Monthly Archives: March 2016

That Moment… #onegoodthing


This week I have watched a student smile in class every. single. day. 

Yes, they’ve smiled before.  But they’ve smiled this week because they’ve not just been successful, they’ve felt successful, confident in themselves.

Excited. Wanting to do more, because they get it.  Waiting for you to call on them… because they get it.

Shouldn’t they be smiling everyday anyway?  One would hope. But when a student has always struggled with math, it takes a while…like 7 months this time, to win them over.  It’s not just me, the RTI teacher has played a huge role in moving this student forward.


You want to reach every single student. 

Some days are tough. 

Dave Burgess TLAP…


But that moment when you know that they know….finally… reminds you why you do what you do.

Lego Toys and Optimization


Getting ready to do some systems of inequalities and so glad I posted ideas from this day a few years ago!

What do students do when give them legos? They create. This particular day, someone made unicorns and airplanes…

the radical rational...

So playing off Fawn’s Funky Furniture…students decided today they would make Lego Airplanes and Lego Unicorns. 

Here’s part of slide from our discussion.


Dummy me, erased other equations and inequalities they had shared when I asked for a function to describe our data. 
In this situation, we were ONLY looking at the number of large Legos used and how our total airplanes constructed would affect our total unicorns.

Good ideas came out in our discussion and almost every single student was on task.  They noticed several things in the data.  One student wanted to use our “vertex form” strategy (thanks mr. Waddell!)  to write the equation.  But they were not sure how to handle the repeated numbers 8 and 6 to find their rate of change.

Here are some of the suggestions from them…


What was great about this lesson, I didn’t correct them.  Their classmates were confirming or disagreeing. …

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“People don’t care how much you know until they know how much you care”

Last summer a colleague left our school.  An amazing educator who cared deeply for our students-who worked countless hours to build a program of integrity – that challenged and prepared our students for life beyond the classroom.  They left, not to go to administration, not to move up the pay scale, not to move to a bigger or even ‘better’ school district. In my opinion, they left because they no longer felt valued.
I’m happy they found a place where they feel needed, challenged to grow and create as an educator.  They found a place they feel valued.  A place to be innovative.  A place with a vision.
Its heartbreaking to me that people actually don’t look forward to going to their job on a daily basis.  Its heartbreaking to know people are actively looking to move on… from a place you love.  Their reason…because they don’t feel valued.
Punch the time clock, go home.
No joy, at all.
And its not fair because our children deserve more.
New and old teachers sometimes struggle. They sometimes need help.  They always need feedback.  They sometimes need guidance.  They always need to know someone cares.  They always need to feel valued.
In the classroom, when a student knows you care – that you value them as a person, as a learner, as a thinker…they’ll go to the ends of the earth, literally.  You can push and challenge and they’re willing to take the next step, braving the possibility of failure because they know you’re the safety net – who will help them gain confidence to try again, should they fail.
When they know you care, they’ll work harder than you ever expected.
When they know you care, they’ll put in the long hours to achieve their best.
When they know you care, they don’t mind going the extra mile, digging in to do the tough stuff.
When they know you care, they feel valued.
They’re inspired.  They become innovative thinkers.  They create a vision of their future.
When they don’t feel valued, they check-out mentally.
When they don’t feel valued, they leave.
We lose talent.
We lose creativity.
We lose innovation.
We lose.
Teachers who care… they don’t go the extra mile for a pat on the back.
But when they feel valued, they don’t leave.

Systems of Equations (part 2)


None of what I’m sharing is new…but its me reflecting on the week…so I can reference back and make adjustments in building a better unit  of learning experiences for next time around.

To address some student questions, here are examples used in class to follow-up.

On white boards:

  • y=x+1
  • Pick a value for x.  Find y.  (Ex. (3, 4)
  • Now, let’s double our equation.  What?!?  Yep, double it. 2(y=x+1)
  • Okay. 2y=2x+2
  • Use your same value for x from above and find y. (3, 4)
  • What do you notice?
  • Let’s multiply our first equation by 5. 5(y=x+1)
  • 5y=5x+5.
  • Use your same x value from above, find y.  (3,4).
  • Did that happen for everyone?  Turn and talk…
  • What if we took half of our equation?  .5y=.5x+.5
  • for the same value of x, it works again (3,4)
  • Then we go to Desmos to see the graph of our equation along with ALL of our versions of the equation.

Its a big idea that I don’t tell them.  They have observed why we can use this “magical” math thing is actually just a different version of the same equation…as one student put it “its the same equation, in disguise!”

But I also feel there is value in diverting from my original plan here to address the student’s struggle to figure out WHY? we do this in elimination, otherwise, it is literally, a “magical math thing” that just happens.

I need to do a better job of this – equivalent expressions / equations – earlier in the year, when we are looking at equations of lines…but also, how can I connect it with scale factors and similarity?  It all comes back to proportionality, but what strategies and tasks can I use to help my students make the connection and really develop a deep understanding?

Next on the list, we graphed our systems we’ve solved in Desmos.  Noticed and wonder…comparing our graphs to the work we’ve done algebraically.  Ohhhhh.  We found the intersection point!  Again, not me telling them, but they see it on their own.  I love that Desmos allows us to graph an equation in standard form.

Finally, I asked students to solve these equations and discuss their results in their groups:

  •   4x -6y   = 12                 and             7x – 4y = -11
  • -2x + 3y = -6                                     14x – 8y = 16

When does 0 = 0? ALWAYS!                   When does 0 = -6?  NEVER!

Again, we looked at the graphs in Desmos…


Several quickly stated the first set was only a multiple of the first equation, so it would be the SAME line!  (yes. secret happy dance!)

And the parallel lines never intersect…the equations were multiples on one side, but NOT on the other, a student noticed.  Its a translation, just moving one line up or down – another student stated.  So, how can I use their intuitive thoughts to build a better lesson?

racing dots

I found Racing Dots on  –  based on an activity, Great Collide by Jon Orr – to bridge between special situations, graphing solutions, substitution and algebraic solutions – will share more on this task later!


Systems of Equations Unit (part 1)


So many thoughts this past week as we began Solving Systems in Algebra I which will likely lead to multiple posts…

Here is the Systems Organizer Student Assessment Tracker.  I’m not satisfied with it yet, I’ve adjusted an old Algebra 2 unit, but I know by next year, this will be one of our strongest, most purposeful units.

I’ve been using the Candy Store problems since Mary and Alex shared them at TMC-Jenks.  A great problem solving task with manipulatives to introduce systems of equations.  My only change is to adjust for the U.S. candies, Solving systems CB S (Thanks for sharing your file, Mary!).  I plan to bring in a candy treat to students to celebrate their journey when we end the unit.

Based on prior assessments, in class observations, I purposefully separated students on skill level for this unit.  I intended it to be for me to have time to focus on groups with weaker algebra skills, while letting the others move on at their own pace.  I pulled those few who tend to “do the work” into groups together which would allow for those who follow along in tasks or let someone else do the thinking, then they copy it down-be required to do their own thinking.

Here’s what I notice – my “algebra” kids struggle, my “struggling” kids soar – with the hands on task!  It just goes to show, students do have good, strong reasoning skills when allowed to think on their own.  Each group gets a cup of pennies and two different types of pattern blocks with a white board and marker – although I think next year, I will hold off on the white board and marker until AFTER they solve the first one – I really want them to rely on reasoning and number sense before trying to jump in and create equations…although that is the end goal.

The beginning was often guess and check, but I loved hearing their number reasoning as they progressed through the problems.  Let me say, I have about 15 students spread between the 5 class who are still mad at me because they did not like the struggle.  I just kept patting them on the back, asking questions and when they began to engage, I’d walk off and let them continue.

After most students experienced some level of success with the Candy Store problems, we reviewed/introduced linear combination (elimination) to solve systems when presented in Standard Form.  I had examples ready, but as we practiced them on white boards as whole class, students were asking the questions:

  • what if the terms match and aren’t opposite?
  • what if nothing eliminates?
  • why does multiplying the equation by a number work?

It was great when it was students asking and not me leading.

In their groups, they received 11 cards – with solutions on one side and system equations on the other.  The cards were placed so all solutions were facing up and a start card.  When everyone in the group had solved/verified, they located the solution and flipped the card to find a new system to solve.


Nothing more than a glorified worksheet – handwritten while waiting at my daughter’s piano lessons.  But the discussions they were having as they solved on the whiteboards were so valuable…immediate feedback, peer assessment.

It was a good day.  The first time since Christmas Break that I felt confident we were moving forward.  (I know… its March.)

I’ve been trying to be more purposeful in ending class and allowing time for reflection. Students were asked to copy 2 of the problems into their INBs, solve and verify – basically creating their own notes / examples to refer back to.

Each student received a sticky note and was asked to complete the sentences:

  • I used to think…
  • Now, I know…
  • Caution…watch out for…

And they placed them according to their level of confidence as they exited the room:


This was on Wednesday.  I felt that they had built confidence, addressed common errors and misconceptions and had seen how the algebra could offer an efficient model in problem solving.  Yet, I still had a few groups who were strong/quicker with number reasoning when solving them.