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…”?