# 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.

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 Must Be Okay…

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It’s impossible to fit everything in.  You would think by 15 years in this game I should be okay with this phenomenon.  Everyday, I try to summarize my lessons with some form of formative assessment: sticky bars, muddiest point, exit ticket, something.  But no matter my best intentions, these summarizing activities are just writings on the daily agenda and not actions conducted by my students.

Beating myself up during self reflection, I can’t understand why everything isn’t happening the way I plan?  In a perfect classroom, all my lessons play out exactly how I think through them in my mind.  In a perfect classroom, students will apply the strategies we’ve explored in new situations.

Today it hit me!  I have to be okay with not finishing.  Now, I’m not talking about not finishing a naked math worksheet or a bunch of Kuta worksheet word problems.  Those are meant to be used for just a portion of a class period, if at all.  I’m referring to rich tasks like the 3 act tasks we were working on today.  Tomorrow, I planned to do another task relating to percent increase and percent decrease.  But why is that necessary?  Why can’t I allow students to continue to make sense of the task before moving on?  The purpose of the tasks in to put students in problematic situation for which they can apply their reasoning and strategies to prove their estimations.  If students think the activity is fun, why not allow them to continue enjoying the mathematics in which they are engaged?

So what I planned for tomorrow will not be used in its entirety.  The Earth will not stop on its axis and the students won’t die from continuing the activity.  Learning will still occur, thinking will be completed and we will be closer to mastery than we were the previous day.  I’ll also have time to summarize the lesson.

I can’t be so tied to the plans I’ve entered into my calendar that it keeps me from productive teaching and learning, from following the lead of my students.