functions

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

The Best Laid Plans…

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For me, formative assessment is not just one of the latest buzz words I use to sound like I know what I’m doing. It’s what I actually use to “know” what I’m doing. Without feedback from my students I feel like I’m walking in the dark, alone. 
So I formatively assessment more often than our required Friday CFAs, common formative assessments. 

In addition to the ticket out the door, observation rubrics, FALs and FAs of that sort (which never, ever count for a grade and still my students do them without griping or apathy…but I digress) I use weekly concept quizzes to capture student understanding of the concept of focus for the week. These are entered into the gradebook. 

Here lately, I’ve been using Google Forms to create my quizzes which provide a wonderful spreadsheet to which I can add conditional formatting that gives me this look to easily identify students’ levels of understanding. 

Therefore, as I go through a unit, I have a pretty good idea of who will show mastery on the common assessment (our unit test) and who will need more time before reaching mastery. This year, the FAs and CQs have been accurate. That was until this Unit 6 assessment. Although all signs pointed to majority of the students showing mastery, this data proved differently. 

Yikes!!  My knee jerk reaction was to have students complete test corrections, discuss common misunderstandings as a class, get student feedback on the test and reassess. The retest results further proved the lack of sense making of written scenarios and the confusion between rate of change and initial value on a graph. 

Does this prove that formative assessments aren’t useful and don’t help prepare students for success? Not at all. Is this an opportunity to reflect, adjust and grow as an educator to help my students be successful? Hell yes (sorry mom). This is clearly an instructors error as proven by the data from both the FAs and the CA. As we build more understanding by looking at this concept through a different lens, I’ll post about our accomplishments. 

Function Carnival

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Two years ago I taught 7th grade.  I wrote about how there was a disconnect between classwork grades and assessment grades and our class “town hall” type meeting to help me gain so understanding. (There’s a Disconnect). On of the biggest takeaways for me was how I helped students review for assessments. 

This school year, I’ve been very intentional about selecting interactive games and activities as well as create study guides which encompass strategies and ideas we discussed as a class. We’ve played musical chairs, Kahoot, Quizizz, a math version of Heads Up and many other things. As we prepared for our Unit 6 Introduction to Functions assessment, I wanted to keep our review engaging but also fresh. So, in a bit of desperation, late on a Thursday night I reached out for help https://twitter.com/mrsjenisesexton/status/824811795839856640

To my dismay, I was left to figure this one out on my own. This is what I came up with:


Identifying Functions Fun House. Similar to a fun house at a carnival where there are multiple mirrors all around, this fun house held multiple tables showing relations. The tables had to be adjusted so that each would reflect a function. All red cards were the x values and the black cards were the y values. 


A game of Clue. Students were given 10 different guess who statements. Based on the clues provided, they needed to identify the vocabulary word which matched the clues. 



Graphing Memory Match mixed the concept of a memory or concentration game with matching graphs to appropriate stories. Side note: students made this activity better by deciding to place all of the graphs on one side and all stories on the other. It helped with the flow of the game. 



Determining Rate of Change War. Using scenarios which compared rates of change, I created two stacks. One stacked is numbered while the other is lettered to avoid mixing the cards. The numbers and letters are ordered the same to ensure the scenarios matched one another. Students played in regular I Declare War fashion, the the card with the greater rate of change being the winner. 

Students were required to work with a partner to compete against or collaborate with another partner pair. This allowed for continued support to build understanding of the concepts within our Function Carnival.