How I Teach Function Notation

Teaching function notation in math can be tricky!  Algebra students in special education will love this lesson.

I’ve found that function notation can be a challenging topic for my Algebra 2 Honors students.  My first year, it was a constant struggle and they always looked so overwhelmed.  So the next year, I totally revamped the way that I presented it and have had much greater success.  My biggest goal is for them to realize that it’s really just a different way of writing things they already know about.

I usually start with telling my students to put their pencils down, watch, and participate.  This always gets their attention.  

First, I tell them that I’m going to write an equation, but that it’s going to look strange.  I write the first equation on the board.  Then I say, “Ok, I’m going to change a few things.”  and I write the second equation on the board.  
How I Teach Function Notation - using hearts and smiley faces to make it painless  |  mrseteachesmath.blogspot.com

I ask the students what the changes are.  Someone always says, “You drew a heart instead of writing x.”  My only response is, “ok”.  Then, I write something like the next equations on the board.

How I Teach Function Notation - using hearts and smiley faces to make it painless  |  mrseteachesmath.blogspot.com

Again, I ask about the differences between the two.  At least one student will tell me that I just drew smiley faces and I barely respond.

How I Teach Function Notation - using hearts and smiley faces to make it painless  |  mrseteachesmath.blogspot.com

Next, I write something like the next two equations on the board.  They will tell me that the difference is an a instead of an x.

I continue this process with the equations below.  I don’t simplify anything at this time.  I just want them to notice that I’m simply replacing things.

How I Teach Function Notation  |  mrseteachesmath.blogspot.com

How I Teach Function Notation  |  mrseteachesmath.blogspot.com
How I Teach Function Notation  |  mrseteachesmath.blogspot.com

Then, I tell my students that we’re changing gears for a minute.  I put this picture up on the board and ask them to silently! see if they can figure out the pattern.  I totally ripped this idea off of Druin at Stat Teacher.  It’s such a great idea (go read it, really!).

How I Teach Function Notation  |  mrseteachesmath.blogspot.com

After a few minutes, I ask if anyone wants to share.  We have a discussion about what is going on and what the notation means.  Then, we talk about how it relates to the problems we did before.  I usually go back and simplify the answers from the previous problems and make sure everything is following along.

All of this takes maybe 15 minutes, but it makes such a world of difference for my students!

What do you do to teach function notation?  What works for you?

Awesome Quadrilateral Project

This quadrilaterals product idea is my favorite for high school geometry!  My students loved the social media aspect and it was so much better than a worksheet.  It really helped them with classifying and remembering the properties of quadrilaterals.
So, I just have to tell you about the best mini-project I have EVER done.  EVER.  It was awesome!
Friday was our last day of school before Thanksgiving break.  We usually have TONS of absences that day and have shortened class periods.  Last year, only half of my students were present.  So in Geometry Honors, I decided to give our unit test over Quadrilaterals on Thursday, and doing a little project on Friday.  

I actually gave very little guidance on this project.  I told my kids that they needed to choose a quadrilateral and create a dating profile or a social media page for that quadrilateral (dating profile, Instagram, Facebook, Twitter, etc.).  They needed to include 10 facts about quadrilaterals.  I told them that they would get 10 points (two homework grades) if they included all the facts and it looked nice, and they would get a sticker if it was extra awesome.  No rubric and very few guidelines - I just wanted to see what they would come up with.

Their projects were amazing.  I love them.  I wanted to share what they came up with :)  I will definitely do this project every year that I teach geometry.  In fact, I might bulk it up a little bit to make it into a bigger project that’s worth a quiz grade.

awesome quadrilateral project - kids created a social media page for a quadrilateral

awesome quadrilateral project - kids created a facebook page for a quadrilateral

awesome quadrilateral project - students created an instagram page for a quadrilateral

awesome quadrilateral project - students created an instagram page for a quadrilateral

awesome quadrilateral project - students created an instagram page for a quadrilateral

awesome quadrilateral project - students created a social media page for a quadrilateral

awesome quadrilateral project - students created a social media page for a quadrilateral

Other great quotes:
Square:  “I’m a quadrilateral with all angles and all sides congruent.  I’m hot because I’m the best of both worlds.”
Square:  “I’m not looking for rhombuses or rectangles because they look too similar to my family with their congruent sides.  I want a more exotic shape.  However, if you don’t have four sides and your angles don’t add to 360, forget it!”
“All my angles sum to 360.  #beat that triangle”
“Isosceles trapezoid has congruent diagonals.  #TwinningTuesday”
Square:  “I can be ya’ll, but ya’ll can’t be me. @rectangle @rhombus”
Rectangle:  “I’ve got all the right angles #LOL #punny”
“That moment when… you realize you’re an awesome kite with perpendicular diagonals, but can’t fly.”
“I’m looking for a trapezoid, because I like big bases and cannot lie.”

Trapezoid:  “I’ve got a rockin’ bod with exactly one pair of parallel sides.”




5 Random Thoughts

I often post teaching ideas and the like, but this was originally created as a place for my reflection and professional development.  In the spirit of professional development, I thought I’d post some of the things I’ve been thinking about lately.


I need a change for next school year.  I love teaching Geometry (honors and/or on-level); it’s my favorite prep ever.  I’m ambivalent about Algebra 2 Honors.  I love honors level sophomores, but I’m getting tired of it.  I don’t know if I want to request a new prep, move to a new school, or move to middle school.  I’m still trying to work and grow as a teacher, but I’m getting bored where I am.  I’ve been making special requests for middle school teachers to see if I like the curriculum.  We’ll just have to see where I end up!


I joined Tsu.  It’s a new social network that looks like Facebook.  They say you get paid to share and interact with others.  You get 1 cent for every share your posts get.  I’ll be real, I’m not going to make any money on this site.  However, I do like that it doesn’t have any ads.  Lately, my Facebook looks like a huge commercial.  It’s nice to look at Tsu where I only see posts from people I’m friends with or following.  Right now, you can only get in with an invite.  So, here’s my link if you want to see what it’s about!  My short code is: mrs_e_teaches_math 
  

I’m starting to notice maturity in some of my freshmen.  It seems like it’s been all of the sudden over the past two weeks.  A freshman boy emailed me last night to let me know that was going to miss a test on Thursday (as he should have), BUT he also listed three alternate times that he could take the test.  I’ve been trying to teach my kids that they need to solve their own problems.  This is a big step for a 14 year old boy.  Yay!  I’ve also had more kids take advantage of homework time during class.  They’re finally starting to see that working now means less homework later.  Maturity!


In Honors Geometry, we expect that students remember the geometry they learned in middle school.  My kids remember the Pythagorean Theorem, but they don’t remember that it only works for right triangles.  I haven’t encountered this in previous years.  Interesting, I wonder what changed.



I have a few kids that just aren’t studying at all in Geometry Honors.  It’s driving me nuts!  We finishing our Quadrilaterals unit.  I’m sorry, but if you’re not going to study the properties of a parallelogram, there’s not a lot I can do for you.  I don’t know how to fix this.

Case in point:
Student:  Can I do corrections on my quiz to get points back?
Me:  This is honors.  We don’t do test corrections.  Have you been doing your homework?
Student:  No.  I just have homework every night and don’t want to do it.
Me: (Seriously, kid?  I only give homework 3 nights a week and this is an HONORS class.)  Maybe you should try that.  
**Not 5 minutes later**
Student:  Will you help me with this?  I don’t get it.
It was a diagram with a parallelogram and missing angles.
Me:  What is confusing you?  This is a PARALLELogram.
Student:  That doesn’t help me.
Me:  Where are your notes?  Let’s look it up.
Student:  I threw them away.
Me:  You may want to copy them from a friend.  What do you know about the sides in a PARALLELogram?
Student:  I’ll just have my tutor do this with me.
SMH

Dollar Store Finds for the Classroom

I don’t go into the dollar store very often.  If I do, there is usually something specific I’m looking for.  Well, the other day I just so happened to be in the dollar store and was just impressed with the amount of things that would be great for a classroom!  I started taking pictures and thought I would share!

Here are some great dollar store ideas and hacks for teachers!  I love these ideas for organization, crafts, and projects!

Construction Paper - I love construction paper for my proofs cut-out activities.  There are so many great uses for construction paper, even in high school classes.

Dollar Store Finds for the Classroom - Construction Paper

Magnetic Containers - How cool are these?!  My whiteboard is magnetic.  These would be so cool to hold little things and just stick on the board.  They would also stick well on file cabinets.

Dollar Store Finds for the Classroom - Magnetic Containers

Dice - Um, 10 dice for $1?  Yes, please!  There are so many activities that can be done with these.  (If you need more than 10, this isn't a bad deal on Amazon!  100 dice for less than $8)

Dollar Store Finds for the Classroom - Dice

Foam Dice - These are just cool.  It could get expensive if you needed a bunch, but think how quiet they would be!

Mrs. E Teaches Math:  Dollar Store Finds for the Classroom - Foam Dice

Playing Cards - I have several decks of playing cards right now, but they were all $1 each.  2 decks for $1?  I can do that.

Mrs. E Teaches Math:  Dollar Store Finds for the Classroom - Playing Cards

Microfiber Towels - I use microfiber towels to clean my whiteboard.  They are the very best.  When they get dirty, I just bring them home and run them through the washer and they’re as good as new!  They do stain pretty bad, but they’re just for cleaning the board, so I don’t care.

Mrs. E Teaches Math:  Dollar Store Finds for the Classroom - Microfiber Towels

Plastic Baggies - I’ve used gobs of plastic baggies in my teaching career.  I put all of my sets of matching cards, task cards, and everything in plastic baggies.  My kids wreck the bags over time, so I don’t want to spend a lot.  I prefer the bags that fold over.  That way I can press them down to squeeze the air out without unzipping the bags.

Mrs. E Teaches Math:  Dollar Store Finds for the Classroom

Plastic Silverware - I saw this post awhile back about taping spoons to pencils to prevent them from “walking off”.  Cheap plasticware would be great to use.  They had all kinds of cool colors!

Mrs. E Teaches Math:  Dollar Store Finds for the Classroom - Plastic Silverware

Zip Ties - Organize any cords in you classroom with zip ties.  There are tons in the package, so you could use them for years.

Mrs. E Teaches Math:  Dollar Store Finds for the Classroom - Zip Ties

Scissors - I have a class set of scissors that I purchased from the dollar store.  When I was buying scissors, I could’t afford to buy the fancy ones that are $3 or more per pair.  I bought them for $1 each from the dollar store and they’re great!  This would be an especially good buy if you use interactive notebooks.

Mrs. E Teaches Math:  Dollar Store Finds for the Classroom - Scissors

Stickers - This was the whole reason I stopped at the dollar store.  Whenever my students make an A on a test or quiz, I put a sticker on it.  My kids love getting stickers :)  Target Dollar Spot usually has good stickers around back to school time as well.

stickers

I bought these :)  For some reason, I think they are SO funny!

Mrs. E Teaches Math:  Dollar Store Finds for the Classroom - Stickers

Special Quadrilaterals Always, Sometimes, Never

My students always seem to struggle with always, sometimes, and never statements.  I made this card sort to help them practice and give them an opportunity to discuss with their classmates.  I used it as their bellwork.  You can read about my love for card sorts here.

Special Quadrilaterals Always, Sometimes, Never - Using a card sort  |  mrseteachesmath.blogspot.com

My students sorted, discussed, resorted, and discussed more.  I was very pleased with the conversations that I heard going on.  A few groups started drawing venn diagrams to help them.  Overall, I was very pleased with the results.

Special Quadrilaterals Always, Sometimes, Never - Using a card sort  |  mrseteachesmath.blogspot.com

I also had students fill out this family tree to help them see the relationships between the special quadrilaterals.  I have another page as well for parallelograms, rhombuses, rectangles, and squares.











5 More Ideas for Using Task Cards in the Classroom


This post contains a Amazon Affiliate links.  This does not effect you in any way.  However, if you make a purchase through this link, I receive a very small commission that keeps this blog running.

Earlier, I wrote about 7 ideas for task cards in the secondary classroom.  Today, I'm giving you 5 more ideas!

Want ideas about how to use task cards for middle school and high school math?  These free activities, games, and ideas will keep your students engaged!

1.  Solve 'N Switch - Students work in pairs and each pair gets their own “deck” of cards.  Each partner takes a card and solves it.  Then, the students switch cards and solve the problem again.  They can compare answers and discuss if their answers don’t match.  When their answer is correct, they move on to the next cards in the stack.  I love using this, but it does take many “decks” of cards.

2.  Tic-Tac-Toe - Students work in pairs and each pair gets their own “deck” of cards.  They draw a tic tac toe grid.  One student will choose a card from the face down stack.  The student will work the problem on the card.  If they are correct, they get to put an X or an O on the board.  Then, the next student takes their turn.

5 More Ideas for Task Cards in the Classroom - Tic-Tac-Toe

3.  Mix, Pair, Share - This is a Kagan cooperative learning strategy.  This is similar to Quiz, Quiz, Trade.  Music is played while students walk (or dance LOL) around the room.  When the music stops, they freeze and pair up with the student closest to them.  They share the problem on their cards and work the problems.  When all of the students have solved their problems, the music starts again.

4.  Traditional Partner Games  - Students work in pairs and each pair gets their own “deck” of cards.  A student will draw a card and solve the problem on it.  If they are correct, they get to take their turn, if they are incorrect, they miss their turn.  The students continue playing until someone wins the game.  My favorite partner games to use are checkers and Connect Four.

5 More Ideas for Task Cards in the Classroom - Board Games

5.  Scoot! - It’s helpful if the desks are moved into a circle for this game, but it’s not necessary.  Give each student a task card and they work the problem on an answer sheet or scratch paper.  Then, students move to the next desk when you say “Scoot!” or “Rotate!”.  When the students have gone through a certain amount of cards, go over the solutions as a class.  My students don’t really like this one because they only have a certain amount of time to complete this card.  However, I like it because it helps me see how long it is taking them to solve certain kinds of problems.  It’s helpful for me if I’m having a hard time gauging their understanding with other formative assessments.

5 More Ideas for Using Task Cards in the Classroom - Secondary Style :)  mrseteachesmath.blogspot.com

I hope you found some useful ideas!  You can always find task cards in my Teachers Pay Teachers store.  How do you use task cards in your classroom?

November Currently

I'm linking up with Farley from Oh' Boy 4th Grade for her November Currently.



Listening…  I bought The Big Bang Theory Season 7 last night.  I’m on disk two :)  I love Big Bang!

Loving…  It’s finally below 80 degrees here in Texas!  It was in the 60’s today and I wore my fleece jacket the whole day.  I don’t mind the heat, but it is nice when it finally cools down.

Thinking…  I’ve been thinking about getting a new custom blog design.  I just can’t decide which designer I want to use or what I’m looking for.  Everything on my blog now I did myself; it’s time for an update.

Wanting…  I really want some new Crossfit Nanos.  I just retired an old pair of workout shoes and would like a new colorful pair.  The teal and the berry are my favorites.  I just can't decide which color!

Needing…  Honestly, I feel like two days isn’t enough for a weekend!  On the weekends I try to catch up on sleep, go to the grocery store, prepare food for the week, do laundry, clean the house, work on Teachers Pay Teachers projects, and update my blog.  I can’t imagine how people with kids do it!

Reading…  I’m not reading anything right now.  I’ve been to exhausted by the end of the day to pick up a book.  However, I am wanting to read the Love and Logic series.


This post contains Amazon Affiliate links.  This has no effect on you, but if you do make a purchase through this link, I receive a very small commission that I use to keep this blog running.




Related Posts Plugin for WordPress, Blogger...
Powered by Blogger.
Back to Top