Unit 5 Linear Functions with Desmos

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I’m sure it has been done before, but here’s my take on teaching an entire unit using Desmos.  Before I begin, I’d be remiss if I didn’t share these articles.  Being completely transparent, I had this Desmos unit idea before my friend Turtle shared these articles with me.  Human Contact is Now a Luxury Good and How Busy Hands Can Alter Our Brain Chemistry a quick synopsis of the articles, working with your hands promotes happy brains and an increase in brain activity.  Too much screen time creates changes in the brain such as thinning and decreases the thinking and has been linked to depression.  Please take some time to read both of these articles.

With that said, my Desmos unit does not include an absence of peer to peer dialogue or teacher student conversations.

Screenshot 2019-04-06 at 7.12.39 PM  In the state of Georgia, 8th grade unit 5 covers linear functions.

Unit Suggested Timeline: 8 – 10 days

Suggested Sequence of Instruction:

    1. Revisit graphs of proportional relationships. 8.EE.5 (To be taught concurrently with #2 and 3)
    2. Connecting representations of proportional relationships. 8.EE.5 (To be taught concurrently with #1 and 3) (1 day)
    3. Comparing features of different proportional relationships. Connect unit rate to slope through a context 8.EE.5 (1 day)
    4. Use slope triangles to derive change in y over change in x. 8.EE.6 (1 day)
    5. Derive the equation for slope intercept form, y =mx + b. 8.EE.6 (To be taught with #4)
    6. Determine slope from a graph, table or linear equation. 8.EE.6 (3-4 days) (To be taught with #5)
    7. Interpreting slope in context. 8.EE.6 (To be taught with #4-6)
    8. Compare and contrast linear and nonlinear functions using tables, graphs and equations. (Emphasize y=mx + b as equation of a straight line) 8.F.3 (2 days)
    9. Create examples and non-examples of linear equations. 8.F.3 (To be taught with #8)

Suggested Activities:

  1. Click Battle  8.EE.5
  2. Sugar Sugar  8.EE.5
  3. Polygraph: Lines, Part 2  8.EE.6
  4. Investigating Rate of Change  8.EE.6
  5. Points on a Line– (with paper overlaps to create the similar triangles)  8.EE.6
  6. Which is Steepest?  8.EE.6
  7. Land the Plane  8.EE.6
  8. Match My Line– (Slides 1 -7) 8.EE.6
  9. Graphing Calculator with Lesson 13 from Illustrative Mathematics Open Up Resources  8.EE.6
  10. Investigating T-Shirt Offers  8.EE.6
  11. Charge!  8.EE.6
  12. Graphing Calculator with Introduction to Linear Function from Illustrative Mathematics  8.F.3
  13. Card Sort: Linear or Nonlinear  8.F.3

I’m Selfish

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There they were, the proof in the pudding in the form of pancakes.  I had to admit, they didn’t taste half bad.  The Cocoa Puffs within them were a bit mushy, but the Fruity Pebbles added an interesting flavor.  The most important piece of this, is I realized how selfish I had been.

I sat on the couch at my friend Nickeva’s house discussing things as friends often do.  Her girls, free to be who they fully want to be, casually asked if they could make pancakes.  “Sure”, without skipping a bit their mother responded.

Thought 1: How many times had my girls asked to be crafty in the kitchen and I shut them down without giving it a second thought?

They moved about the kitchen with ease, this wasn’t their first time making major moves in there.  A 3rd grader and a kindergartner, real chefs in the kitchen as their mother continued to sit on the couch with me.  Thankfully, they invited my girls to join in on making the masterpiece.  There were laughs mixed in with directions.  I saw them pull out the bag of Fruity Pebbles.  What would they do with that?  Aren’t they making pancakes?

Thought 2: Look how free they are to create without my input.  How naturally creativity comes to kids when we allow them to explore and investigate.

While the pancakes cooked, I saw them pull out a plate, fill it with water and dish soap.  Then came the straw.

Thought 3: That’s wasting dish soap!!  My girls know better than to do that!  Ugh! Why am I like that?

That visit blessed me more than I realized in that moment.  My girls walked away inspired, with a feeling of accomplishment.  The next morning, they were all about making breakfast!  (Although I had to draw the line at cooking the bacon.)  I reflected and realized how my unbalanced focus on money stifled my children’s creativity.  How my need for control and order limited the opportunities they had to explore passions and investigate things that intrigue them.

This got me thinking about the students who enter our classrooms everyday.  How many of them have been stifled at home and are desperate for a moment of creativity?  How many of them crave to have a chance to investigate and explore? How are we contributing to the opportunity gap, by not allowing our children, our students to tap into their natural curiosity and innate abilities?

I’m certain if I were to inquire, Nickeva would tell me about the times she guided her daughters around the kitchen or how she sign them up for cooking classes.  She would mention the various opportunities her girls have had prior to the pancakes on that Saturday.  What does that mean for me?  What does that mean for you?  Time and repetition of opportunities.  Guidance without majority of the control.  Being the guide on the side.  And I think the most important part is understanding this life is bigger than you and me.  What are we doing with the time we have with our own kids, with our own students.  What do we communicate to them when we limit their opportunities?

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The Push Without Relationships

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“As much as he pushed me, I never doubted his love for me.” – Billy Donovan about Rick Pitino

As an educator, what does this quote mean to you?  In hearing this, I couldn’t help but think about the students I have encountered in my career.  Not the ones I tagged as a model student.  Not the ones I would say to their parents, “I wish I had a classroom full of them!”  No, I thought of the ones who had me in tears, who had me wanting to holler and throw up both my hands.  The ones who I whispered to myself about them, “you are not my enemy”.  The ones who when they were absent I secretly rejoiced because I knew the class would run smoothly.

I thought intently about would they feel about me the way Billy still feels about Rick.  I reflected on what would cause a player to say that about their coach.  What would cause a student to say that about their teacher?  Relationship.

I truly believe that educators desire to push their students to their max potential.  Okay, well most educators.  I’ve been in conversations with teachers who have the best ideas for instruction that will engage their students.  In collaborative planning, hopes are high and expectations are as well.  Walk into their classrooms and it appears the conversations had during planning were nothing more than lip service.  Students, aren’t engaged.  They’re actually calling out, calling the teacher by their first name and walking about freely.  They’re up opening the classroom door for no apparent reason.

How can there be such a disconnect?  Relationship.  You can have the best laid plans for your classroom, but without relationship those plans can easily go awry.  Relationship makes room for the necessary pushes needed to get students to want to persevere through the low floor, high ceiling tasks.  It’s relationship that encourages students to receive the push that helps them work in spite of the shaky foundation they may have.

All it takes, a simple “it’s good to see you” or “I’m glad you’re here” as students enter the classroom.  A smile (before December) when they pass by.  Attentively listening as they share their thoughts or perspective.  It takes a more intentional honoring of what your students say during instruction.  A high five, when they share their mathematical thinking.  Making turn and talk a pervasive practice in your classroom to show you value each students’ input.

Relationship is the important aspect of teaching that gets you through the tough moments.  It causes you to see past the misbehavior of students and see them as a person, a human.  Without it, your days are longer than you want them to be.  Without it, you students resent you for wanting and doing what’s best for them.  Without it, will they ever say, “I knew he/she loved me…”?

 

 

A Case of Teacher Envy

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Okay, before I begin, let me be clear.  I am grateful for the position in which God has blessed me.  I know He has placed me in it for a reason.  With that said, I must admit, I have a bad case of teacher envy!

When you have the opportunity to observe other teachers, you get to see a lot.  Some days can be really dark and you find yourself in need of something to lift your spirits.  For certain, I know of 2 classrooms in which I find a math sanctuary.  I know, at any given moment when I walk in, there’s going to be some goodness for my math soul.

But have you ever seen something in another teacher’s class that made you cry, “I wanna do that!!”  I kid you not, just about every time I walk in @tenaciousXpert 8th grade class, my math soul cries out, “I wanna do that!”  From small groups set up in the four quadrants of the coordinate plane created on her floor to the reinforcing of vocabulary when she calls on the groups, “someone from quadrant four answer…”.

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When you talk with her about her students, she holds them in high regards.  I have never once heard her utter the words, “My kids can’t…”  I’ve only ever heard her talk about what she’s planning to do to ensure her students reach the level of the standards.  She talks about the cognitive processes and executive functions.

You probably can’t imagine why I might be jealous of her.

Because of this:

While working on this standard:

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

 

She intentionally built small group activities for students to see the connection between why the interior angles of a triangle  add up to 180 degrees, to finding the exterior angles of triangles to the angle of parallel lines cut by a transversal.  So methodical and purposeful.

When she told me about her plans for Pythagorean Theorem, I really wanted to hate on her, but that’s not a part of my nature.  I could only celebrate with her, as her students developed aha moments which carried them through accomplishing Taco Cart.  The class worked together to conceptually understand WHY a^2 + b^2 = c^2!

(Yes, she cut out foam pieces for this activity.)

Each time she sent me a picture, my math soul cried, “I wanna do that!”  While I thought I was doing big things in my class in this unit, she is setting up real world scenarios in her classroom.

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“LIKE, WHO DOES THIS!” my math soul shouted.  I want to be her right now, I remember thinking.  To see the kids make connections is so exciting to me, I always want to be there for it.  I want to be a part of the math goodness.

Then there’s this!

NEED I SAY MORE!  But I will.  With tasks such as In and Out Burger, she instills perseverance and math proud in each of her students.  They go home and work on math over the weekend because…wait for it…they are too excited about the math to wait until the next class period.

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I miss that, I envy that she has the opportunity to expose her students to their full potential each and everyday.  But I’m grateful I can witness her greatness.

Checking My Bias at the Door

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As a non-white educator, my biases are not called out, well, at all.  But that does not mean I should not be aware that biases exist.  I’m going to be completely transparent in this post so…warning

For my entire career I have worked within Title 1 schools on purpose.  While in undergraduate school, I had the opportunity to volunteer at a Non-Title school where I developed the bias “*these kids are entitled and I am not valued here”.

*Definition: white kids with parents who are lawyers, doctors, pilots, etc., kids of privlege

From that point, in 2003, I decided I would never teach in a Non-Title school.  Driven by my bias, I concluded what I had to offer would be wasted on *these kids.  The exclusion of a group based on their level of privilege; it’s harsh as I type it out but it is my truth.  And what was it I had to offer?  My philosophy has been to approach learning from a social emotional stance, providing students with a voice on how they learn best and meet them where they are.  Sidebar, this philosophy has evolved over time but the essence has remained the same.

So who did I feel was deserving of my teaching love and affection?  Students within Title 1 schools, more specifically, schools whose students looked like me.  I want to believe it all happened by happenstance, teaching at schools with a large African American population.  I would not say, I sought out these schools, especially not as much as I avoided Non-Title schools.  Over the past 15 years, I have poured my all into the children I taught.  Expectations were all ways high, the work was always intentional, the thought was always **my kids could.

**Definition: African American students from low socio-economic areas.

Still blinded to my biases, I was awarded the opportunity to support teachers within my school district with math instruction.  Two of the three schools I support have a high Hispanic population.  Enter screech sound here.  What?  How do you teach ***those kids?

***Definition: Any student who has English as a second language.

I immediately began to do some “research” on how to teach ***those kids.  I reached out through Twitter and email to educators who have worked in schools with high Hispanic populations.  The message was all the same, “Good teaching is good teaching, nothing is different”.  My biases began to creep to the surface.  Then my new supervisor stated the same thing to me as we stood in the parking lot.  Her look lack judgment but her words exposed my bias.  The exposure was hard to swallow, but necessary to digest.

So I asked myself, what makes *these kids and ***those kids so different from **my kids.  Answer, me! It was my own biases which didn’t match my belief of every kid deserves a solid foundation in mathematics and the flexibility to learn in their own way.  So now that I am naked before you, let me share my next steps in hopes that when your biases are exposed you can work to eliminate them.

Yes, I have a bias, now what?

Define what good teaching is and what it looks like.  For me good teaching starts with a context which automatically engages the learner.  This context allows the learner to bring their own knowledge to the table and and naturally discover what they know and what they don’t know.  It looks like consistently identifying misconceptions and developing a plan to intentionally address the misconceptions in a timely manner.  Good teaching allows for student goal setting and self assessment in addition to the formative assessment pieces determined by the teacher.

Be conscious of your thoughts.  Where are your expectations?  Be intentional about keeping the bar high no matter who is in front of you.  Reflection helps to check your “bar level”.  If your thoughts are focused on what the students can’t do instead of what they can and build from there you may be encountering your biases.

Remember your why.  What’s your philosophy?  Why are you an educator?  Check your actions and thoughts against your why.  If they don’t match, change your actions and thoughts.

Confess your flaws to a trusted colleague or friend.  Someone who is a critical friend and will call you out on the biases and help you work through them.  Not the person who will feed into your biases and deepen the level of the roots.

 

I Hate Math

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Every math teachers’ most hated words, or at least something close.  I pride myself in making math fun, understandable, and relatable to my students.  I view instruction as a way to dispel myths created by negative experiences within math classrooms.  This year, I even implemented I Love Math month to combat math stereotypes and myths.

I’ve read and heard countless messages from students this year about how their perspective of math has changed.  But there were 3 vocal mindsets that had yet to change.  I began with encouraging words and motivational speeches to try and change their thinking.  And yet, negativity still prevailed.

So about March, I made a decision.  As my pastor puts it, I decided not to hug their fears.  When they would say statements like, “I’m not good at this” or “I hate math”, I responded with, “That’s unfortunate”.  When they would sit in their seats and not make an attempt while everyone else was engaged, I didn’t acknowledge them.  The bible puts it this way (in a different context of course): “…wives, submit to your husbands; so that even if some of them do not believe the Word, they will be won over by your conduct, without your saying anything, as they see your respectful and pure behavior.” 1 Peter 3:1-2 CJB.  What does that have to do with me and teaching? At some point, it isn’t our words that change the behavior and mindset, it’s our actions, passions and desire to do the right work.

What caused those students to come around was observing the enthusiasm of their peers and our stick-to-it-ness of challenging their fixed mindset.  Not giving into their demands of being less than their very best.  Not wavering from my core belief that math makes sense.  And establishing boundaries to say, this is where I begin and end and where you pick up to do the rest.

In the end, my hope is that they realized, when they put forth their best try, positive results occur.  My hope is that they realized it is a decision they must make in order to overcome the obstacles in which have been constructed in front of them.  My hope is that they realized love comes also in the form of encouragement in words and actions.

I’m not saying this is the antidote to the world’s problems, but it worked for me this year.  Every sickness does not have the same cure.  You will have to find what works for your relationship with your kids and that fits your core beliefs.  But I can guarantee you, when you lead with love (for math, kids, teaching, serving, etc) you will never lose.

I Love Math 2018- Day 2

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February 14th kicked off I Love Math month for my kids!  I learned about this idea in a session at #NCTMRegional2017 in Orlando.

Here is the list of events and slides.  I used components from Youcubed’s Inspirational Maths Week, visual patterns, Clothesline Math and 7th grade concepts you are reviewing.

Day 2 created a buzz within the room as students worked in groups to create equations which would result in a solution of x = 4.  Students were given the added incentive of creating a complex equation which I defined as an equation which included fractions or decimals, were multi-step and/or used the distributive property.

Each group chose one equation to share with the class in which everyone worked to prove or disprove the solution of x = 4.  Below are some of the equations shared within 3 of my 4 classes.

 

Things were so intense with selecting a winning team in my 4th academic class I needed the math AP to come and select the winning equation.

To see students so excited about mathematics was very encouraging and completely worth the 5-15 minutes spent each day during I Love Math month!

Video of Day 2 equation sharing