Interpreting Distance Time Graphs

On the 3rd day with a new group of students, I had visitors from some other districts in our classroom.  I was nervous – I really didn’t know these students yet and they certainly didn’t know me.  I had chosen Interpreting Distance Time Graphs lesson from MARS to begin our semester.  Although this is listed under 8th grade, it leads to some great discussions and uncovering of ideas and misconceptions.   The Keeley & Tobey book also lists “Every Graph has a Story” in the Formative Assessment Strategies.  This was the ideal lesson to introduce our first unit on functions, while trying to be intentional with planning FAs.

Pre-Assessment

Telling students it is only for feedback, not for a grade seems to drive most of them to really share their thinking.  After reading their responses, I had some ideas of how I wanted to change the lesson up a bit from times past.  The first time I ever used this lesson was around 2011-2012.

Let the Lesson Begin

We began our actual lesson with only the graph in this picture.  I asked students to jot down 3 things they noticed about the graph.   Pair share.  I called on students randomly with my popsicle sticks, then allowed for a volunteers (this was something @druinok and I had read in EFA2, which allows everyone to be heard).    We then read the scenarios aloud and at the table groups, they discussed which story was model by the graph.

Next I took one of the scenarios we didn’t choose and asked them to sketch a graph on their whiteboards to model it.  We had about 5 different overall graphs – I drew on the board and let them discuss at their tables which they agreed/disagreed with.  Then we shared our thinking.  Some very good sketches and great discussions.

Open Card Sort

Many years ago, a colleague shared the idea of open sorts, something she had learned from a John Antonetti training.   I instructed students to remove only the purple graphs from their ziploc bags.  (Side note suggestion- use different colors of cardstock and this allows them to quickly grab the cards they need, ie the purple graphs, green scenarios OR blue tables.  I used to have all the same color and we wasted a lot of time sorting through which cards we needed).  In pairs, they were sort the graphs any way they wished, the only requirement, was they must be able to explain why they sorted them as they did.  Again, sharing whole class led to seeing some details we had initially noticed.  If you’ve never done an Open Sort – let go and let them show you their thinking.  You might will be amazed and wonder why you’ve never done this before.  They love to think.  We should let them.

List 3 Things

A couple of years ago, I began asking students to list 3 things they noticed or knew about their graphs – anytime we were interacting with a graph.  IF you ask them to do this enough, it eventually becomes habit.  I also like this approach because it gives them a chance to survey the information in the graph before they start worrying about / answering questions.  Today, I asked pairs to label their whiteboards A – J and I set the timer.  They had to share/discuss/jot down 3 things about each graph.  Once again, I used popsicle sticks to randomly call on a few students.

Graph & Scenario Matching

Using the “rules” listed in the lessons powerpoint, students were then given time to discuss and match graphs to the scenario.  This went so much quicker than times I’ve done this lesson before.  I believe it was because they had already interacted with the graphs twice…they were not “new” to them.  I will definitely use the Open Sort and Name 3 Things before matching tasks in the future.

I gave them a chart to record their matches.  We then shared out our matches.  Each time, I neither confirmed or disputed their matches, but rather would call on a couple of other students to agree/disagree.  After some discussions, I came back to the original student to see if they agreed / disagreed with their original match.

One of my favorite graphs is this one –

And our final sorts…  And again – Scenario 2 is always up for some debate.  It reads: Opposite Tom’s house is a hill.  Tom climbed slowly up the hill, walked across the top and then ran down the other side.

Though every student did not get every match exact, there were several a-ha’s during the lesson and questions asked.  I look forward to reading their post assessment.

I’ve used this lesson as written many times with much success.  However, just making some adjustments prior to the matching made a vast difference in the amount of time students needed to complete the task.

Let me know how this lesson has gone / goes for you if you use it.

Developing Definitions

I’m back!  Nearly 2 months? Yikes. Some fellow teachers on Twitter were committing to blogging once each week.  I think  that’s reasonable – besides, usually my best reflection comes during the moments I blog.  Reflection – seems to be the first thing I push aside when I just don’t have the time.  Yet, its the most valuable use of my time.

I’m sharing some successes from Kagan Geometry (one of my favorites by the way).

I was going to be out for a number of days due to being seated on the jury for a trial (give me 100+ teenagers over the courtroom anyday!).  I wanted to leave something productive.  I did short videos (<10 minutes) filling out certain pages in the INBs in addition to other activities.

The first Kagan activity was for vocabulary.  Each strip of paper included examples and counter-examples for each term.  I modified from the round-table recording it suggested.  Students were asked to pair up (a new partner for each new term) and develop their own definitions.  I loved it simply because most were terms students had previously been exposed to in middle school.

When I returned to the classroom, I ran through all I had left during my absences to address any concerns/questions.  Several students commneted how they liked (appreciated) doing the definitions this way.  Their comments ranged from – ‘You actually had to think about the terms; Talking with someone about it really helped you process what it was before writing it down;  The pictures of examples / nonexamples really helped understand the word better.’

Yesterday, we developed more definitions about angles.  When I told them what we were doing – they were excited about the activity.  Listening to the conversations – I was very happy with their discussion / questions / specifics they included in their definitions.

I remember several times in the past doing examples / non-examples, especially when using Frayer Models.  I believe taking it out of my hands/mouth and giving them the opportunity to work in pairs really enhanced their understanding of the terms.  Even when discussing HW  today – they used appropriately terminology.  Yeah!

Another Kagan activity I used as a LHP activity

from Kagan Geometry

– very similar to Everybody Is a Genius’  Blind Draw.  Students were placed into small groups and given 12 cards with written directions.  Person 1 chose a card, read the directions, gave others time to think and draw a diagram with labels.  The reader confirms/coaches/praises others’ work.  A new person chose a new card and the rounds continued until all cards had been used.  One thing I appreciated about this – another card asked students to draw a ray from E through M.  This allowed students to realize differences in very similar diagrams.

Again, when I returned to the classroom, students shared how this activity was different from anything they’d done before, saying it was both challenging but helpful in that it helped to clarify certain misconceptions they had; especially with labeling the diagrams.

I have learned the Kagan strategies help students develop and process concepts.  There are “game like” activities where students must find their match and discuss.  Visual, Auditory, Kinesthetic – something for everyone.  Its not an end all – be all resource.  But the amount of HW / practice is minimal when I’ve used these strategies correctly.  I am a firm believer that they help start a strong foundation to build upon.  Hey – if students are smiling and laughing while “doing definitions” – its gotta be good.

#myfavfriday paper thermometers

A super quick post – @wahedahbug tweeted looking for data for Algebra I students to collect / put into a table and work with.  One of my favorites is creating a paper thermometer.  Most students know water freezes and boils at 0 and 100 degrees Celcius and 32 and 212 degrees Fahrenheit.  So that’s where I start with my students, asking them to leave a few spaces between the values on our “thermometers”.

Next, I ask them to find the “middle” of each of the values, and again the “upper and lower middles”.  Most will simply average to find the mean.  We record these values, then use differences to compare to find our rates.  9/5!  If you like, sure, change it to a decimal – whatever works best for your students.

I’ve been using the “vertex” (h, k) model for lines – so, pick a data point and create your equation to model your data.  Pick a different data point…does it give you the same equation? 

I remember the very first time I ever did this activity at an Algebra for All workshop – I was amazed…it was the conversion equation between Fahrenheit & Celcius! LOL – really?  I should have known that! duh.

I love using this because the students recognize the equation from science class and now they “know” where it came from!

#MyFavFriday – Kagan Geometry

Last week I stood glancing at a shelf of books left behind by my colleague.  I’m not sure why I didn’t notice it before – but there on the middle shelf was a Kagan Geometry book.

Two days this week I’ve smiled at the end of the day and it felt great.  Becky Bride has compiled simple to implement, engaging activities.  I’ve read snippets about the Kagan books – but never really sat down to read/do any of the activities.

Boss-Secretary

One of the activities this week was using a strategy called Boss – Secretary.  Students work in pairs.  The boss tells the secretary what to write, explaining their reasoning for the steps/work.  IF the secretary sees the a mistake, he/she respectfully points out the mistake to the boss and praises her/him when they corrects their work.  If they work through it correctly, the secretary is asked to praise the boss, vice-versa.  After completing a problem, they switch roles.

The students have been funny with this simple, yet VERY effective activity.  Speaking of resumes, tough bosses, etc.  One asked today – do I really have to praise them when they do it correctly?  I’m really not a praise-y kind of person…  I said a high 5 would suffice.

Here is what I love about this – Students are talking/explaining their work so the secretary can do it.  Secretaries are listening, following directions, hopefully picking up on any mistakes.  I’ve heard multiple times – student exclaim – oh, now I get it.  They’ve all said they like this activity – its helped them really figure out “their thinking” – having to say what they’re doing – is difficult, and sometimes what they say/tell the secretary to write it not exactly what they meant.

This is a great formative assessment activity to observe / listen to students.  I’ve learned a lot about their thinking this week and I believe they have as well.  When students, notice plural, ask to do an activity again because it really helped them, well – isn’t that what we’re here to do?

INB LHP assignment

As a left-hand page assignment in the INBs, I asked them to pick one problem they completed as a secretary – and they had to write out the boss’s diaglogue to solve the problem.  (midsegments or isosceles triangles this week).

Another activity in the Kagan book was something I have completely taken for granted… Processing altitudes.  Students draw one of each type triangle, and are asked to draw an altitude. Pass their paper to the next person, who then draws another altitude, etc.   Even after a couple of examples / illustrated definition for reference…they still struggled with “drawing” it.  What?  If they cannot draw an altitude, how can they actually know what one is in order to use it to solve problems?

Applying Some Brain Research

Its been many, many years since I taught geometry – but I always remember students confusing medians, altitudes, perpendiuclar bisectors and angle bisectors of triangles.  I remember attending a David Sousa How the Brain Learns training several years back.  An example was shared how students often confuse concepts that are closely related because they are often times taught on the same day.  Concepts are stored by similarities, but are retreived by differences.  When we teach similar things on the same day, they are stored together, at the same time – when students are asked to retrieve that information, there’s not enough distinction between the two – therefore, they are often mixed-up, confused.  Hmmm.

So do I choose to teach each of these similar concepts (special lines/segments in triangles) on separate days – but is that even enough space between?  Should I skip a day between them?  Anyone with experience pacing it out this way – please share successes / need to make adjustments!  I really think this is an opportunity, by using Bride’s processing lessons – to make a difference, giving students the chance to build concrete understanding of these other-wise intertwined concepts.

If you’re not familar with the Kagan series – I think its definitely worth checking out.  There is very little prep time – other than working through the lessons yourself.  All blackline masters needed are included in the book!

I am soooooo excited about using more of these strategies in the weeks to come!  🙂

My Favorite Friday: 2>4 & Tetris Group Costume

Its been one of those weeks.  Well, its been one of those years.  Its definitely not my students – they.are.amazing.  But I just don’t feel like I’m moving forward.  I’m stuck.  And I don’t like it.

Favorite #1 “2 > 4!”

Sitting in my room all alone this afternoon, I pulled up twitter and found this from @maxmathforum and absolutely love it.  SOOOOOOOO worth five miniutes of your time!  It was a wink to remind me – everything will be okay – eventually I’ll find my flow again…  just remember to listen to my students…  they’re the reason I’m here.

@jreulbach @Borschtwithanna @cheesemonkeysf Coloring Pascal’s triangle made me realize I wanted to do math forever: http://t.co/B5LzTwEC — Max Ray (@maxmathforum)

 Favorite #2 Tetris Group Costume

Its Homecoming week – I’ll be leaving to go chaperone the dance in just a bit…

Several of us have often tried to do a group-themed costume…

The Clue Characters – including the envelope.

The Seven Dwarfs

Black-Eyed Peas

 

This year – inspired by a tweet months ago…TETRIS!

6 – posterboards, cut 4 11″ squares out of each color

7 – foam boards

tape – 4 pieces together to form puzzle piece

hotglue to foam board, cut out excess white

elastic or ribbon toattach / hang around your neck

let the most talented one create the gameboy on a foam board (project onto board, trace, color with markers!)

 

Its a quick, cost-efficient costume! 

We met afterschool one day to make our Tetris pieces.  We shared how we so missed the collaboration we once had.  When you have the opportunity to share ideas – when you’ve got a go-to person(s), somehow, it limits the amount of stress.  With changes in schedules / room changes – we are not all in the same wing like we were for nearly 8 years.  We had common planning – and each week we met in what I believe was a true PLC.  Though most of our meetings were focused on students and not content – making sure we kept up with those who were falling behind – making sure we had made contacts home – we shared strategies that worked for certain situations – we made sure we used resources available to keep the students on track…we had the opportunity to share ideas.  Not.Any.More.

It has been so hard – being taken away from something you were a part of from the beginning – a venture you believed in whole-heartedly.

We all agreed that this year seems like…work.  And that makes me sad.

Just like our Tetris pieces – apart, we may seem a bit odd – but together…we made sense.  So a shout-out to my dearest friends – those who encouraged me, challenged me, helped me become a better teacher.  I miss each of you.

#MyFavFriday – Intro to Logic Lesson

I always remember dreading to teach conditionals, inverses, converse and contrapositives.  Last year at a KLN meeting – a colleage, Susan, shared a lesson – she and her department had developed after training with Quality Core last year. 

Since I’m now teaching geometry again, I decided it was a great time to try it out!

It was a beautiful lesson.  However, with students who struggle with reading, I definitely see myself modifying just a bit.

Students were confused in the beginning – but after talking about the choices, taking time to do a sort with a partner / small group and talking about the different statements – each one can successfully identify and/or write each statement.

Susan’s Intro to Logic & Proof Lesson

This lesson includes reading, speaking, students get up and move, discussion, small group card sorts (inverse, converse, contrapositive), practice assignment also asks students to create their on set of statements (writing).

Simple.  So effective.  Thanks to Susan for sharing this with me!

My Favorite Friday – Chicken Tortilla Soup

Yes, I know its Saturday – but I crashed before 8 last night and slept a solid 10 hours.

With football season underway (Go Lakers! 2-0, woohoo!) and Marching Band out for their first performance today, that means one thing – cool fall days are not too far away!  Which means soup weather!  Our family is not soup fans when its hot outside.

This is actually my SILs recipe – but it truly is my very favorite!  Its best made a day or two early, so the flavors can meld.  I have even frozen leftovers and they turned out just yummy!

Chicken Tortilla Soup

1 can diced green chiles

1/4 cup onion, diced (2 TBsp dried minced onion)

1/4 – 1/2 tsp garlic powder, to taste ( or add fresh minced garlic)

1 can diced tomatoes, with juice

1 can Rotel tomatoes & chiles

1 quart tomato juice (or a couple of cans of V-8)

4 cups chicken stock

1 tsp ground cumin

1 tsp chili powder

1/4 tsp black pepper

2 tsp. worcestershire sauce

1 beef bouillon cube

2 chicken bouillon cubes

1/2 – 1 lb. skinless chicken breasts

 

In large pot, cover chicken with water and cook until done – about 15 minutes (reserve 4 cups of stock for soup).  Set aside to cool.  In large pot heat chiles, onions & garlic.  Add all ingredients (except chicken).  Heat to boiling, reduce heat to medium and simmer 45 minutes-1 hour.  Meanwhile, shred chicken and add to soup.  Serve with tortilla chips as crackers, garnish with shredded cheese, sour cream, cilantro or diced avocado.  Refrigerate or freeze leftovers.

 

I totally stole this pic from betty crocker – but it looks very similar. 🙂  And I like this wooden bowl, too! (wishlist!)

 

If you are a black bean or corn fan in your soups – add ’em!

For a great gift – use dried minced onions, garlic powder, bouillon cubes and create a spice packet of needed ingredients in small ziploc bag.  Attach cooking directions to gift bag containing canned chicken, chicken stock, and remaining ingredients.  I think worcestershire is the only thing not able to include in soup-gift pack.  I would *LOVE* a gift like this!