# Midpoint – on a different day than Distance

Standard

In years past, I’ve usually taught Midpoint and Distance on the same day or at least on consecutive days.  After a reminder of some brain research last fall – how our brains store information by similarities but retrieves information by differences – I decided to try things in split them up this semester – hoping to lessen the confusion students often face (do I add or subtract with midpoint/distance formulas?).  Again, this confusion stems from teaching a procedure without paying close attention to in-depth student understanding.

I chose to introduce “Midpoint with Coordinates” the same day we were working with segments, bisectors, midpoints of segments.  No bells/whistles here – just the basics

I gave students a grid index card and the points A(2, 1) B(8, 11) and C(8, 1) to attach to their INB RPH.  Simply starting with locating the midpoint of the AC and BC.  But also asking them to compare/contrast the coordinates of ACE and BCF each time.

Finally, asking them to locate G, the midpoint of AB.  Walking around the room, it was quite fun watching the various strategies.  The great thing was asking students to share their different strategies.  One used rise/run, several “counted diagonals” from A and B until they got to the middle, one used the midpoints of AC and BC and traced up from E / over from F until he found where G was located.  After discussing methods using the graph, a student stated “I just added my x’s then divide by 2 and added my y’s then divide by 2.”  When discussing how the coordinates were alike/different, a student asked “Isn’t that, what C____ did? Just averaging the x’s and averaging the y’s?”

So, I never actually gave them the “Midpoint Formula.”  Awesome.  Of course, we went on to practice the skill a few times.  I also chose 8 questions from Key Curriculum’s Discovering Geometry (did I mention, I *LOVE* this book?!?!? And have since the mid-90’s!)  – that required a  bit more thinking beyond skill/drill.  Two questions that led to some great discussion today was:

Find two points on segment AB that divide the segment into three congruent parts.  A(0,0) and B(9,6).  Explain your method.

Describe a way to find points that divide a segment into fourths.

But in class, I offered another – what about if I need to divide it into fifths?  Students worked individually, pair-share – then class discussion.  Quite different approaches.  I loved it.

What was even better, a student asked, “But  the examples we’ve used all have an end point at the origin.  Will it still work if the endpoint is not at the origin?”  Aaahhhhhhhhhhhh! That’s music to my ears!  Wow. Wow.  I love it.  I love it.  I love it.

This is a nice little open question to share with your students.  It definitely allowed me to see student understanding of the task by their work / responses / discussion.

Standard

# INBs – A New Adventure

All summer long I searched for ways to improve my literacy in math class – I learned so much chatting with my tweeps during our #lit4math book study.  It helped me redefine what literacy is / should be in math class – not just about reading.  And writing.  Not about creating something completely new – but improving what I already do to emphasize communication – discussing – giving students opportunities to make connections.

As I ran across various posts on the Interactive Notebooks – I knew this was something I wanted to do.  At first I had the wrong perception – thinking the interaction was between student and teacher – I struggled, wondering how in the world would I find the time to “grade” and evaluate that many notebooks efficicently and effectively and keep them in students’ hands for continuous learning???

After reading – mostly from @mgolding – I realized I had it all wrong.   The interaction was between the students and their own notebooks – to provide them with opportunities to engage with the information I gave them.  I was overly excited when I saw @mgolding would be presenting at #TMC12 – then crushed to find out my session was at the same time. boo. and I would miss out.

Listening to conversations that came out of her session and reading more once I returned home only confirmed my decision to move forward with INBs.  My science colleague had decided to pursue this learning tool as well – so grateful to have an in-person to collaborate/share ideas with too!

During the first Global Math Department meeting, she brought calm to me – answering so many of my questions in her session that night – thank you, thank you, thank you @mgolding!!!

I have begun my venture with INBs.  I feel a bit stronger in one class than the other – but I have been upfront with my students – this is a learning experience for me as well.

# Some things I’ve quickly learned:

1. I MUST keep my TOC up to date – its easy to get off track if I don’t!
2. I MUST do the INB along with students – having completed the pages myself – knowing exactly what I want to go on them;
3. I MUST practice any foldables / graphic organizers to make sure they’ll fit/work.  I may have a great idea in my head – in theory anyway- but I have to put it to the paper to see if it will acutally do what I need it to do!
4. I MUST think about what I want to accomplish with the LHP assignments.  This is the one I tend to struggle with some…thankfully I have lunch with my colleague and bounce ideas to get feedback.

# Flip 4 Answers

I plan to blog my list of RHP ideas later, but for today, I want to share an idea that came from my students.  Its similar to something I saw @mgolding share at #TMC12.  She had used post-its to cover hints/work/solution to an assignment she left with a substittue teacher.

When asked to create a practice quiz, one of my students used an index card to cover their work – thus “Flip for answer.”  When  I shared the student’s example, I never dreamed others would follow.  Yesterday during our first cumulative test – I oberved several others started playing off the concept.

As I look at the sample below, a CWP (color with purpose) would be VERY easy to assign…I think on Monday – that may be a good warm-up – turn to page 12 and CWP…  positive or negative or zero or undefined, even identifying which letters model parallel & perpendicular.

Another idea I think I’ll lean toward using for my LHP assignments – is the use of “Open Questions” – an idea I got during a book chat last fall from More Good Questions Small/Lin.  The second part of RHP 12 was an example of this…give coordinates of two points: with zero slope, undefined slope, positive slope, perpendicular to the slope in part c.

I believe the INBs require me to be more organized in my example choices.  It helps students be more focused / organized as well.  Looking through INBs yesterday – those who were having some trouble with their INBs / not completing their LHP assignments – seem to be the same (few) students who were struggling to make the connections I need them to.  This confirms to me the choices I am making – since most are finding great success.