## Algebra 1 Unit 2 Interactive Notebook Pages | Relations & Functions

Here are the notes I used this year for the 2nd unit of Algebra 1:

Day 1:
We started off the unit with a classifying variables sort. This was a good way to jog students’ memories about their prior knowledge, and it also served as a jumping point into domain and range!

From there, we went into what a relation, domain, and range is, and how it relates to independent and dependent variables.

We then made the distinction that there are two types of relations, discrete and continuous, and we must pay attention to context to determine what type of relation we have.

From there, we started to talk about all of the different ways we could represent a discrete relation, and how we find the domain and range from each representation.  We used this foldable, which went over great with the students.  They caught on super quickly, and they mentioned that they liked having one example to do together, and one to do on their own for each representation.

Day 2:
We started off with a word problem to review domain and range in a (discrete) relation.
From there, we filled out a Frayer vocabulary model for functions, to make sure that students really understood what they are and aren’t.

Then, using the definition for function we just wrote down on the Frayer model, we made a cheat sheet to refer back to that tells us all of the different ways a relation (discrete or continuous) would NOT be a function.

We practiced classifying functions using a card sort from Amazing Mathematics.  Instead of cutting and pasting, we decided to color-code instead! Love it! (In the words of one of my students, this is the page that has “fourteen thousand graphs.”)

We then filled out another cheat sheet, this time for domain and range of continuous functions.  Students reasoned together through the inequalities and we talked about what a bound actually means (we used a lot of basketball references).
We practiced finding the domain and range for continuous relations (as well as determining whether or not they were a function), using the following set of notes.  PS: It took me a LONG time to figure out how to make a parabola or a trigonometric wave using Microsoft’s shape tools.  I feel overly proud of this set of notes! You can download them here

Day 3:

We began with a recap warm-up on domain and range for continuous relations.
To make sure that students didn’t forget about discrete relations, we went back and did more practice with determining their domain and range, and also stating whether or not the relations were functions.

Day 4:
We started off with a reference sheet on function notation and how to read/say it.
From there, we did a lot of practice with function notation.

Inside this set of notes, we really emphasized interpreting what we were being given in a problem (input or output value) and what the problem was actually asking us to find (input or output value), before starting the problem.  This helped students from making a lot of careless mistakes.  After we practiced function notation in both directions (evaluating a function, and solving for an input given the function’s output), we mixed up the problems and even threw a few variables and function compositions in there!

Day 5:
Recap warm-up on function notation.  Problems 5 and 6 both spurred amazing conversations about order of operations.

After doing this recap warm-up, we did my function notation mystery sum activity, which was a blast.  It encourages students to collaborate together and it’s really high engagement each time.

From there, we continued talking about function notation, but now in terms of a graph.  Interpreting what the function notation was telling us was such a huge part of the previous day’s lesson, that I wanted to see how they could do when we attached a context to the problem.

Inside, we worked on graphing functions, and using the graph to find an x-value.  Some students preferred solving for x, but others were impressed by my tracing over on the graph method.  To each their own–that’s the beauty of math, in my opinion.

Day 6:
Recap warm-up over function notation with graphs, and then we reviewed for the test.

Day 7: Test!

## Algebra 1 – Unit 1 INB Pages | The Foundations of Algebra

Here’s what went into our INBs for the 1st unit of Algebra 1:

Day 1:
We glued in a reference sheet for the real number system. Our textbook uses I for the set of irrational numbers.  I went with the same notation this year, but I think I’m going to go with R-Q for next year, since I is used for imaginary numbers, later on.

To practice working with these definitions, we did a real number system sort, which I found from Amazing Mathematics! My students enjoyed doing it, and it spawned many great conversations about the difference (however subtle they may be), between the sets of real numbers.

For homework, students did this Always/Sometimes/Never sort, which is also from Amazing Mathematics. They were given about 20 minutes in class to begin their assignment, and then had whatever was left as their take-home assignment for the night.  This one was even better than the last card sort, in terms of spurring student conversations.  Students were justifying with counterexamples and providing fully flushed out reasons for where each card should get placed.  It was awesome!

As a note, we also keep a binder for the class which holds extra handouts, like additional reference sheets and homework assignments that don’t go in the INB. My favorite reference sheet that didn’t go into the INB was this real numbers flowchart that I made.  The day of teaching my lesson on real numbers, I noticed that using the “Venn diagram” approach wasn’t meshing well with some of my students.  That afternoon, I went home and made a flowchart handout that they could refer to, in addition to their INB pages.  Next year, I think I’ll just use this flowcharts in a mini-book format for notes, instead!  I found that students started making more connections about the sets each number belongs to (i.e. not only is a number natural, but it’s a whole number, and an integer, and a rational number), and students were able to remember the questions they need to ask themselves when determining the best classification for a real number.

Day 2:
We started off with a recap warm-up on the real number system, which we covered the day before.

From there, we did a translating expressions sort, also from Amazing Mathematics.  (Can you tell I love her sorts?!).

From there, we used our key words and started defining what a variable is, and what an expression is.

For homework, students did the following problems.  They had about 15 minutes of class time to get started.  We color-coded “turn-around words” in pink, “parentheses-words” in green, and “equals words” in blue.  Students marked the page in highlighter before beginning to translate the expressions.  They mentioned that this made the process much easier for them!

Day 3:
We began with a recap warm-up over translating expressions.

From there, we talked about evaluating expressions and also reviewed the order of operations.

From there, we discussed the properties of real numbers and students made up their own examples for each property.

For in-class practice, students did the a properties of real numbers puzzle from Lisa Davenport.  A student volunteered to glue it into my notebook.  Notice the lack of glue?  Notice the crooked edges?  It was a very sweet offer, but I’m I don’t think it’s one I’ll be taking again any time soon.

Day 4:
We started with a recap warm-up over evaluating expressions and identifying properties of real numbers.

Next we took notes on combining like terms and the distributive property, cutesy of Sarah at Math Equals Love.

Day 5:
Recap warm-up over distributing and combining like terms.

What is a solution?  What does it mean to be a solution?  What does it look like?

Up next, we focused on solving and verifying solutions to 1-step and 2-step equations.  I’ve found that verifying a solution is a skill that students struggle with more than solving (at least in Algebra 1), so I wanted to make sure it got emphasized.

Day 6:
We filled out a foldable for solving 2-step equations.  Those pesky fractions are going to be our friends by the end of today!

Day 7:
Recap warm-up over solving equations.

Day 8: Review

Day 9: Test!

## {FREEBIE} Test or Quiz Retake Form

Last week each of my classes had their first test.  Most did quite well, but, like normal, a few did not.  In my school, the math department policy is that students are allowed to retake tests, but not quizzes.  Honestly, I wish it was the other way around, but that’s a topic for another post.  Since tests are worth 40% of a students grade at my school (we have a 10-40-40-10 grade distribution for homework, quizzes, tests, and final exam), it is important that students do a retake whenever they have performed poorly on an assessment.  Not only should they do a retake for the sake of their grade, but also so they are in a position to better understand the material going forward.  Math is constantly building on itself, so I’m glad that students have the opportunity to go back and revise their learning.

The past two years, I have used a retake form created by someone else in my department, but I never quite liked it.  Although it asked students honest reflection questions, I felt like it was a bit condescending to students and I questioned if it might prevent some students from pursuing a retake opportunity.  I used it anyway since everyone else in the department used the same form, but silently feeling like a bad teacher because of it.

This year, I wanted to create a new retake form.  Over the summer I had played with a few different versions, but it wasn’t until today (the day before my students actually need the retake form, lol!) that I came up with something that just felt right.  It asks students to reflect without pointing any fingers or making them feel guilty for not doing well the first time.  It’s straight to the point, and requires them to revisit the material in new ways so that they can improve their understanding.  Tomorrow I am going to walk through the retake form together as a class so my students know what my expectations are for it and have an idea about how to productively go about preparing for a retake opportunity.

If you would like to use this retake form in your own classroom, you can download it for free from my Teachers Pay Teachers store.  While you’re there, make sure to follow my store so you don’t miss any other resources I post!

## How I do Homework

Friday evening I was tagged in a tweet that was asking about my homework policies and I just had too much to say in to fit in 140 characters or less, so I figured I’d write a blog post as a response.  One thing I make sure to do in class is to always call “homework” a “practice assignment.”  You’ll never hear the word “homework” come out of my mouth at school because that seems to open up a very unproductive can of worms.  Practice Assignment is clear to students and it can be worked on both at school and at home, and also reminds students why they’re doing it.

A bit about me, I teach on a 7-period a day schedule.  On Mondays and Fridays each class is 51 minutes long, Tuesdays and Thursdays are 46 minutes long to account for a 30-minute advisory class that happens twice a week, and Wednesdays are 43 minutes long to account for our early release professional development sessions.  I definitely am not a teacher whose sole purpose is teaching to the state test and “exposing” students to 100% of the topics in the textbook.  I like a much more balanced approach.  I think it’s important enough to go slow enough that students actually have a chance to absorb the material, but it is also important to me that we get through the required material as to not disservice them for their next math class.

I also believe in homework.  This has become quite controversial over the years, especially in the online teacher communities.  However, I do believe in a balanced approach to homework.  Maybe 15 questions a night, and it’s rarely due the very next day.  I have homework due on quiz or test days, which allows students a bit of wiggle room to work around their schedules.  I think homework does so much for students.  It gives them a chance to play with the material more on their own so they can really figure out what questions they have.  It teaches them how to self-advocate for themselves when they need help.  It teaches them time-management skills to work around their busy schedules and how to prioritize tasks.  To completely get rid of homework at the high school level seems like it would be quite a disservice to students, in my opinion, and doesn’t seem like it’s setting them up for success in their next endeavors (whether that be entering the work force or higher education).  However, I do acknowledge that each teacher certainly knows what works best for their own class, so the no-homework approach may be just right for other groups of students.  It just doesn’t work for mine.

The past couple of years, the math department at my school has focused on paring back our pacing guide a bit to focus on the core concepts in a deeper way, and our state test scores shot up 13% each year in a row.   Focusing on 90% of the topics and pairing back the most peripheral 10% has done amazing things for our students.  Exposure to content means nothing if it’s at a pace students can’t absorb, but there is a tricky balance.  If you’re only getting through half of the pacing guide each year, that’s definitely not setting up your students for success either.

Anyway, to get back to the main topic, I treat each class a bit differently when it comes to how we do in-class work and homework, so I’ll break up what I do by subject:

Algebra 1 + Support:
Info: This class is 2-periods long each day.  I have them the first two periods of each day. Students are part of a cohort of 30 students that take math, English, and science together each day.  They have been identified by their 8th grade principals for being at extreme risk of not graduating and their parents have agreed for them to be in a special program at the high school to help them be more successful.

Students pick up notes and homework as they walk in the door each morning.  We record homework assignments on our practice tracker after our daily warm-up problems have been completed.  As we are taking notes together in class, students are encouraged to switch back and fourth between notes and similar homework problems.   Most days there is 15-40 minutes of work time.  On our practice tracker, we write down the minimum required number of problems to enter the classroom the next day.  Let me explain how this works:

Let’s say that the homework sheet has 15 problems.  If they are given 30 minutes of homework time that day, as a class we come up with the minimum expected amount to be finished during that work time.  The class might decide that, given the time they have to work in class that day, they think everyone should be able to finish at least 6 of these 15 homework problems during our in-class homework time, so we write this on our practice trackers (min=6).  The next morning, I stop each student on their way into the classroom.  They must show me that they have completed at least any 6 of the 15 homework problems to get inside the classroom.  If they have failed to do so, they sit outside the classroom to work with our aide and finish up those problems with 1-on-1 help while the daily announcements are being played, and then come back to join the class who have already begun to work independently on the daily warm-up problems.  Students are given one grace period to be “stuck outside,” after that a call home is made to discuss ways we can help the student be successful at staying on top of homework, especially when class time is being given.  Now, since only 6 of the problems were required to be done the next day, students have until the next quiz or test (whichever comes first) to complete the remainder of the assignment.  All homeworks are graded on a 3-point completion scale.  Quizzes normally are given once or twice a week. NOTE: if a student emails me the previous night letting me know that they will not be able to complete their minimum required amount for whatever reason and what their plan is to make it up, then they are allowed in to class, no questions asked.  Again, I really want students to learn how to advocate for themselves, so this is part of that goal.

Practice trackers get turned in on the unit test date, and then a new one is handed out the next day to start off the new unit.  Students have mentioned how much they like using the practice trackers because it helps them remember their homework, and they have also commented that they like having the minimum required amount since it makes them stay on top of things and helps them focus better during work time.

I also offer a “double stamps” policy in all of my classes (except for Statistics because it’s college credit) where if a student finishes an assignment the day I give it to them and brings it back before I go home that day, not only does their practice tracker get stamped as 3 points “all done” for that assignment, but they get a bonus 3pt stamp for working so hard at completing it that day.

Lastly, I accept homework late up until the unit test.  I also allow students to “move up” points.  Let’s say they just got the minimum done and didn’t do more before the quiz where homework gets stamped off.  They’d probably get stamped for 1 point or “a bit” completed.  If they did more before the test, they could improve their score and I would re-stamp their practice tracker for 2 points.

Algebra 2 and Geometry:
Exactly the same as Algebra 1, except for the minimum required amount and having to show me the assignments at the door.  They also don’t usually get 15-40 minutes of homework time each class, since these are only 1-period long classes.  Most days, they get 5-10 minutes of work time.  Other days, they get a bit more.

College Credit Statistics (MTH 243 and MTH 244):
Since this class is dual credit, homework is inherently done differently.  Each Monday students are given a quiz over problems taken from the prior week’s assignments, and once they are done, they begin working on an Algebra and Geometry review to make sure that their other math skills are staying fresh.  After everyone has finished the quiz, students work together in groups to complete the weekly Algebra and Geometry review.  During the last 10 minutes of class, I allow them to ask me to go over any 2 of the 10 questions with them as a class.  At this point, the rest of their homework is assigned, corresponding to whichever sections of the textbook we will be covering that week.  Homework is always assigned on Monday and due the following Monday so students can manage their time as they see fit, in order to work around their schedules.  The general format of the statistics class is:

Monday: quiz and Algebra & Geometry review.  Tuesday, Wednesday, Thursday: new notes.  Friday: work day where students are able to work on their homework assignment together for the period.

Late work is not accepted in this class due to the dual credit aspect.
____________________________________________________________________________
I could write a ton more about how homework works in each class, but I’ll leave it here so I don’t end up boring you all with a novel.  If you would like me to go over anything in more depth, or have a question about something I forgot to address, please let me know and I will make sure to answer it right away.  Thanks for reading!

## 3 Thoughts on Teachers Pay Teachers

Today, the question about what the #MTBoS thinks about Teachers Pay Teachers (TPT) was brought up.

Some love it, some hate it.  Here’s my take.

I LOVE Teachers Pay Teachers.

1. My first  year teaching, I had 4 preps, one of which was Geometry.  I had a non-traditional high school path, and had never taken Geometry, myself, so I was extremely nervous (All of those proofs! Back then, they had me shaking in my boots.). There wasn’t enough time to create everything myself, maintain my sanity, and have my lessons be to the quality that I desired.  It just wasn’t possible.  So, I went to TPT and found a curriculum for Geometry–complete with notes, homework assignments, quizzes, and activities.  It was expensive, but cost the equivalent of 14 hours of work.  There is no way I could’ve created a twenty-fifth of the materials available in that product in the same amount of time, so it was well worth it for me.  And everything in it was AMAZING–truly, high quality materials.  There is no way I could’ve provided the same level of quality for my students that year without it, PLUS it saved my sanity.
2. I should disclose that I am a TPT seller.  I have a small store, but it’s definitely a passion for me.  I find that TPT drives me to create better and better materials to provide to my students and makes me more creative.  What I would’ve provided to my students without TPT would be a 9/10, and what I’d provide with the intention of selling a product on TPT would be a 10/10.  I don’t think people realize the amount of hours it takes to put a quality product on TPT.  Maybe it takes 10 hours to create and perfect it, and another 5 hours to do the finishing touches.  Those extra 5 or so hours really take a resource to the next level, but the time commitment is not practical at all for a teacher that doesn’t have the monetary incentive attached.  5 extra hours of work for just one resource would be a crippling time constraint to do regularly, if there was no other benefit.  Even doing it for a resource that would be shared online for free wouldn’t make sense to commit that much extra time to a resource.  Sure there are some bad products on TPT and there are some amazing resources offered for free from the #MTBoS community.  Generally speaking, though, I find the distribution would be as follows:
Like any online purchase, reading customer reviews on TPT can help you easily stay in the upper quartile of the TPT distribution.
3. I really like the idea that teachers can get recognition for their talents through TPT.  Teaching has a pretty low ceiling as far as job recognition goes, and TPT definitely helps with that. Teaching can also be a financially difficult profession to choose.  It takes a lot of money to get the Master’s degree required to be a teacher (at least for my state), which leaves many with crippling debt. TPT can provide supplemental income that can help the financial strain that many teachers face, allowing them to actually stay teaching.  In addition to the monetary assistance that TPT can provide helping to keep teachers in the professions, I think it makes many of the sellers feel more valued, which definitely helps to avoid teacher burnout.  I find a overwhelming sense of pride in my TPT store and it makes me feel valued as a teacher.  I know how hard teaching is, and I know how little we get paid, so it makes me feel so valued as a teacher each time someone decides that my product is worth spending those hard-earned dollars on and bringing into their own classrooms.  It makes me feel like what I’m doing is good and I’m appreciated in the teaching world.  I also hope that I can be that life-saver for someone else out there like that Geometry curriculum was for me in my 1st year teaching.

## Meal Prep for Teachers, Vol. 1

Teachers are some of the busiest people I know and frequently sacrifice doing things for their own well-being (like making home-cooked meals) in order to make the best lessons and classroom environment for their students.  My first day of school is this upcoming Tuesday, so I wanted to make sure that I had food ready to go for the week.  I like to have variety in what I eat, so I chose three meals to make (the order shown below is the order that I cooked them).

To try to force myself to get better at cooking and also eat a proper meal each night,  I’ve decided I’m committing to cooking 3 meals each Sunday morning to last me through the week.  Each evening, I’ll quickly make a side to go with it (steamer veggies, minute rice, fruit, etc.)

A bit about myself: I have minimal cooking skills and I don’t do mushrooms or fish.

# Meal 1: Root beer Pulled Pork Difficulty Level: 0/5 Time: 7 hrs and 10 min (10 min prep + 7 hours cooking)

Recipe from: me!

Food Ingredients:

• 4 lbs of pork shoulder
• 36 oz of Root Beer
• 1 18oz bottle of Sweet Baby Ray’s Sweet & Spicy BBQ Sauce
• 8 Hamburger buns.

Supplies:

• Crock Pot
• Crock Pot Liners (optional, but makes cleanup non-existent).
• Hand Mixer (optional, but makes shredding pork take <60 sec instead of 5-10 min)
• Large Bowl
• Colander
• Large Mixing Spoon

Instructions:

1. Place crockpot liner inside crockpot.
2. Put pork shoulder in crock pot.
3. Pour root beer in crock pot.
4. Put lid on crockpot and let cook on low for 7 hours.
5. After 7 hours, remove crock pot liner and dump contents into the colander in the sink to drain.
6. Place remaining meat in large bowl (I use a Tupperware container that I will keep the leftovers in). On the lowest setting, use the hand mixer to shred the pork.
7. In the bowl with the shredded pork, add the bottle of BBQ sauce.  Use the large mixing spoon to evenly distribute the BBQ squce.

# Meal 2: Maple & Mustard ChickenDifficulty Level: 1/5Time: 20 minutes (5 min prep, 15 min cook time)

Changes I made: Instead of pounding the chicken breasts flat, I just cut them in half, lengthwise.

# Meal 3: Sausage & Veggie Skillet Difficulty Level: 2/5Time: 60 minutes (30 prep and 45 cook-some prep happens while cooking has already begun)

HUGE Time Saving Tip: Start the potatoes first.  They take 25 minutes to cook.  While they are cooking, cut up all of the other veggies so they are ready to go once the potatoes are done.  Don’t be like me the first time I made this recipe and do all of the chopping first, and then have 25 minutes of nothing to do while the potatoes cook.  It took 90 minutes instead of an hour.

# What’s The Verdict?

I liked each of the three meals that I made this week, which isn’t something that normally happens.  I ended up freezing half of the pulled pork and half of the sausage skillet to use in later weeks.

The sausage skillet and the pulled pork are both repeat recipes that I’ve made in the past.  My favorite of the three is the sausage and veggie dish, although it is the most involved–you really are cooking for the entire 60 minutes of the recipe.  I’m not much of a sausage fan, so I’d like to point out that not all sausages are made the same.  Most are not my thing, but I’ve found a couple that I really do like.  Experiment around a bit and find one that you like because it really does make all the difference for this dish.  The pulled pork is my second favorite.  It’s so easy and so flavorful.  A really quick dinner to reheat, as well.  The chicken was good, definitely nothing wrong with it.  I just preferred the other two a bit more.  I plan to eat the chicken with steamed green beans and brown rice. I think that’ll be a really tasty and healthy meal.

Total Time: 2 hours and 30 minutes (not counting the 7 hour cook time for the crock pot pulled pork, which I started before I went to sleep the night before).

Overall, I’m really happy with my meals this week.  No duds! Woo!

## My No. 1 “Teacher Hack” For Interactive Notebooks

Making things for interactive notebooks can be tedious, at times.  If you’re like me, you use a composition notebook so students will (hopefully) resist the urge to tear out pages for scratch paper.  The issue with composition notebooks, however, is their sizing.  A full sheet of paper is much too large to fit, but a half sheet makes the page feel a bit empty.

Also, unless you want to make everything from scratch to perfectly fit in your interactive notebook, you’re a bit stuck on what to do to get full-sized materials you may have used in the past to fit.

My hack: print any normal sized paper at 80-85% the size and, after cutting out the paper, it will fit PERFECTLY into a composition interactive notebook.  Use this hack to make the world your oyster.

Here’s how to do it:
1.  Make sure your document has been saved as a PDF.
2.  When you go to print, select the following setting:

Rule of Thumb:
If the margins on the original paper are 1″, print at 85%.
If the original margins on the paper are .5″, print at 80%.
If the original margins on the paper are at .25″, print at 75% (not common).

Here’s the difference it makes:

This has saved me a TON of time making interactive notebook pages, and also allows the writing space to be much larger for students.  Sometimes a half-sheet can be cramped.  Hopefully this teaching hack can help save you a ton of time, like it does for me!