OA.8 that… suggests that parentheses might well be used much earlier…” (http://commoncoretools.me/2012/04/02/general-questions-about-the-standards/#comment-1609)
 
Then, discussing 3.OA.8, Bill says: “The thrust of the comment in the progressions document is that one need not expect fluency with this [order of operations] right away. I agree the exact boundaries are not really spelled out here.  Perhaps a good rule of thumb would be to expect students to be able to deal with fairly simple expressions like 5+3×10, but not to be too aggressive about insisting they can deal with more complicated expressions.” (http://commoncoretools.me/forums/topic/expanded-notation-and-order-of-operations/#post-1188)
 
So here’s a specific concrete question meant to feel out the boundaries.  This is a NY sample question for 4.OA.3:
“Students from three classes at Hudson Valley Elementary School are planning a boat trip. On the trip, there will be 20 students from each class, along with 11 teachers and 13 parents.
 
Part A: Write an equation that can be used to determine the number of boats, b, they will need on their trip if 10 people ride in each boat.”
(http://engageny.org/sites/default/files/resource/attachments/math-grade-4.pdf)
 
Recognizing that you could not write an equation, the expression would be (11 + 13 + 3 × 20) ÷ 10, or an equivalent expression.  Does this fall within the expectations of 4.OA.3?
 
Thanks,
Brian

[bcohen]

Duane,

Because 2.MD.6 requires “…equally spaced points corresponding to the numbers 0, 1, 2, …” on a number line diagram so that it accurately represents “whole numbers as lengths from 0” we are using ‘closed’ number lines (with all numbers shown) to address this in grade 2.

In grade 3, we begin using open number lines in ways like Bill’s example above.  We also use the strategy to solve problems involving operations with non-base-10 numbers (ex., elapsed time) because it side-steps issues of regrouping non-base-1o numbers.  When we use open number lines (beginning in grade 3), we like the jumps to be ‘relatively’ proportional (i.e., a jump of 100 should take up more space than a jump of 10), but we do not focus on making the jumps exactly proportional.  One of the benefits of the open number line, in my opinion, is that it relies on and fosters number sense and its appropriate use in computation.  While asking students to make the length of jumps ‘relatively proportional’ seems like it supports this sort of number sense, focusing on whether the length of each jump is represented precisely to scale seems like it would undermine the same goal.

For what it’s worth,

Brian

[bcohen]

Thank you for refreshing this topic, vbyrnes and Duane.  And thanks for the clarification, Bill.

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