June 1, 2014

Quadratic Functions Unit

Well, my students and I have been in quadratic functions for quite a while now! Especially since our EOC testing fell in the middle of it all. 
I also feel like I did much better job this year with letting them explore/figure out the intricacies before we formalized in their notebooks. So, for example on the "factoring" pages, we spent a day just using algebra tiles to understand what was truly happening and the relationships between the numbers. Then we formalized. 
All that to say, quadratic functions took a long time! But my students really seem to have a good understanding.

So... here are my notebook pages.

Man, as I'm uploading, most are blurry. So sorry!! Silly phone camera :(

Our Learning Goals/SBG page.
I plan to implement SBG more next year and these pages are allowing me to dabble in the idea without fully committing yet.

Investigating a quadratic function for the first time...

Focus and Directrix pages from Sarah. The kids LOVED seeing their parabolas take shape in the wax paper. I know that focus and directrix aren't technically in my algebra 1 standards, but I just couldn't resist!

The same properties of quadratic functions pages that I did last year. Still worked well and still a hit!

Angry birds and vertex form. 

Standard Form and a summary page from here. I tweaked it a little to fit my needs. 

Here's a better picture of the summary page. 
Original idea and post HERE

Then the discriminant and quadratic formula.
The students and I derived the quadratic formula (yep, that ones officially in my standards) but I haven't taped it into my notebook yet. The big orange box is where it will be taped soon. 

The factoring and completing the square pages took multiple days and I wanted to give students plenty of time to explore with algebra tiles. I gave lots and lots of problems that students built and answered with the tiles before we ever formalized and talked about procedure. 

I really liked doing it this way because students understood the factoring method. We were un-doing the distributing and pulling everything back apart. There was so magic wand waving - just some great mathematical understanding happening. 

Also with completing the square. We built lots and lots of squares, filling the missing corner and then looking at side lengths and x-values before every going through just the process. 

Well, these are most of the pages! A lot happened in class between all those pages, so sorry I can't bring you in for that! Hope something helps!

May 18, 2014


Sorry that I've been MIA for a few weeks now! Lots and lots going on...

I'll wrap up my First PBL series soon with my student presentation information and a reflection on the entire process. There were definitely some things that I loved and some things that I didn't. It's always about trying new things and a growth mindset, right?

Since the last time I posted, my Algebra 1 kiddos have finished their End of Course testing. So glad that big, looming test is out of the way! I can focus on finishing up those last final details now. 6 class periods left!
Have you seen this pin floating around pinterest? Cracks me up!!

Our sweet furbaby also gave us a scare last week.

Full disclosure, we are some of those people that love our animals way too much. They are most definitely part of our family. This spoiled princess had a lump on her left shoulder region for about a week and it didn't go down. We took her to the vet and they were definitely concerned. Did a biopsy - waited 51 excruciating hours for results - no cancer and no tumor! Praise the Lord!!! The Mr. and I cried when we received the good news!

Also more good news!!!!

I have been selected as a 21C Grant recipient in my district!!!!!
This means I will have a class set of 30 laptops beginning in the fall. 
Beyond. blessed. and. excited.

Back Story: I teach 8th grade at the same junior high that I went to for 8th grade. Never planned on that happening, just a fun coincidence! :)
The head of the 21C committee (and the woman I'm fiercely hugging in the picture above) is our district's Director of 7-12 Instruction. She was also the building principal of this school - the one I attended and now teach at. Such a fun and sweet moment that she got to award my grant in one of the same classrooms we were both in 13 years ago. Fun day!!!

My face. Oye.   

Out of the 24 grants awarded throughout our district, SIX were in my building. The other recipients and I had a conversation and attributed this feat to our incredible principal. He is inspiring, positive, and a world class leader. He brings out the best in people and makes us all want to achieve greatness. It was also mentioned that we don't know how long our little junior high will be able to keep such a great leader as our principal. Fingers crossed that he stays for a few years before moving on to bigger and better things.

Another fun thing that I've been working on...

I don't know about you, but around this time of year I get soooooo distracted with thoughts of next year. I would rather redo my syllabus, fantasize about room arrangements, and create a teacher planner than lesson plan for tomorrow. Oops. Please tell me I'm not the only one with this issue?!?!?!

Anyway... I looked around the internet and just didn't fall in love with any teacher planner. I am so stinking picky I wanted it to fit what I needed exactly. And didn't want to feel like I was paying for pages I would never use. I have other places that I record grades and parent information. I needed a place to lesson plan, conveniently store standards, and take meeting notes. So... here it is!!! I am pumped! This will probably take the place of this binder for this year. We'll see how I like it!

And yes, as always, I'll give away the file for FREE. 
But side note about that, it just really burns me up when I see stuff I've created and given away show up on Teachers Pay Teachers. Has this happened to anyone else?! Makes me furious!!!!! I try not to get cynical and remember all the wonderful teachers that I benefit from and hope I'm doing the same for others, but really, come on?! I had to go all Creative Commons Non-Commercial 3.0 on someone's butt earlier this year.
Don't sell what isn't yours! Alright, rant over.
Enjoy the file :) But don't you dare turn around the sell it!

A special thank you for the free chevron file!
Also the free washi tape png files
and Kimberly Geswein for the free font called KG Eyes Wide Open.

See, creating and giving away for free really does make the world a better place. :)

Well, I guess that about wraps up this post full of random musing. I will try to go lesson plan for these final days of the year when all I really want to do is enjoy the outside and get ready for next year! Have you seen this syllabus by Rob Patin?!?! Drool worthy. I will be revamping my syllabus soon!!

May 1, 2014

My First PBL Unit - Day 5 & 6!

Here are the previous posts:
Day 1
Day 2
Day 3
Day 4

Here is how I started day 5...
Teams talked and most came up with C because it got the closest to the most points. BINGO! We talked about what was wrong with all the others, especially A since it tripped up a couple groups.

After that, groups got to work using their simulation data to create scatter plots.

They created one scatter plot for each of their survey choices; a, b, c, d. They compared sample size to number of people with that choice. They made their line of best fit based on that, and then predicted the outcome of each choice for our entire town's population.

Here are some in-progress shots...

And here are some finished poster shots...

 (yes, the one above has a couple errors. They fixed them next class.)

consisted of groups finishing up and preparing their presentations. I told them they had to tell us which product they were launching and show the data to support their claim. The rest was up to them!! I have a few groups that filmed commercials, one that is making an infographic, one made an online animation with voice over, and of course a few that are using powerpoint. Tomorrow is presentation day and I am SO excited!!!!!

April 22, 2014

My First PBL Unit - Day 4!

Here are the previous posts if you've missed them:
Day 1
Day 2
Day 3

We ended the previous class by recorded our large set of data into our notebooks. We began this class by finding the percentages of each response for every person surveyed this far, our class and our large group. I have students the following information to help them format their page and guide their calculations.

I told them to add together every number in the highlighted boxes and put their total where I have red type. Then I told them to use their own data in every place that was caps and italicized. It worked pretty well actually. Only minimal chaos for a few minutes as students were confused :)

We wrote down the bottom sentence "we will use an online spinner to simulate a random sampling of our data" and then discussed that actually meant. I told students that I wanted to pretend that I had all 187 people surveyed gathered together in the gym at the same time and I wanted to randomly pole 5/10/30/etc. of them at a time. They grasped this concept and we talked about sample size for a bit. I

I asked the question "is it possible for all 5 people that I randomly select to choose a?" They all agreed yes, that's possible. I then asked "is it more or less likely that all people choose a if I randomly select 20 people?" Everyone agreed that was less likely to happen, although still possible. This lead us down a discussion path about larger sample size = more accurate information.

After I felt like students had a grasp of what that last sentence meant, and why we were going to simulate random samples, we used the spinner feature on Math Is Fun, found here. I chose this spinner because it was very user friendly and allowed my students to easily manipulate the section percentages. I demonstrated on the projector how to change the percentages to match those that each group just calculated.

Once each group set the percentages and clicked "update," we were ready to simulate!

I showed how you can set the number of spins, simulating how many people we were choosing at a time. The bar graph under the spinner records the results. I also stressed the importance of hitting the reset button between each random sampling, otherwise the graph would just continue counting and we wouldn't have accurate results. One person in each group usually took it upon themselves to make sure reset was pushed each time. You would hear "RESET!" from across the room at random times. It was pretty funny!!

We recorded our simulation results on page 125 in our notebooks. I showed this to help with formatting.

We didn't have time to start our scatter plots yet, but groups did set up their large grid paper in preparation for graphing. Here's one so you can get the idea.

We'll start creating our scatter plots using simulation data next class!! My students are taking their MAP Test and then going on job shadowing before I see them again for math content. :( It will be about a week before we get back to this project.

So... now that I'm really into my first PBL unit, do you have any advise or pointers? Any things you would have done differently than me? I am completely open to suggestions!

UPDATE: Day 5&6 are here!

My First PBL Unit - Day 3!

Here are Day 1 and Day 2 if you missed them.

Both of those days were full block classes, meaning we had 80 minutes. Day 3 was a "fast Friday" schedule so I only saw them for 40ish minutes. 

When students brought back their survey results, they tallied up each answer choice and then put that data in our shared class spreadsheet. Here is an example from one class.
I projected the spreadsheet so all students could record their important information.

We recorded data on page 124. I showed this... as a reference.

We talked about if our class data was a good representation of the larger group, and how we could then project for an even larger sample size, like our town or state.

This took most the class period. Students used the last 10-15 minutes to brainstorm how they wanted to present their final projects. I think a couple groups are going to make a commercial!! I'm excited to see them!

UPDATE: Day 4 is here!

My First PBL Unit - Day 2!

Here's DAY 1 of the unit if you missed that post.

On Day 2 students arrived in class and finalized their questions in their teams. We completed page 122 in our notebooks about the project. Here is the slide I put on the board to help direct students.

Once each group finalized their wording and choices, they emailed me their questions. I quickly compiled all the questions into one document and made sure formatting was cohesive. I printed each student one copy of the survey to use. We talked about how we needed a lot of data but didn't want to ask a lot of people. We decided that each student would ask all of the survey questions to 10 individuals, making sure they hadn't already been asked the questions from another classmate. When we come back to class next time and compile our data, every team will have 200-250 pieces of data! Perfect.

We also briefly discussed biased data and how we need to make sure to collect random samples. We also need to ask our questions without swaying the participant's vote.

We then set up page 123 to survey our class. Like so...

Each class of students decided that just asking the questions wouldn't get us a good survey - people would be influenced and pressured to vote a certain way. Guess that high-tech way each and every class period decided to use to be anonymous in our surveying? The good 'ole Heads Up, Seven Up approach! Heads down on the desk, eyes closed. The surveying group read their question and answer choices and then recorded the votes. It worked quite well!! HA! I'm just glad they recognized bias and came up with a solution to prevent it! After the class surveys, each group used their data to predict for a larger sample size. I didn't direct the students about how to predict, so groups used different methods (find percent and multiply, set up proportions, use some logic). Worked for me! They all did something mathematically relevant so I am happy.

Since our next step was to survey people outside our class, we went ahead and created a foldable to cover some vocabulary. I have used this foldable for two years now, with a couple tweaks, and really love it. The idea is originally from Sarah at Everybody is a Genius, found here.

Next class, we will compile our data and begin to do some mathematical analysis!

UPDATE: Day 3 is here.

April 14, 2014

My First PBL Unit - Using Data in 8th Grade Math

Well, I'm embarking on a new journey. Read my first thoughts about PBL here.

I'm using the What Will They Think outline from the Buck Institute published at PBLU. While I'm tweaking a few things, the main project description is here if you want it.

DAY 1: The intro

I created a glog to organize all the pertinent information students might need. I'm using it like a project overview page would be used. It's here if you want to check it out. Here's an image if you don't want to click around.

First we watched the Coca-Cola video and talked about how companies do research before they launch new products. We also discussed the Taco Bell Doritos tacos and Jelly Belly flavors. I told them that they were going to be researching and launching a new product. We then brainstormed what they would need to know in order to accomplish this. I made a list on the board and then we created our driving question from that list. 3rd Hour came up with: How can we use research and data to find out what products people want?

From there, I put students into groups of 3 and they brainstormed product ideas and possible answer choices. We talked about needing clear and viable answer choices or our data would be unusable. As they finalized their ideas on a piece of blank paper, I gave these guidelines:

After they had their ideas down, they passed their paper one group clockwise. I set a two minute timer and groups critiqued and offered suggestions. I put up these guidelines for that part:

Once all the rotations were complete, we had about 7 minutes left of class. Each team had a different color to write their comments, this helped students clarify if they had questions later and also provided a bit of accountability; here were how the group papers ended up.

I told them to review the comments and suggestions from their classmates and also get ready to finalize next class. I gave these guidelines:

Next class period I foresee us creating our surveys and making some predictions. I'll report back after Wednesday!

UPDATE: Day 2 is here.
UPDATE: Day 3 is here.
UPDATE: Day 4 is here.

March 30, 2014

Project Based Learning - My Questions


Oh good, did you like that image and follow it here from twitter or Pinterest?
Were you thinking I was going to give you a lovely list of bullet pointed answers for all those questions?
HA! Not a chance! I don't have those answers!
But I would like to invite you to stick around, continue reading, and contribute your ideas.

All edits and updates will be in red.

*I'm attempting my first full PBL experience - Eekkkk!!! Wish me luck!!! Even if I don't soar on this one, at least I'm headed in the correct direction, right? I'm focusing on having a "growth mentality" like Tim talks about HERE. I'll chronicle my journey in this post.

This post might ramble and meander a bit; my thoughts are not completely formed yet and I'm sure that will show...

I'm not content with my current level of technology integration. I recently posted an update on my workshop/stations model and it really has me thinking. These stations are helping lots of students, less are falling through the cracks, but it's all in the context of a very teacher-directed atmosphere. I do not do stations every day, we recently did a volume investigation with rice, but I still feel like that was more me-centered and student-centered than I would like.

I've read a lot of articles about project-based learning and really want to move towards that model, but I just can't quite figure it all out. I'm hoping you can help me think through these questions and together we can figure it all out. I'll update this post over time (a thousand times if I need to) if we can start a conversation and pull together resources. I'd love to host that! I think it'd be beneficial for a lot of teachers!! Or if someone is already curating and hosting that, please point me in their direction and I'll jump on that wagon. I just need to see this thing in motion; I need to see it working.

Here are some current questions/thoughts rattling around in my head:

-- I can begin a unit/project cycle with an entry event that peaks the students' interest and gets them curious. It needs to be a real and relevant problem that is understandable to 8th graders and yet complex enough to require driving questions and a real solution.
Emergent Math's PBL Curriculum Maps HERE
Intel Unit Plans HERE
PLB U by Buck Institute HERE 

--After peaking their interest, I can lead a discussion to provoke some driving and enduring questions. Here is my first conundrum. If I want these questions to be student-created, what if they don't think of the right things to allow for enough mathematical discovery? I guess I could prompt/lead them? I should make sure my entry event can lead to enough? So in reality these questions are not completely student created, I knew what I wanted them to create, I just let them get there on their own without me giving them here are your questions to answer. Right??
Conversation with @RossCoops31 on twitter regarding driving questions:
ME Do different students work on different driving questions or do all students answer the same few questions?Thx!
ROSS: I usually do one essential (driving) question that is decided upon by my class (Google Form).
ME: So do all finished products cover relatively the same information? Do you have Ss work individually or groups?
ROSS: Either group/individual works! All products different, but demonstrate same understandings.

--Now that we have our guiding questions I will give my students the requirements of the project. "In X many days you (or your group) will be responsible for _____." This will be some sort of synthesis of information and presentation that utilizes technology and is published to a global community, I'm thinking a blog. Wouldn't the best way to give these requirements be a rubric? Does someone out there already have and use a wonderful rubric that I could see?
Rubrics from the Buck Institute (bie.org)
Project Design Rubric HERE
Collaboration Rubric HERE
Critical Thinking Rubric HERE
Creativity and Innovation Rubric HERE

--Alright, so students have their interest piqued, they are genuinely curious, they have formed their questions, and I have given my rubric. Now they research and synthesize and create. I roam around the room for however many days it takes to finish up these projects, giving feedback and guiding, and then students present. I really like the following quote from the Buck Institute for Education regarding this phase: In real inquiry, students follow a trail that begins with their own questions, leads to a search for resources and the discovery of answers, and which ultimately leads to generating new questions, testing ideas, and drawing their own conclusions. With real inquiry comes innovation - a new answer to a driving question, a new product, a new solution to a problem. The teacher does not ask students to simply reproduce teacher- or textbook-provided information in a pretty format. Are you inspired yet?!?! I know! There are so many great resources like the Buck Institute that make me want to jump in with both feet but I have trouble finding real teachers talking about doing this in their classrooms. I feel like I'm moving that directions, using Mathalicious and 3-Act Math and similar things, but I don't think I'm quite there. These are engaging and definitely better than traditional lecture, but I'm not pulling off a true PBL classroom.

This is one of my largest question marks at this point. How big of a problem do I really need? I feel like the lessons at Mathalicious and YummyMath and Robert Kaplinsky aren't big enough. They have pre-determined questions and a set order of business. These are fantastic problems, but I don't think I'm letting the students really ponder, inquire, and direct their own learning. People doing this, what types of tasks do you use? Are they on a blog somewhere I could see?? 

--Sorry, little bit of a tangent there, back on track.

--So students have created and presented, to both their classmates and a global community online, and I've made sure we've nailed down all the mathematics that were needed throughout this unit. I figure at this point I might have a day or two of formalizing. Here is how mathematicians write about/talk about/use the ideas we all just learned about.

--So did we do it? Are we done? Was that Project Based Learning? Is that how my units can all look in the future?  How long should one of those cycles take?

Here is where I definitely need your help!
Are you currently doing this? Do you know someone who is? Do you have any rubrics created that you'd be willing to share? Do you have any of those entry events that are large problems and could facilitate lots of mathematics? Can you share about part of this process that I completely missed the boat on? Please share your thoughts, ideas, wisdom! Please!! This is an area I'm very unsure about (as if you couldn't already tell) and I'm definitely leaning on my PLN here.

If you don't have anything to share, are you a teacher that is also hesitant and curious about this whole process? Could you please comment and let me know I'm not alone! :) Maybe a few of us together can convince those with the answers to share the goods. I promise to come back and update any useful information I receive.

Other teachers' comments/emails:
Ben Mahas (@greenemiddle) posted on twitter: "Help answer @MrsHestersMath questions are about implementation of pbl. bit.ly/21c-pbl I'm interested as well #mtos #mathchat"
Shelley via email to me: Thank you for your post about PBL. I have many of the same hesitations and have been looking for a place where someone is sharing what really works in a classroom. I hope you can get some answers to those questions and thank you, in advance, for posting those answer.
Rick via email to me: I have a lot of the same project based leaning questions. Thanks for the post. I'm right there with you. You're not alone!

So - those of you with some expertise, please share!!!!

Some Twitter People to follow for PBL
Buck Institute for Education @biepbl
Geoff Krall @emergentmath
Michael Gorman @mjgormans
Dayna Laur @daylynn
Chris Fancher @cfanch
Jerry Blumengarten @cybraryman1
Mrs. Telannia Norfar @thnorfar
Ross Cooper @RossCoops31
Jolene Speckman @JoleneSpeckman

Some General PBL Links
Edutopia's page HERE
Buck Institute HERE
Buck Institute's Recommendations for Teachers HERE
Jerry Blumengarten's page HERE
High Tech High HERE (a school pulling this off on a very large scale!)

March 25, 2014

Math Stations - Update

Well, I've been using stations for a few weeks now and wanted to post an update and ask for some advice.

Here's a tweet from a few weeks ago so you can see the general layout. I've changed it a bit lately, but generally it's the same. The back right grouping is where they work on computers doing TenMarks, the back left group is quizzes/hw/etc, and the front 12 are new content with me.

Things I'm loving!
  • Students are getting targeted remediation. I am setting student-specific goals through TenMarks. I also have this taped onto each desk in the TenMarks station... very helpful!
  • I feel like I'm reaching more students since I'm only giving instruction to about 12 at a time.
  • 8th graders have a relatively short attention span - 17 minutes and then rotating is helping to keep them focused.
  • Students are accomplishing a lot in one class period. Targeted, timed things to accomplish are working very well.
Things I need to improve:
  • I still feel the need to monitor/watch the back groups. I need to let this go! 
  • I want to give students more than 17 minutes for TenMarks. Hopefully when I get for more computers (I'll have 10 total soon) I can move to only having three rotations of about 25 each.
  • It's really hard to say the same thing over and over, especially now I'm doubling up in each class period. I have to be very careful and not leave anything out because I've already said it about 12 times!
Sorry I don't have pictures of this workshop thing in motion - I'm always with a group of kids! That's another thing that's hard. I used to grade during the few minutes that students were working on quizzes or homework. Now, I'm with a group of students while others are quizzing, meaning I don't have time to grade/check email/nothing! Bell to bell!! It's hard!

So what are your suggestions? Any ideas for my 'improved' list? Any general thoughts or ideas to add?

March 23, 2014

Pythagorean - Part 2

Part 1 with my new intro for this year is HERE.

Our finished right triangle pages looked like this...
I know that's kind of a crazy picture. I used my CamScanner app and sent it to a student that was in ISS so she could check her work before moving to the next activity. 

If you don't have CamScanner I highly recommend it! I can scan and save as a high quality pdf right from my classroom - huge time saver!

Anyway... next we completed this little booklet. 

It was all about the relationships between areas and side of the squares formed. Never once did my students plug into a formula while completing their book - I love this! The types of problems are from Christa Lemily here, I just made it into a little booklet for their INB. The students were all commenting about how easy it was and how much sense it made. When we completed our town map next, the students were breezing through. I had to show one example about how mathematicians organize their work because we hadn't been showing work before. But conceptually, they did great!

They completed the map with more ease than my students did last year, and these students are classified as "less advanced" than my students were last year. That, to me, says the intro and conceptual booklet worked!! YAY!

Next we calculated distance between points.

When you flip the flap down that says "Calculating Distance Between Two Points" it looks like this...

Yes, I know, the distance formula is not explicitly an 8th grade standard. But if I'm doing distance between points on a coordinate grid why wouldn't I mention it?! We talked about how they would see this formula later and it contains the same math as the Pythagorean Theorem. We color coded the same work in both methods so students could see the connections. Hopefully they'll remember this at least a little next year and go look it up. Fingers crossed!

So there it is, my week of Pythagorean Theorem and distance. Got any helpful critiques or suggestions?

Here are your files:

March 21, 2014

Making Sense of Linear Inequalities

We were treasure hunters today!!!! And the students LOVED IT!!!!

I gave them a map of our town (a different region than I used here) and told them I was going to give them clues about some recently confirmed buried treasure. They laughed and got into it - thank goodness - because I would have sounded like an idiot even more than I already did trying to talk in my best pirate voice.

I told them that part of their clues were going to include roads and part were not, they needed to show those things differently on their map. Many used a darker line to show included roads.

The clues were:
  • The treasure is somewhere south of 8th street.
  • The treasure is either on Tiger Boulevard or east of it, but definitely not west of Tiger Blvd.
  • The treasure is either on or north of 14th street.
  • The treasure is west of J street.
This gave them a relatively small region of town where the treasure could be located.

Then they did a partner activity. They had to build a barrier and I gave each partner a paper with two maps, one with a shaded region and one without. They had to describe their shaded region to their partner using clues like mine, and then listen as their partner described. It really made them focus on precise language and boundary lines.

When we transitioned to inequalities on a coordinate grid they were pros already! The dotted line/solid line made prefect sense and shading towards the region that satisfies the inequality also made sense. Success!!

I will definitely be using this type of introduction in the future!

What innovative ways do you use to introduce this (or any other!) topic. I'd love to steal them :)