Algebra Ane - Introduction To Relations In Addition To Functions

Unit five for my Algebra 1 kiddos is an introduction to relations together with functions.  My goal amongst this unit of measurement is to review pre-algebra concepts such equally ordered pairs together with graphing points on the coordinate bird together with emphasize vocabulary.  The EOI my students volition stimulate got inward the jump volition stimulate got questions that specifically inquire them to position which relation is or is non a function, position the domain or arrive at of a given relation, together with split upward variables equally subject or independent.

After nosotros acquire dorsum from Christmas Break, nosotros volition complete upward this unit of measurement amongst notes on portion notation together with determining the dominion that a portion follows.  I can't wait!  I'm soooo laid to acquire to Unit vi - Rate of Change together with Linear Functions.  I think I dearest to learn most gradient together with graphing to a greater extent than than anything else.  With Common Core, that volition hold upward shifting to 8th plane which makes me extremely sad.  When that happens, I gauge I volition stimulate got to uncovering a novel favorite unit of measurement to teach.

Here is our tabular array of contents for this unit of measurement together with then far...

I already posted pictures together with templates for the ordered duet foldable together with coordinate bird foldable.

We made a frayer model to hash out an of import vocab word: relation. 

Relation Frayer Model

Then, nosotros discussed diverse ways to stand upward for a relation.  I focused on the iv types that my students volition meet on their end-of-year exam: ordered pairs, input/output table, coordinate plane, together with mapping diagram.  My students were convinced that an input/output tabular array was the same equally a stalk together with leafage plot.  At to the lowest degree they stimulate got heard of a stalk together with leafage plot...

Ways to Represent a Relation Foldable - Outside

Ways to Represent a Relation Foldable - Inside

Once nosotros had defined a relation, nosotros could straightaway define a specific type of relation: a function.  

Function INB Pages

Can you lot tell I dearest the Frayer Model for vocabulary?  We made i to summarize what nosotros learned most functions.  I gave them the Definition of a portion together with cipher else.  Then, I went through all of my released EOI seek questions together with copied together with pasted all of the relations and/or functions into a Smart Board file.  I asked for a volunteer.  I showed them together with the entire shape a moving painting of a relation.  I instructed the students who had non volunteered to write downward portion or non a function.  Once everybody had written downward their answer, the educatee who volunteered said their reply aloud.  Next, I had all of my students concur upward their dry out erase board to demo the student.  After seeing the responses of their classmates, the educatee had to create upward one's heed whether they should proceed their master copy reply or alter their answer.  Only afterwards going through this procedure did I expose whether it was a portion or not.

This was a novel means of doing things for me, together with I kinda liked it.  I stimulate got students write their answers downward together with demo them to me a lot.  But, I rarely stimulate got students demo their boards to other students.  It reminds me of the "Poll the Audience" characteristic of Who Wants to Be a Millionaire.  I gauge you lot could say that the mortal who has to phonation their reply aloud is inward the "Hot Seat."

Function Frayer Model

My students loved this.  I had lots together with lots of students wanting to volunteer.  The conversations that ensued betwixt students were AWESOME.  I also did something novel this year.  I didn't learn my kids most the vertical business seek to start with.  I sort of permit them uncovering it for themselves.  Of course, this worked improve inward some classes than others.

We ended this day's lesson past times completing the function/not a portion bill of fare sort that I dearest together with stimulate got used a lot.  I used it terminal twelvemonth amongst both my Algebra 1 together with Algebra 2 classes.  And, I used it amongst both classes over again this year.  This bill of fare sort is available from Math Tales From the Spring.

Function / Not a Function Card Sort

The side past times side day, I had students create examples together with non-examples of functions.  And, nosotros summarized the vertical business seek strategy that nosotros had arrived during the previous lesson.  To give my students farther practice, I assigned an error analysis chore from Algebra's Friend.  My students are terrible at next directions.  Even though I told them that they were grading the answers given on the paper, I withal had students who answered portion or non a portion instead of right or incorrect.  My IEP students were peculiarly bad most making this mistake.  I simply don't know how to acquire them to tiresome downward together with read the instructions.

Domain together with Range INB Pages

Next, nosotros moved into our give-and-take of domain together with range.  I used the DIXROY mnemonic device amongst my students.  I don't really know how many students fifty-fifty work this to aid them think the pregnant of domain together with range.  DIX: Domain, Inputs, X-Coordinates. ROY: Range, Outputs, Y-Coordinates.  I did meet a educatee write the acronym on their index bill of fare to work on their semester test, together with then I gauge at to the lowest degree i educatee has institute it helpful.

Domain together with Range (DIXROY) Notes

Domain together with Range / Representations of a Relation Practice

This half-sheet was stolen, ahem, borrowed from Mrs. Hester.  She posted a moving painting of this organizer from her 8th plane interactive notebook, together with I savage inward love.  So, I typed upward i at the terminal minute.  I uploaded the template for you lot below.  Everything isn't perfectly aligned together with centered, but it was the best I could do amongst the express fourth dimension I had.  If I wasn't such a procrastinator, my notebooks would hold upward better.

Independent together with Dependent Variables INB Pages

Last year, some of my students really struggled amongst the divergence betwixt subject together with independent variables.  So, this year, I laid out to learn this subject better.  I'm pretty certain I failed, but I'll portion amongst you lot what I did anyway.  

Independent together with Dependent Variables Notes

We took notes over the divergence betwixt independent together with subject variables.  I filled out the arrows to a higher house 3 dissimilar ways for the 3 dissimilar sections of Algebra 1 that I teach.  None of the ways led to universal understanding.  When I await at a scenario, I tin easily tell you lot which variable depends on the other.  This is the subject variable.  Thus, the other variable is independent.  Easy.  

Many of my kids cannot do this.  I volition think I stimulate got come upward up amongst the perfect instance that volition brand all things clear to all students.  Ms. Hagan's Outfit.  The Weather.  Which i is dependent?  Which i is independent?  They volition tell me something similar this: "The atmospheric condition depends on Ms. Hagan's outfit."  This leads to me saying, "So, if I alter my outfit, the atmospheric condition volition change?"  It sounds crazy.  But, they volition reply yes to this together with really hateful it.  I don't think my kids sympathise the news "depend."  Or, perhaps they don't sympathise drive together with effect.  

There were basically ii groups of students inward each department where I taught this lesson.  The students who idea this was the most obvious affair nosotros had e'er done inward Algebra 1.  Why inward the globe would nosotros pass an entire 50-minute menses on this lesson?  Then, at that topographic point were the students who missed every unmarried question.  They would flip the subject together with independent variable.  Every unmarried time.  I was almost tempted to tell them to simply write the reverse of what they idea the reply should be.  Okay, that's terrible.  And, I would never really do that.  But, why can't my students acquire this?  

I created a bill of fare sort that I idea would stimulate got 10 minutes tops.  We spent at to the lowest degree 35-40 minutes on it.  And, some students withal didn't finish.  

Independent together with Dependent Variable Card Sort

* I accidentally glued i duet on backwards.  The set out of songs performed should hold upward independent, together with the duration of the concert should hold upward dependent.  Oops.  I was inward a hurry, together with it shows!  

I did a quick google search for sets of independent together with subject variable scenarios.  I institute such a onrush www.ixl.com.  I copied together with pasted these scenarios together with edited them to take the names.  I idea this activeness would hold upward besides slowly for my students if I left the names inward the scenarios.  I think I could stimulate got left the names in, together with my students STILL would stimulate got struggled.

I passed out a canvass containing the twenty statements.  I gave students these instructions:

1. Cut out the twenty rectangles.

2. Recycle your trash.

3. Pair upward the statements.

4. Have Ms. Hagan banking concern check to brand certain your statements are paired upward correctly.

5. Classify each contestation equally subject or independent.  Arrange these inward ii columns.  

6. Have Ms. Hagan banking concern check your classifications.

7. Glue these inward your notebook on page 52 together with 53.  Be certain to label the columns equally subject together with independent.  

Students were okay amongst steps 1-2.  But, Step 3.  Oh my goodness.  "How am I supposed to know how to duet these up?"  "This is together with then hard."  "What's a potluck?"  "Is that where people acquire together together with smoke pot together?"  "This is impossible."  "What does the news duration mean?"  "You hateful pickles come upward from cucumbers?!?"  

I would become around together with banking concern check my students' statements to brand certain they were paired upward correctly.  It was non out of the ordinary for students to entirely stimulate got 3/10 pairs made correctly.  They were pairing upward statements that had NOTHING inward common.  It was a nightmare.  

H5N1 few of my high-achieving students caught on early on together with were able to consummate this activeness amongst fiddling assistance.  The residual of my students.  I simply don't know.  This isn't supposed to hold upward that hard.  They couldn't acquire them paired upward permit lone split upward them equally subject or independent.  I was frazzled.  My students were frazzled.  

If you lot stimulate got whatsoever insight on how to learn independent together with subject variables, delight travel out a comment.  I'm begging you.      

I stimulate got uploaded the PDF templates that I created for my students to work below.  If you lot can't acquire them to load, delight brand certain that you lot stimulate got Flash/Shockwave installed.  If problems persist, experience complimentary to ship me an e-mail.  I volition hold upward happy to attach the files together with ship them to you!

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