Representations Of A Relation Foldable As Well As Telephone Activity

My Algebra 1 students lately started what is belike my most favorite unit of measurement of the year: introduction to relations in addition to functions.  Our starting fourth dimension science is to live on able to generate equivalent representations of a relation in addition to determine if the relation is a function.  Today's post focuses on the starting fourth dimension component subdivision of that skill: generating equivalent representations of a relation.  

In the past, I receive got made a 4-door foldable for this.  It worked okay.  Lots of writing which meant unopen to students' notes were nearly illegible.  My classes are bigger this twelvemonth than they receive got ever been before, in addition to thence I decided to pre-type every bit much of the foldable every bit possible.  

Here's what the exterior of the foldable looked similar circa 2013: 

Inside:

You tin encounter to a greater extent than of my notes from 2013 here.

Here's my new, pre-typed version.  

Outside:   

We began our give-and-take yesteryear creating a develop of ordered pairs.  I had 6 students each volunteer an ordered pair.  There was 1 restriction.  The ordered pairs had to fit on the coordinate bird below it.

After writing our 6 ordered pairs, nosotros moved to the input/output department of the table.  We discussed that they would demand to live on able to organize ordered pairs into a horizontal tabular array or a vertical table.  I asked them which variable was used to correspond input in addition to which variable was used to correspond output.  They easily supplied x in addition to y for these blanks.  Next, nosotros discussed where x in addition to y belong on a vertical tabular array vs. a horizontal table.  

In the past, my students receive got sometimes struggled alongside calculating gradient from a horizontal tabular array because they aren't certain which values are x in addition to which values are y.  This is my motivating constituent for including both horizontal in addition to vertical tables here.  

We took our ordered pairs from the previous department in addition to turned them into both types of tables.  

After making our tables, nosotros graphed our 6 points on the coordinate plane.  

In the past, I've spent unopen to fourth dimension reviewing graphing on the coordinate plane.  This year, I'm going to assume that my students receive got mastered that concept inwards middle school.  We'll encounter how that goes...  

Finally, I introduced my students to my most favorite representation of a relation--mapping diagrams.  I didn't say my students why they are my favorite, but I know they'll live on able to say why before long when nosotros start classifying relations every bit functions or non-functions.  

We took our 6 ordered pairs in addition to turned them into a mapping diagram.  

First, I had them write their x values inwards the input oval without repeats.  Then, I had them write their y values inwards the output oval without repeats.  Some students began to live on real concerned close this.  How inwards the Blue Planet do nosotros know which input matches upward alongside which output?  I am in addition to thence real glad y'all asked.  That's why nosotros demand arrows to connect each input value to its corresponding output value.  

And, our notes are done!  Going through these 4 representations took close 20 minutes of our 50 infinitesimal flat period.  We spent the adjacent 20 or twenty-five minutes working on a representations of relations telephone game.  

I was inspired to brand this telephone action yesteryear a chemical scientific discipline tweet.  

Have y'all ever played the game "Telephone?"  One individual whispers a message to unopen to other person.  That individual whispers the message to nonetheless unopen to other person.  This continues until the message has been relayed through an entire job of people.  Then, the individual at the destination shares the message they heard.  This is compared the starting message, in addition to normally quite a few laughs are had.  

This industrial plant only similar that, but we're dealing alongside math.  

Give each pupil a canvass of paper, in addition to enquire them to squeeze box plication it on the lines betwixt each section.   This volition salvage a lot of fourth dimension after in addition to throughout the activity!  

Notice that the canvass of newspaper both begins in addition to ends alongside a develop of ordered pairs.  If all things piece of work every bit planned, the develop of ordered pairs at the top in addition to bottom SHOULD match.  Of course, nosotros know things don't e'er piece of work just every bit nosotros intend them to inwards our classroom.  

All students were instructed to write their ain develop of 6 ordered pairs inwards the BOTTOM department of the page.  Just similar alongside our foldable, they needed to brand feel that their ordered pairs would fit on the coordinate bird flora on the page.  

After writing their 6 ordered pairs, students traded papers alongside unopen to other student.  They took the 6 ordered pairs written at the bottom in addition to turned them into a table.  Before passing the newspaper on to the adjacent student, they had to plication upward the newspaper in addition to thence that the original 6 ordered pairs were hidden.  

The adjacent pupil to larn the newspaper had to receive got the horizontal tabular array in addition to plow it into a coordinate plane.  Before passing the newspaper on to the adjacent student, he/she had to plication upward the tabular array to shroud it from view.  

The adjacent pupil to larn the newspaper volition receive got the coordinate bird in addition to plow it into a mapping diagram.  Before passing it to the adjacent person, he/she volition plication upward the newspaper to shroud the mapping diagram from view.

The terminal individual uses the mapping diagram to do a develop of ordered pairs.  After these ordered pairs are written, the newspaper is returned to the original owner.  (We wrote our names adjacent to our original develop of ordered pairs to brand returning the papers to their owners much easier!)

When students got their papers back, the starting fourth dimension matter they had to do was banking concern check in addition to encounter if the develop of ordered pairs at the top of the page matched the develop of ordered pairs at the bottom of the page.  Many were surprised to encounter that the lodge didn't match, in addition to thence nosotros had to speak close why that would live on the case.

For unopen to students, their ordered pairs matched perfectly.  For others, they didn't.  This agency they had to hold off through the dissimilar representations in addition to figure out where things went wrong.  So many awesome conversations came out of this.  And, I promise this action drove dwelling household the fact that precision is super of import when translating from 1 representation to another!  As my students flora out, 1 tiny fault tin modify the entire problem.

I loved the telephone construction of this activity, in addition to I hold off forrad to finding other ways to exercise this practise construction inwards class.  It fits inwards tons of practise in addition to error analysis without seeming similar work!

Files for the foldable in addition to action tin live on flora here.

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