Week 2 Sunday Summary #MTBoSchallenge & #made4math

Week 2 is complete.  I am still trying to find my groove with having 1st hour prep.  I am a morning person, so I am ready to interact with students as soon as we arrive.  Sitting down for plan time, I lose my momentum.   Paired with having to be out of our building by 3:00 due to renovations, I have no time to sit and process the day’s events.

3 Things That Happened This Week
I finally got my anchor chart board with sentence starters and questions completed.  I am very pleased with it and have been trying to model/give students opportunities to practice in class discussions.  Here is a link to a file of the starters.

I giggled when I saw Sarah saying she “totally stole” from me…that’s what #MTBoS is all about. Sharing and making our classrooms better for our students!

I am using visualpatterns.org as one of my daily tasks to begin class.  I wanted students to have a page in their INBS to record these…

Here is the file.  Print 2 up and front/back for a booklet for your INBs. 

I shared Thursday how I was a bit hesitant to allow my students to go with their process of locating the midpoint given coordinates of endpoints.  I know.  There are those that say just tell them the midpoint formula.  I could but this is the method they are owning.  Basically, they are finding the distance between the coordinates, then “moving” half the distance will put them at the midpoint. 

But then I got to thinking about the actual standard:

CCSS.MATH.CONTENT.HSG.GPE.B.6
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Midpoint is the most common and yes, we’ll use it in proofs later.  But if I go in Monday and ask them to find 1/3 point which would be a 1:2 ratio, or a 2/5, 2:3? Will their method actually prove more efficient because it is actually the same process for both?

2 Things on My To-do List
I have 3 tubs that still need to be unpacked from our renovation move.  I have my shoe boxes on the shelves, but I need to get those labeled correctly.

Finish an Intro to Matrices Unit, I hope will work as  flipped/blended learning unit.

1 Good Book to Read
Thanks to @mathymeg07 for sharing Wonder by RJ Palacio. 

Megan said it is a book everyone from 9-99 should read!  Right now, the Kindle version is on sale for $2.50.  I am making posters of Mr. Browne’s Precepts for my classroom, such great lessons to live by.

Midpoint – on a different day than Distance

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.

Distance & Midpoint on a Map

Been playing with this idea for a couple of days – here’s a rough sketch.  Rather than having students work a gazillon problems – I’ve decided to use a school map.  I ran a copy of grid paper on a transparency and overlayed on a map of school – copied, added a rough set of axes.  Placed points throughout.

Questions range from:

• Calculate the distance between Room 137 & Room 114.
• Find the coordinates between Room 137  & Room 114.  What room are you closet to at this point?
• Connect Ag, Kitchen, Cafeteria & Workshop.  What type of quadrilateral have your formed?  How do you know?   Prove it.  We have not covered types quads – but they can use their BYOD to find this information if needed, right?
• Connect Library, Room 128, Room 116 and Room 114.  Is it a rectangle?  Or a square?  (LOL) How do you know.  This always comes up in discussion – I must say I love the “disagreements”.
• Connect Room 145, Room 142 and Band.  What type of Triangle have you created?  How do you know?  Prove it.
• Connect the Gym, Library and Tan Hall – Find the perimeter & area of this triangle.
• What about having them “map” out their schedule and calculate “as the crow flies” distances between their destinations.

Anyone else have better ideas?  Other uses for this?

I’m thinking it was @k8nowak who did a scavenger with other geometric concepts.

Geo-board Investigations

I was clearing out some files this weekend and ran across this packet from a presentation at KCTM in 2002.  I had just completed my initial National Board Certification earlier that spring (still didn’t know if I had certified yet) and thought these lessons were worth sharing.

I’m not sure if you’ll be able to read the first two pages – orginal files are long gone and just by happenstance I rance across this packet.  Reading through it – its almost like I was “blogging” 10 years ago – but it reminds how important reflection on your lesson will always be – how much you can learn about teaching by pausing to think about student thinking/responses.  Whether you use actual geo-boards, paper/pencil or modify to www.geogebra.org – maybe they will give you some ideas for your classroom.

Geo-board Investigations

• Parallel & Perpendicular Investigation – use rectangle properties to find relationship with slopes
• Amusement Park – distance between 2 points (I hate using distance formula and often allow students to find slope triangle, then apply Pythagorean Theorem)
• Midpoint Investigation
• Midsegment Investigation

 

 

*I used the reinforcement tabs for students to write coordinates/label points on geo-boards.  BUT don’t let them peel and stick…just leave on paper and drop over the geo-board tab.