## Hallelujah! Finding two-step function rules from tables

Maybe this method that I discovered from an exhaustive internet search is well-known to most, but maybe it’s not.  So, I decided to post it just in case.  That and, quite frankly, I am so freaking excited about it and my husband will have NO idea what I’m talking about if I decide to spew it all over him!

When I was in school a billion years ago, many things were taught as “guess-and-check.”  For instance, factoring quadratics. (I learned an awesome no-fail method for that last fall from my cooperating teacher during my internship- I’ll post that sometime soon.)  I don’t know about any of you, but I HATE guess-and-check.  Besides, how do you even TEACH guess-and-check?

What prompted my diehard search for an easier way of finding function rules?  My kiddos.  I was out of work last week due to an emergency surgery (yeah, 4th week of my first year teaching is a fabulous time to have your gall bladder removed!), so my sub covered the lesson involving finding function rules given a table.  She’s completely competent (she’s my ESE teacher for one of my classes and she’s certified in math), so I don’t think it was a lack of instruction on the concept.  She probably taught them the same exact way I would have: guess-and-check until you’re good enough to just “see” the rule.  Well, the majority of my poor kids don’t get it- at all!  So, today I was frustrated due to the gazillion questions during their end-of-unit test.  Clearly, if they are all asking questions about the same test item something needs to be done.

Cue in research.

I found this explanation in a math forum.  I’m so happy I did.  It’s not the prettiest or clearest of explanations, so I’ll try to make it a bit prettier here.

Take, for instance, the below table.

 Input, x Output, y 1 7 2 11 3 15 4 19 5 23

The first thing you do is take 2 sets of numbers (ordered pairs):

(1,7) and (4,19) ; any 2 sets will work

Next, find the difference in x-values and y-values:

x-values: 4-1 =3

y-values: 19-7 =12

Notice that the difference in y’s is 4 times the difference in x’s:

3 * 4 = 12

Therefore, 4 is your multiplier for the rule.

So, we know that 4x plus or minus something = y.

From here, it’s easy to tell what we have to add or subtract to get y.

4(1) = 4

4+3=7

Thus, y= 4x + 3!

Again, this may be somewhat common knowledge in the math community at this point.   However, I figured if I was clueless to this method then maybe (hopefully!) someone else is, too.  At least, that is what I am going to tell myself to fall asleep tonight!

I cannot wait to show this to my kids tomorrow!!!

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## Homework Conundrum Solution

OK, so I am SO done with collecting/grading for completeness homework and I’ve only finished the second week.  After some “soul-searching” and cues from some model veteran teachers, I spent a good part of my long weekend developing an easier-on-my-sanity approach to homework, classwork and rewards.  I stole compiled various ideas from teachers and developed something that I hope think I can live with.

So, here it goes.

I will remind you (or let you know if you didn’t peruse previous posts) that I am teaching 3 sections of Intensive Math for Algebra using the Agile Mind curriculum.  I would personally not assign as much homework as is required through this curriculum though.  I have been warned on numerous occasions by another teacher teaching this that I am NOT TO DEVIATE from anything.  You can add activities, but you are not suppose to alter assignments, content, etc.  This has its pros and cons for a brand-spanking-new teacher, but I’ll elaborate on those some other time.

My two-week-old homework system:

Students are given 10 minutes during class to (hopefully) compare and discuss solutions with their partners to the previous night’s homework, as built into the curriculum.  When they are finished, they are to make sure my personal (and district) required information is included on their homework: Name, Period #, Level of Understanding (1-4 scale), logical attempt to problems, answers in full sentences (district requirement).  They were warned that they would receive an Incomplete if any of those things were missing (I honestly didn’t return incomplete for certain things, but always for name (duh!  How do I know who did this?), complete sentences and for lack of logical attempt on MOST problems.)  OK, so are you picturing my mound of homework, current, overdue and incomplete, toppling over on my desk?  Or how about the HOURS I’ve spent looking through each and every one of these, some two or more times?  Yeah, definitely not working for me.

Ideas I compiled:

From the other teacher using this curriculum:

She is using weekly punch cards/ scratch off cards that she created prior to school starting.  While students are doing their Opener (or Bell Work or Warm Up, etc.), she walks around to check their homework and initials the day’s “punch” if they completed it.  At the end of the week, they can scratch and utilize the prize if they received 5 out of 5 “punches.”  She gave me a list of her rewards which included: homework pass, 5 minute hall pass, extra bathroom pass (she limits the number of times they can use the restroom during a quarter), double your highest grade, etc.

From my fantabulous cooperating teacher last fall:

She uses weekly check sheets to keep track of homework, classwork and make-up work completion.  She uses a 1-5 point scale to determine completion on all of the above.  Each day has its own row for classwork/ make-up work and then another one for homework.  When she is checking for homework she also has them show her their notes from the day before.  At the end of the week (she might have done it on the day of a unit test, I don’t recall right now), she collects the check sheets and grades them.

My final outcome:

Creating the scratch off cards seemed like a daunting task for me to take on right now, but her ideas sparked the fire under my behind to do something about my homework situation.  Instead of scratch off cards, I created reward cards to be put in a jar, box, something for kids to choose a homework reward at the end of the week.  I used most of her ideas, nixed a few, and added my own.  These are the ones I’ve gotten so far:

• Free homework pass (they love these, don’t they?)
• Hall pass (get out for 5 minutes when needed)
• Cheat sheet on a quiz/test
• Pick your partner for the day (I have assigned seats, I know many will love this one.)
• Sit in rolling chair for a day (they fight over my extra teacher chair)
• Choice of candy from me
• Eat food in class pass

I’m planning on asking them what kinds of rewards they would like, too- maybe.  I figured these would be good ones to start with and I can always adjust as the year goes by.

Below is the check sheet I created.  I am planning to grade the classwork and homework separately because my PLC decided they should be separate.  Notice on the bottom it states that if the student receives either a 4 or 5 on every homework they can pick a prize (the ones listed above).  I am hoping this gets more students to complete their homework PRIOR to class.  I plan on walking around the classroom during their Opener to check their homework and classwork.  I also like how the make-up work is listed on the check sheet, too.  This will help me keep kids who are absent accountable for what they missed.  Some of the classwork they would not be able to complete without being in class, but a good deal of it they can.  To deal with late homework, I will cross off the 4 and 5 on the check sheet and initial it, so that when they show me their completed homework at some other time, they can only get at most a 3 on it.

Did you notice the “Party Points” on the bottom of the check sheet?  On my whiteboard, I have had “Party Points- coming soon!” since the first day of school.  They have been eagerly awaiting for me to launch this (I haven’t divulge much information).  Below is the description for Party Points that I am planning on going over with each class tomorrow.

I tried to gear Party Points towards behavior, not academics, but I did throw in the “A” points.  I am also hoping they don’t feel like the big prizes are unattainable.  I want to stress the importance of working hard for rewards with them (sense of entitlement, anyone?).

So, there you have it.  Please feel free to offer suggestions to help make this better- I am all ears!

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