Building Those Pathways #eduread

A big part of our Make It Stick discussion this summer was giving students opportunity to retrieve information.

Another aspect, I’ve battled with in using INBs was giving students all the information instead of letting them decide what’s helpful and create their own notes.  Very few ninth graders are skilled in creating their own notes – so how can I help them develop this skill?

So here’s what I came up with…

The workbooks have an intro to each lesson – a couple of paragraphs, highlighted vocabulary and usually some type of graphic or example.  Here’s what I did yesterday…

Step 1:  Read (2 minutes)

Step 2: Pair (1 minute) – share 1 thing you read.

Step 3:  Whole-Class (I scribe what they share) something you read that you think is notable – something you feel is important or that you want to remember, something that made you wonder.  I labeled each slide for each class so I could reference it today

Then they worked in their groups to complete a lesson and practice.

To begin class today, each student had their white boards.

Step 1: Brain dump (1-2 minutes depending on class) – list anything and everything they can recall from the past two days in class.

Step 2:  Give one, get one! (1 minute) – meet with 3 different people, look at their list and get one thing from them to add to your list.  Let them get one thing from your list.

Step 3:  Return to desks.  Pull up slide from yesterday’s share… and I asked, anything you wish to add?  And we added to our list from yesterday.

You can tell they are not asked to retrieve this way often enough.  It was hard for a few of them – only a handful of things were on their lists initially.

I loved the openness of the brain dump.  It helped me really see their focus/thinking.  One student listed things from 2 weeks ago, which made me think he had not fully processed this week’s work yet.  I had graphs, details from specific problems, a list of vocabulary – but everyone had something written down.

Give one – get one, I heard them saying:

“Oh yeah, I forgot about that!”  “Where did you get that idea?” “From the science lab bacteria problem.” “When the extra truck came in to fill the pool.”

I reminded them – like walking a path across the field to my granny’s house ( a story I told them during our 1st week) – we are trying to wear a path…  So what do you think will happen tomorrow when we do a similar routine?  I’m looking forward to their growing list of “all things functions.”  Everything they have listed is exactly what I would have had them copy down from my notes (minus a few details of course) – the big difference, its their thoughts and ideas, not mine.  I even had students list discrete and continuous! Go figure.

My intentions are to take their generated lists and allow them to sort / connect them (Making Thinking Visible) to create their own page of notes later in the unit.

It was a good day.

Real Life Water Line

After some good old Dan Meyer Graphing Stories last week, we began our next phase of functions by predicting what our graphs (#s coops & water height) would look like for these containers:

And then we actually scooped water to see how close we were…

Walking around, listening to conversations…
“NO. It can’t go back down, you’re still adding water, so the height of water keeps increasing.”

“It might slow down or speed up, but it won’t decrease until we empty the vase.”

“So we need to reverse the steepness…where it’s steep, we need to flatten it out and where it’s flT, we need to make the graph steeper.”

I required them to complete a group graph to predict before I gave them their scoops to start data collection.

Several had to go back and finish details like labels and scales on graphs…a good reminding activity.

One student asked – do you do activities like this often?  It makes it (math class) fun.  

It was a good day.

Recursive Models #8minreflection

When planning my first unit with sequences, I just assumed Recursive models would wait until Algebra 2.  Last week, my students took their first benchmark for the year and what do you know, but a question about  a recursive model.

F.IF.3  Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

I’m struggling to see the difference in these 2 standards.  As I look at examples, I feel they are much the same or at least co-exist within a problem.

As I watched students during their benchmark, I was aware of the recursive formula question.  When I looked all of my classes results, only 38% got it correct.  As I looked at their response distribution, most students picked an example that at least corresponded to the give sequence in some manner.  However, one class in particular, response distribution was 35%, 18%, 29%, 18% which says to me they are unsure of the notation.  The subscripts are throwing them off.  Something I need to help them make sense of.

I briefly introduced recursive models Friday, but we worked with them more today.  I had a student ask, so is this like a function of the term before it?  Hmmm.  Sort of.  Yes.  Across the board 3 of my classes are very strong in terminology and understanding functions.  So this was a connection.  I saw students eyes widen and they nodded at our discussion.  Alrighty then.  Let’s try another.  And there ya go, the connection was made, they were able to “see” the process within the model.

Student Reflection

I wrote 3 different models on the board.

1 minute, think to yourself:  How are they alike?  How are they different? Now, turn to a friend and share your thoughts.

1 minute, think to yourself:  How do I know which model is which? What do you see/look at to help you decide? Now turn to a friend and share your thoughts.

So many good things shared.  Its amazing how I can have 4 different ways of seeing something, but yet, each is beneficial somehow.  Some of their comments: Two of them have a1(first term), some have d, some have r.  But what I heard again and again – they all have (n-1) but the location is different.  What does that location of n-a tell us?  Once, its a factor for repeated addition, another its an exponent for repeated multiplication and the recursive, its a subscript for the term before.

So, their conclusion…the math is not hard.  Knowing what the notation means makes it difficult.

Radical Rummy

I received this file about 5 years ago at KCTM in Bowling Green.  Kari from WKU shared it.  I apologize I cannot remember her last name to give credit.

She actually used it to play a card game style activity.  I copied sets onto different colored cardstock and laminated, I have enough sets we usually do groups of 3 people.

I do this activity along with Go Fish for simplifying radicals. 

There are four different forms of each value.  Students use calculators to match cards with same value.  We create a poster as a whole class.  Then notice and wonder. 

I like how students develop their own understanding of rational exponents, negative exponents and radical forms.  It’s a great intro activity.

https://www.dropbox.com/s/hsywphtj5sty9jn/Radical%20Rummy.pdf?dl=0

Complicated to Doable

This was the Visual Pattern for the bell ringer and some of their thoughts…

So we ended up with some form of these 3 equations in both classes today…

I got tired of writing step # and total blocks so I asked if we could shorten it a bit…so we defined n and x as those quantities!

And majority of students raised their hand saying those equations looked hard or confusing…

Until…we picked a step number.  Woe.  That’s doable.  We substituted 4 as our step # and all they saw was addition, subtraction, multiplication, parenthesis…  we just went from this complicated thing to something I even do without a calculator!

And the arithmetic showed each equation actually resulted in the same values.  

Flexibility with Numbers

Is that part of numeracy?

Each week, I have used a different thinking structure/resource as my bell ringers.  On Monday, I model, but the rest of the week, students work within that structure.

My intention is build a tool box of sorts. 

Four 4s to review Order of operations.  Krypton and Math Dice would also work here.

WODB.ca to help students see that several different ideas can be correct because of good reasoning.

We actually did visual patterns during class a couple of weeks ago, but this week, I am using non-linear examples.

Yesterday, my thoughts lingered from a discussion (several, actually) about this number pattern…

The top version was in a problem set and 90% of the students skipped it because “I’m not very good with fractions” (YET, I added every time).  I’m not talking my struggling learners, I’m talking…everybody.

It erks me, they didn’t even look at the problem to investigate what’s changing, what’s staying the same…they saw fraction and went on.

Do you immerse them in fractions to build that confidence to at least pause… and take a look?

Next week, we will start class with Counting Circles, the following week Counting Circles with some fractions involved somehow.  Or should I use the clothesline here, somehow? 

A long weekend will give me some time to think on these things.

A Fun New T-Shirt

I was super excited about these new tees we ordered last week. 

Just in time for our first home football game, faculty/staff tailgating.  There was also a vintage blue with red font.   Yep. We were the cool kids at the game…well, except for our student section.

They wore all white and had a paint war an hour before the game on the backside of our track.  Always goofy fun seeing them covered head to toe in paint.  Uhh. No hugs, or even handshakes…an air – high five was about all I could take.

I’m proud of the work so many have been putting in to make a change in the culture of our building.  Hoping it will continue and carry through…overflowing to our classrooms and our students…creating a place they want to be…a place they can laugh and learn and create good, lifelong memories.

Fitbit Fun

So here’s my fitbit screen this evening.  Hmmm.

I remember when I hit 1,000,000 and thought that was a big deal. Nah, not so much anymore.

I notice a lower average than I would like but I was pretty lazy this weekend.

I also notice my lifetime steps is not crazy far from 2,000,000. 

I wonder if I’ll hit that mark before the end of the year?

If not, how many steps per day would I need to average in order to get there by December 31?

If I averaged 10,000 steps a day, what day will I reach my new goal?

I wonder what questions my students might ask?