Category Archives: Coordinate Geometry

Week 2 Sunday Summary #MTBoSchallenge & #made4math

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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.
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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.

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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…

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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. 

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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. 

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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.

Setting Personal Social-emotional Goals pt. 2 #julychallenge Post #17

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This morning as I responded to a commented from @bpagirls on my post about an Essential Questions Board, a thought hit me, so I typed it in my reply so I wouldn’t forget…

… I have just realized as I type, why not add a spot for personal-social goal-setting on my organizer for each student to set, write and reflect.

It stems back to this post and one of the 14 ways to think about good teaching post, 3. Include social-emotional learning goals as well as academic goals.

I got that I needed to do this, but I was not quite sure how to set and record these goals.  My plans are to include a place on the back of our unit organizer students receive at the beginning of each unit.  These are formatted in a booklet style to fit our INBs.  Students can set a personal/social goal to focus on for the duration of the unit. Ideally, following the SMART goal format.  Commit to it by writing it on their organizer.  I will ask to see it, but they may choose whether to share with a peer.  Wouldn’t it be great to have accountability partners for the unit? 

Throughout the unit or even at beginning of class, ask them to read it to themselves.  Maybe even allow someone to share their progress.  Revisit them as we end the unit and write a brief reflection:  How did I do?  Did I meet my goal?  If not, did I at least move toward it? What do I need to modify?  Follow the format: 2 stars and a wish for their quick-write reflection.  Celebrate their progress, maybe through our Shout-Out Board (more on that later).

I realize this type of goal setting may be tough for students… I am hoping after completing this task, it will allow for students to generate ideas.

Initially, I think goals can range from:
Improved / good attendance
Be to class on time
Being prepared for class
Completion of assignments
Asking for help
Asking questions or participating in class discussions.
Attend tutoring if needed
Work in a group with people I don’t know.
Share my ideas in class
Share my assessments and progress with parents/guardian
Choose better practice/study options
Listen to others ideas
Evaluate how my choices are impacting my learning.

Here is a sample of the back of my unit organizer.  I plan to insert personal goals below the unit reflection.  Here is an updated version of a complete unit organizer and student assessment tracker. Feel free to modify for use in your personal classroom. Thanks to Crazy Math Teacher Lady and Math = Love for inspiring through their posts?

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My next task is to locate a fill-in the blank for a SMART to include on the first unit.  Kind of a madlibs style to get us started.

If you have a system in place or use LIM or AVID in your school, I welcome input and suggestions.

Purple Circle Card Sort

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Last spring, I placed equations of circles after distance between 2 points.  The idea came from a mini-investigation in my Discovering Geometry book (formerly Key Curriculum, now Kendall Hunt). 

Earlier in the semester a new colleague shared the success her students experienced with the Formative Assessment Lesson Equations of Circles 1.  I decided to use this lesson…

In my early geometry class yesterday, we literally stared at circles.  It felt like a wasted class.  No matter what example I referred back to, or what question I asked, it just didn’t work.  Thankfully, I had planning immediately following and I was able to reflect very quickly.  For my last geometry class of the day, I adjusted my sequence of leading examples.  Reviewing our previous work from last week. 

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The remainder of the lesson went smoothly.  A quick white-board quiz at the beginning of class today allowed me to address some small errors.  Once again, I had them create their own notes/examples in their INBs.  Yes, a few are still lacking, but the majority are very thorough in what they are including.  Asking questions about specific what-ifs, like one student brought up none of our examples today had a center located at the origin, so I asked the class if they could remind her.  Several went on to include a similar example on their page.

The lesson continued with a collaborative pair.  They were given 12 equations to sort by center and radius.  There were 4 blank blocks in their grid that required them to create their own equations.  At the beginning, some were “cheating” so I stopped them to remind them 1 person picked a card, explained why they were placing it, the other person had to agree and understand before taking their turn.  They are getting better at disagreeing and telling why when their partner is making a mistake.

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Their assignment was to create an artistic picture incorporating 5 different circles and listing their equations on the back. Short, sweet, simple.  Can’t wait to see them.

Dice #tlapmath

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Well, @druinok shared this amazing find from Dollar Tree!

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First of all, let me just say, JEALOUS!  But soon after, she shared an idea from #tlapmath Walk the Plank ideas to make lessons Pirate-Worthy.  So, being on the road home from a visit to my brother’s near St Louis, I had plenty of time to think. Hmmmm.

Here are a couple of  thoughts. 

Roll the dice, generate 3 sets of coordinates.  Prove what type of triangle they form.  Find the perimeter. 

OR roll 6 sets of coordinates.  Which triangle is “closest to being equilateral”?

Create coordinates for a quadilateral.  Prove what type of quadrilateral.

In a group, compare your quadrilaterals.  Who has the one closest to being a square? Rectangle? Or other polygon. Why?

Use your 8 coorindates and can you arrange (x,y) pairs to create quadilateral closest to _____?

Pythagoras, His Formula and a Teacher Who Didn’t Teach

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So a simple lesson today. 

A segment on a grid and asked students to find the length of it. Yep, most sketched in their right triangles and pulled out the Pythagorean Theorem.  But what if we don’t have a grid? How can you find the distance between the two points without graph paper? Or if one of your points is (543, 97)? 

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After their sharing, while practicing, some wondered, “Is it okay to use the slope if its in lowest terms?”

Good question.  Does it matter?  What could you do to determine if it matters?

And their suggestion:

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…with their finding.  Makes me smile when they answer their own questions.

Best part of lesson today?  Their INB notes.  A post by @justinaion made me wonder how I could be more purposeful in student notes.  Today’s notes…after completing the lesson, students put their whiteboards away, and created their own notes.  Some had step by step instructions.  Others had pictures drawn, paragraphs with a couple of examples.  But in the end, they wrote what was important to them. 

I loved the question a student asked while walking out the room.  “How am I supposed to find the distance with three coordinates in space?”

My response, How are you supposed to find the distance with three coordinates in space?  A smile with an a-ha look on her face…you just…yes, child, you knew how all along.

A day when I didn’t teach a thing but my students left knowing something new (well, except for the kid who sulled up because I wouldn’t TELL them ‘the formula’, use your device) …its been a good day.

Even better, a FB post from a former student-

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Writing Equations of Lines – with Some Novetly

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So I picked up some packs of foam number cubes at Mighty Dollar last week.  I sat wondering – what could I do with these?  Finally, during supper one night – an idea came across.  I’d use them to generate coordinates of points and students could write equations of lines.  Hmm.

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But as is, all points would fall in Quadrant I.  On half of the dice, I added a negative to 1, 2, 3 and the other half, onto 4, 5, 6.  So, have students roll the dice…thanks to ROY G BIV, we’ll know what order to place them for some consistency.

2013-02-03 14.56.50  Students record the coordinates of 3 points.  2013-02-03 14.57.33

Directions will be:

  1. i. Find the slope between RO & YG.
  2. Write an equation of a line that passes through RO & YG in slope-intercept form.
  3. Write an equation of a line parallel to ROYG and through the 3rd point IV.
  4. Write an equation of a line perpendicular to ROYG and through the point IV.
  5. Find the midpoint coordinates.
  6. Calculate the distance between RO & YG.

Yes, skill and drill – but with a bit of novelty, hopefully to engage the students a bit more than a black & white worksheet.

I’ve read several posts about activities similar to this – they are not easily assessed.  Students in the group – hold each other accountable.  I prefer same ability grouping – this allows students who are able to move along – while I can spend time with a student who has been absent/struggling to catch them up.  I purposefully walk around the room and spot-check each group to ensure they are on the right track.  If students are recording their coordinates/work/equations – its very easy to take up their work and spot check 2 or 3 sets to ensure correctness.

stoplightcups

Sometimes when working in small groups  such as this – I like to have the stop light cups out – If students are okay, the green cup is showing, if they have a question – but can keep on going, the yellow cup and finally, if they need my help – the red cup showing.  I can easily glance around the room for a quick look to see how everyone is doing.