Week 1, Late.

I was going to jump on board the MTBoS 2017 Blogging Initiative .  I was planning to take a deep breath, close my eyes, and plunge in.  But for some unfathomable reason, I read “submit by midnight Sat., Jan. 7” as “submit by midnight Sun., Jan. 8th”.   Oops, I missed that first boat; fortunately, no one is going to dock points!  I’m determined to not let Week 2 drift by, but a part of my brain is still on Week 1’s theme, “Favorites”.

My brainstorm for Week 1 included a task from Visual Mathematics Course II and the folks at The Math Learning Center.

Original Version, Submarine Task

Its annual use qualified it as a “favorite”, although over the years I used it in various ways.  An assignment, a formative assessment, a group task, a summative assessment.   I always required diagrams and equations that supported each other, and eventually figured out to omit the question to allow students to focus first on understanding the situation.  That would be Version 2 (with all verbs in agreement as well.)

In the spirit of You Can Always Add here’s Version 3:

The Submarine Task, Version 3

A submarine cruises in an ocean. First it dives down, then climbs up, dives again, and finally climbs up.

Before you read my ideas, what would you do with this version?

What I think I would do, feel free to poke holes:

First, do some Noticing and Wondering  Ask students to make a sketch of what is going on.  Have students suggest not only what questions they could ask, but also what information they would need to answer their questions.  (BTW, typically the question in V2 is, “Where does the sub end?” I am curious what, if anything, will be different for V3.)   Then, allowing private think-time before working in small groups, give them this:

Which of these sets values fit this situation, which do not, and why?   Use visuals and equations to explore each list and be prepared to justify your reasoning.  Use values exactly as they appear, and in the order given.

-200, 150, 115, 180, 100

                                     -200 -150 -115, -180, -100

                                      -200, -150, 115, -180, 100

                                     -200, 150, -115, 180, -100 

                                      -200, 150, 115, -180, -100 

Compare what this task is asking of students, and what the others versions ask.  What do you notice?  What are your thoughts on the lists?

Continuing with my ideas:  Perhaps give the lists to groups on strips of paper so they can move them around a sort them.   I am dying to know which lists students accept and which (if any) they reject; should be an interesting discussion!  In my mind, V3 would be appropriately placed after some reasoning  and conjecturing about adding and subtracting integers, during a time when there is still room for questioning and sense-making, and before students practice fluency.

Since they have done most of the heavy lifting already, end with this:

1.  Chose one set of numbers to answer the questions you asked.  Be sure to include ALL of your work.

2.  Use a second set, including your work.  

3.  Compare the strategies:  How are they the same?  Different?  Which one is “better” for you and why?  (Do not describe what you DID; your work should already clearly show your steps!)  

A possible sequal to  V3, although probably not immediatly:

Which of these lists of values fit the Submarine Situation?  Explore with diagrams and equations and be prepared with viable arguments. 

                        -142.5, -157.8, 315.25 , -273.0, 198.75

                         -3,127, -1098, 4105, -3627, 2503

                          218.5, 105.6, 162.4, 298.3, 57.7

                          -410, 119.5, -338.26, 937.01, -705.635

                           -5/6, -3/2, 1/4, -2/3, 5/12

For each situation that DOES fit, answer the questions you previously asked. For each situation that does NOT fit, you may change ONE NUMBER so that it does work. Justify your choice.

And a couple of Reflections, if you’re into that sort of thing:

  1.  Understanding why subtracting a negative value results in an increase to a higher value is often perplexing.  Why do you think this kind of calculation exists if it feels so awkward?

        2.  Consider these two questions:

                       What is the distance between the highest and lowest elevations?

                      What is the difference between the highest and lowest elevations?

Would your answers to these two questions be the same?  Why or why not?  Would your work to find these answers look the same or not?  Explain.

If you made it all the way through this post, THANK YOU!  I would appreciate feedback on any or all of these areas in the comment section:

  • The value (or lack of value) of this post, with specific, non-judgemental suggestions for improving it and/or my blog.
  • Strengths you see or improvements needed in the task and lesson suggestions. What would you do differently and why?
  • Actually use Version 3 and/or some of the additional materials and let me know how it went!

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