Monthly Archives: July 2016

Stars of the Week Vol 1

Maybe it’s just me: I star A LOT of stuff in my blog reader and I star (ok, “heart” now) a lot of tweets, but then never go back to them! So I thought I’d try to post weekly things I’ve starred so (a) you can enjoy (b) I can remember and (c) the posters can get a shoutout. ūüôā

PSA: You don’t have to make a fancy post to let someone know you’ve appreciated something they’ve done. A tweet, retweet, or blog comment can really mean a lot to #MTBoS newbies members! I’m going to try to keep these posting going weekly, as well as tweeting someone when I use their stuff! ūüôā

My starred posts this week:

Not a post, but if you’re in the Southern US (we’re going ahead and defining that as “Tennessee-adjacent”), be sure to add your name & info to the roster! Hope to plan a mid-fall tweet up!

This first post from Hannah (@girl_got_range) is a great long form about vulnerability in teaching and in life.

Go ahead and read all of @Anniekperkins‘s¬†first 5 posts, but be sure not to miss the latest one¬†about how her “uncompromised beliefs” ended up being a bit, well, compromised.

For something a bit more lighthearted, check out Casey’s (@cmmteach) ABCs of TMC.

Getting a chance to hang out with Brian (@_b_p) at TMC reminded me yet again of his quiet succinct genius. Be sure to follow his blog for little nuggets of awesomeness, like this great way to introduce end behavior. I can see many ways to use this same setup, such as limit notation and his example of sigma notation.

Sarah (@mathequalslove) collected some great resources from 3 different blogs-I love the last one about asking what question each expression answers. And I love the cubic meter. And I love the crime scene. Ok, I guess I love all three!

Also check out her broken circles first day activity. And while you’re at it, Amy’s (@zimmerdiamonds) first day ice-breaker with a secret agenda¬†(watch the periscope video here). ¬†And then check out Beth’s (@algebrasfriend) entire collection of first day activities. Basically I need a month of first days.

If you’re looking for a one-stop shop for expert advice for a newbie or oldie, be sure to check out Elissa’s (@misscalcul8) new How To posts. She’s already made them for teacher moves, questioning, and building relationships (I also predict an organizational one soon). Even if you’ve heard¬†some of the stuff before, I bet you haven’t heard¬†all of it before!

Because Julie (@jreulbach) likes to mock me, she is going all gung-ho on Algebra II¬†the first year in over a decade that I haven’t taught it! Be sure to join her blogroll and submit posts to her recaps! Also check out her post on reliving TMC16 through video!

In those TMC videos, I would recommend Joel’s (@joelbezaire) Math Game with the Lame Name and Gregory’s (@mathtans) genius cubic formula parody¬†song¬†(I’m still amazed how he was able to write that!!)

And now some of my starred tweets:

And as a reward for making it through, let’s end this first post with a song!

Category: Stars of the Week | Tags: ,

#TMC16 Twitter Session: Dot Replies, Convos, and Diving In

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At TMC16, while walking back from lunch with Hannah (@girl_got_range) and Tom (@trigoTOMetry), someone brought up the fact that even though we are at¬†Twitter Math Camp, we still need some help navigating Twitter. After a few tweets, Glenn (@gwaddellnvhs) and Justin (@JustinAion) graciously offered to host a flex session on it Monday afternoon. I attempted doing sketch notes during the presentation, then attempted again when I got home, but, er….well, I’m just a digital gal, I guess! ¬†So here are some of the major things we learned:

First and foremost, WTF is a dot reply?

WTFDotReply

Here is the word doc if you’d like to modify it or share it. ūüôā

After four different attempts at trying to create something pretty, it’s just going to be easier to blog about following Twitter conversations–something with which I always struggle! I always have FOMO (fear of missing out) on part of the conversation!

Justin came up with the clearest way of describing a Twitter convo: imagine the original tweet is the trunk of a tree, and reply thread is a branch. If you are a leaf on the branch, you can only see that branch. BUT if you are at the trunk, you can see the whole tree.

For example, let’s say I see a tweet in my timeline from @AddieTheCorgi; I see it’s a reply, so I click on it and get this:

Capture

I’m only seeing the branch that @AddieTheCorgi’s leaf is on. BUT if I click the “trunk” of the tree (the first tweet at the top), I can see the WHOLE TREE!

Capture1

As long as you click “reply” (and not start a new tweet thread), a dot reply will still be threaded as shown above. Here is more of the tree:
Capture2

Well,¬†almost the whole tree. Sometimes they sneak “view other replies” in there, so clicking on that will zoom into that branch:

Capture3

Also, see that hint from Megan right above? That does work, but only when replying to yourself. And turns out there’s also this issue with replying to yourself and taking out the mention:

Capture5

So certainly reply to your own “trunk” if you have more than 140 characters, but let people know it’s a continuation!

Just like it’s ok to jump into a conversation whenever you want, it’s ok to ask to be removed from a conversation as well. A “Please remove my mention, I don’t need to be in this thread anymore” should work (unless some people reply before they see your tweet, but it should get to it to stop shortly). It’s also ok (and appreciated) to reply to just one person if it only involves them, even if that person isn’t the original tweeter. I know I get lazy sometimes and just hit reply and start typing, but it would be beneficial if we all took a second to (a) click on the original tweet to see if someone already replied your exact thoughts (guilty as charged!!) and (b) @mentioned and #hashtagged with intention. It’s not cool to slap a popular hashtag (or person) onto an unrelated tweet just to try to gain audience. It IS cool to @mention someone when you’re sharing something they did or helped with.

Also worth mentioning is when the mentions in a thread start getting unwieldy: start a hashtag!

And just because I wanted to prove to myself I could make one, here is a “5 Top Tips for Twitter” infographic (made using Canva):

5 Top Tips for Twitter

For further reading, I recommend Hannah’s comprehensive gdoc of our flex session and also Michael Fenton’s (@mjfenton)¬†post with great tips (where I first learned WTF a dot reply was).

And if you’re not on twitter yet, please join! Or if you are on Twitter but don’t feel a “part” of it yet, just like in real life, it takes time to build friendships and followers. Join in a chat, reply to a conversation, ask someone a question about their latest blog post. We need your voice in the #MTBoS!

Alg II Files: Inequalities

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(More files and FAQs here) Oh, holy moly. I thought it was a good plan to have all the inequalities in one chapter, like I did with equations and graphing. We could revisit all of our graphs and equations again, notice similarities/differences…yeah, not so much. Much like any traumatic event, I’ve blocked out many of the details. I just remember ending each period completely frazzled.¬†anigif_enhanced-3605-1414077090-9

So, well, here you go. Do with it what you will.

(file) I tried doing the “test each region” method of compound inequalities. I’m pretty sure I don’t like it and prefer the draw-each-number-line-then-shade-overlap method.

Here’s some homework:

Unit 6 1

(file) Hey, you know what would be really cool?  If we did a notice and wonder with some pre-solved absolute value inequalities!

Alg II T 6_2 Notice Wonder

(blank file and file with solutions) Oh, wait, I meant “not cool.” How I was being tested this day, when after 10 minutes one group’s contribution was “they all had absolute value bars.” So we did some formalized notes the next day.

(file) I just really don’t want to talk about absolute value inequalities, okay? Let’s talk about something more pleasant, like two-variable inequalities. Happy sound of everyone shading!

(file and homework file). Then I tried combining a graphical approach with quadratic inequalities:

(file) No. Just no. To be honest, even though it’s in Algebra II, I’ve always kept these until Precal and taught it using sign charts. I think that’s a good place for it.

We did all love some systems of two-variable inequalities!

(file) Now would have been a great time for linear programming, but we were running into final exams, so I just did one more lesson: radical inequalities

(file) You can see here I went back to the draw-two-lines method of finding the solution.

Then this chapter was finally done and we had a study guide:

unit 6 2

(file and video key part 1 and part 2) And I think that’s all I want to say about this chapter!!

 

 

Category: Alg II | Tags:

Alg II Files: Systems

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(See more Alg II files and FAQs here)

So this was an interesting chapter…one that I think I improved from last year, but could still have used more connections and also some more activities (e.g. double stuf oreos wafers and creme).

It started with a great discussion:

(hey guys, hold out for a couple more chapters when I got a new phone that does pictures a whole lot better! Sorry for the random quality until then.)

 

(file) So, guess what? I had been teaching the types of systems wrong for a long, long time! To recap from that post, the correct way is:

Category One: Is there at least one solution?
Yes: Consistent  No: Inconsistent
Category Two: Are they the same line? (Technically, ‚Äúcan one be formed from the other with algebraic manipulation?‚ÄĚ)
Yes: Dependent No: Independent

So the correct categorization would be:
Independent and Consistent: One Solution
Dependent and Consistent: Infinite Solutions
Independent and Inconsistent: No Solutions

Then we did some substitution, some new stuff here: being really conscientious on boxing equal things and also looky there in #6, doing substitution with quadratics!

(file with these questions and more practice)

and I even went a little crazy and did this:

(This may also be why so many of my students remembered how to expand (x – #)^2–we did them a lot of them throughout the year!)

Elimination.

I was pretty proud of the practice I prepared for the pupils:

unit 5 2

(file) The last set was interesting when they didn’t choose the method I thought they would!

Did I hear someone say they’d like to see more textbook-like systems of equations word problems? Here you go!

(File with these & more practice problems) But I was able to add a pretty cool activity from Amy (@sqrt_1) where the students made their own word problems. The only thing I changed was condensing all the work onto one page for easier grading:

unit 5 4 unit 5 5

(instructions and worksheet) It was a nice day and a lot of the students had fun with it (how often do they get to break out the colored pencils and color? I also gave bonus points for the most creative one from each class and put my favorite one on the test!). I will say next time I will have them show their work that they tried it! (I said they had to do it on their notes, but not turn it in.)

Have I told you how much I like doing group speed dating?

unit 5 6

(file) Then it was study guide time!

unit 5 7

(file and video key part I and part II) As I said, a lot of room for extensions, activities, and connections in this chapter that I just didn’t have the time to incorporate. TBH, if it’s the night before the lesson, go ahead and use some of my stuff, but if you have time to plan, please go see all the more awesome things there are out there in MTBoSland!

 

 

Category: Alg II | Tags: ,

Alg II Files: Let’s All Translate Some Graphs!

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[More files and FAQs on my Algebra II files page!] One big change I made in Algebra II was making an entire graphing chapter. Usually, we would learn a function, solve it, then graph it, repeat. Now, using Jonathan’s model, they all got mushed together in one unit, which actually really helped them with (a) things that are similar with all the graphs (shifting, stretching) and (b) things that are different. It also solved the issue that I had before where if we were in the quadratics chapter, they would just write y = (x – 2) + 6 for the equation, leaving off¬†the most important part! Now they realized why that was so important! I was reeeeeealy pleased with how well the students did on this unit. I needed to keep spiraling back to these through the rest of the year, though, because when you graph all at once it’s a long time before you graph again!

When we last left our intrepid reporter, she had just finished translations of linear functions, so now we’re ready to jump into absolute value. The first part that they did mostly on their own:

Unit 4 1

Second part where we made sure everyone was on the same page:Unit 4 2

(file¬†and a practice WS file)¬†I REALLY liked those questions on #1 that I stole from some worksheet; you’ll be seeing them for the rest of the chapter! Like on the quadratic NoteTakerMaker!

(file¬†and homework)¬†Again, we were just focusing on graphing by translating in this chapter. Let’s try translating some square root functions!

Unit 4 3

(file) And then it’s time for some John Travolta!

(file) This was the last function we were going to study, so we spent a day doing a Desmos “Match My Function” Activity Builder:

Unit 4 4

You can find it here. I think this was the first activity builder I made all by myself, so it’s not very elegant (it was before hidden folders so I had to monitor students not scrolling down to the answer!). I also had some students say it was too easy to just use sliders until it matched, so next time I would definitely add some Desmos-style questions like “Here is Addison’s (wrong) equation and graph. What would you tell her to correct so it matches?” and “How would you explain to your friend how to move a function left or right?”

Then a group speed dating day:

Unit 4 5

(file¬†and yes the graph answers are included!)¬†Some sort of dry-erase graph is a must for this activity so partners can see work! If you don’t have individual graphing whiteboards, take Tina’s (@TPalmer207) suggestion of buying a pack of job ticket holders and printing off graphs to put inside.

Then it was study guide day:Unit 4 6

(file and video key part 1 and part 2) As I said at the beginning, for the most part the score were GREAT on this test! Was it because we ended up going pretty slow through this unit? Or because they had graphed most of these before in Algebra I? Or because all the graphs were together? I don’t know the reason, but I will definitely put this portion of restructuring Algebra II into the “win” column!

Alg II Files: Functions & Graphs

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TMC has got me all mathy-feeling, so here’s another unit! Or at least, the first part of it!

I didn’t really change much to this chapter as from previous years, but I’ll go ahead and post everything so it’s all in one place. As usual, find more files and FAQs on my Algebra II Files page.

Let’s begin with what is and is not a function:

(file here) I took the NAGS from Sarah at mathequalslove and I think the rabbits came from Shireen at MathTeacherMambo. (Definitely 2 of my top five math blogs).

Here’s part II, but according to my calendar, I did part 1 and 2 the same day.

(file) I’m just going to warn you if it’s the first time teaching Algebra II, the struggle is real when trying to find function values from a table or graph. Just be prepared.

Also the magic parentheses for evaluating a function = amazing. We took the parenthetical promise (h/t mathequalslove again) in Unit 1 that said every time we substitute in a value, we put it in parentheses. And we’re going to be substituting for x, so let’s go ahead and put the parentheses first like: ¬†3( ¬† ¬† ¬† ) + 2 then INPUT the INPUT INTO the parentheses!

Here’s some homework:

Unit 3 1

(file) Then it’s the ever-popular graph stories!

Unit 3 3Unit 3 4

(file) Then…it’s time for….domain and range!!!! ¬†Y’all, I just totally had a genius idea: have them figure out what the scale/domain/range should be for the graph story graphs first! One of you try it out and let me know how it goes. But since I didn’t think of that until just now, here’s what I used:

Unit 3 2

(file) Since we’re doing this before we did inequalities, it’s domain and range PLUS learning interval notation. Note the color with a purpose! I have them “box in” the graph before they think about writing the interval. I also use Sam’s domain and range meter, sometimes breaking out the spaghetti to use if I feel like picking a million tiny pieces of spaghetti off the floor.

Here’s some slightly lagging homework for the chapter:

Unit 3 5

(file) Then it’s a graphing line “review.”

(file) As you can see, I always go back and forth on graphing standard by converting or by x and y intercepts. Here’s¬†the boring homework file.

Now here’s some exciting stuff! This is a pretty magical activity¬†that is a really good introduction to the (h, k) form. Just read question 1 and let that awesomeness just sink into your brain.

(file) And some practice:

Unit 3 6

(file) Then it’s time for a study guide:

Unit 3 7

(file) And of course a study guide video!

Off to make another post!

Category: Alg II | Tags: , , ,

Alg II Files: Quadratics!

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(If you want more Algebra II files and for FAQs (including fonts), look here!)

Part of switching up the order of Algebra II involved moving up solving quadratics (which used to be Chapter 5, after equations, lines, systems, and matrices). I like how nicely this worked with Unit 1, however, I definitely needed to spiral more through the year, I wasn’t very good at making sure they saw all these different types of equations again through the year. But here’s how solving quadratics went!

(file). ¬†This is basically how every lesson went this year: “Oh, man, I’m going to make the COOLEST note-taker-maker and it’s going to have SO MANY CONNECTIONS and it’s going to be awesome!” and then about 20 minutes into class…

Rookie+mistake+my+friend+rookie+mistake+_a03d46fda15b807172bf373f62c1a14d

Usually it was a case of “Trying To Fit An Hour’s Worth of Class into Forty-Seven Minutes” but other times I think I aimed too high, or didn’t plan for so much review, or maybe it was just “First Time to Teach a Lesson Never Goes Well” issues.

Anyway, as you can see, I didn’t get finished with my connections the first day, but I think you can appreciate where I was going with it-my students always seem to think “factor” means “solve” and “simplify” means “factor” and such. And also they forget that they can solve quadratics without a linear term without factoring,¬†just like they did last chapter! (Although I will admit I often get into factoring-robot-mode and forget that, too!) I think with three minutes left in the class, I decided to focus on factoring/simplifying for the moment, then go back to solving.

The next couple of days were spent factoring trinomials by guess and check. (Hey, spell-check, “trinomials” is a word and I did not mean “binomials”). We used whiteboard for easy guessing and checking. You can read all about it here! If you’ve always been wary about guess and check, I ask you to go give it a read and maybe try it out next year. It’s not your momma’s guess and check!

[Updated 7/9 to add the following picture] Ok, so I bet you DIDN’T go and read all about the cool guess and check method, did you? Well fortunately for you, Susan (@Dsrussosusan) tweeted me a concise picture of it!

Unit 2 7

Thanks for the great example, Susan!

Hey, for the rest of y’all, want some homework?Unit 2 1

(file) Or maybe some group speed dating cards?

Unit 2 2

(File). As mentioned, I may have gotten lazy and just handwrote the answers on the back of each. Perfect is the enemy of the good, eh?

Ok, now back to solving quadratics! ¬†News flash: I use a lot of terms that I just think students should know by now. But they don’t! Even if I didn’t do it formally each time, I started each equation/function intro with “how do you spot it in the wild?”

Those weird symbols meant we asked ourselves HOW we were going to solve it before we actually started solving.

(file). Make sure you play the “Guess Which 2 Numbers I Multiplied Together” game that I stole from someone on the #MTBoS (please tell me if it’s you!). Start with 10. They’ll chose 5 and 2 and then 10 and 1. Nope, it was 20 and 1/2! Tell them you’ll make it even easier…they just have to name ONE of the numbers. Give them 20. Someone will say 1/2 and 40. Nope! 1/5 and 100! Then say maybe it will be easier with a smaller number, like -1. Nope, it was 1/pi and -pi! ¬†Then finally give them one more chance…name one number out of 2 that I multiplied to get zero. TA-DA! And that’s why it’s the Zero Product Property, kids, and not the “0 or 1 or 10 product property.”

And why we’re blowing minds, let’s talk about imaginary numbers!

(file) Truth: I just introduce imaginary numbers as a way to solve a problem we couldn’t before (I start with the story about the caveman owing more sheep than he had, so he tried splitting it (fractions), but then he still owed more sheep (negatives) then bring in Pythagoras and the madness of irrationals and how we end up making/discovering new categories of numbers in order to solve previous unsolvable problems. If I teach this again, I’m also going to use the tidbit from The Thrilling Adventures of Lovelace and Babbage¬†about how one of her tutors didn’t believe in negative numbers (and this was in the 1800s! Not that long ago!)). I don’t get into doing operations with them, or rationalizing them, or even the cool power pattern unless I have a few random days free later in the year.

Then it’s time for a big ol’ bag of practice:

Unit 2 3

(file) ¬†Another truth: Not every single practice activity has to be filled with razz-ma-tazz. This has some nice self-checking built in, and I just wander from group to group. I’m in the camp that sometimes you just have to do a lot of practice and I’d rather have them spend all period in groups¬†working on all of these problems, then spend half the time trying to do the practice¬†and play a game, then not finishing, then just copying the rest from their partner. Not to say I don’t love a good activity, I’m just sticking up for the worksheets because¬†somehow worksheets started to be shorthand for bad teaching and I don’t agree with that. And I’m giving you permission to NOT spend hours converting a perfectly passable worksheet into an (awesome) activity and maybe watch Halt and Catch Fire instead?

Ok, let’s get back to something we can all agree on: the quadratic formula!

(No file, but there is a page 2) Well, except we don’t all agree on how to write it. Notice the beautiful splitting into 2 fractions (and you can still sing “all over 2a!” during pop goes the weasel) which is a masterful tip I learned from Jim (@mrdardy). (We do have to talk about recognizing the right answer during multiple choice tests, though).

Am I the only one that talks about “pretty” numbers? And gross decimals? ¬†I am? I’m cool with that.

Hey, remember what I said about worksheets? Yeah, here’s one that is based on¬†Amy’s great activity. I feel so guilty-like I just undid millions of MTBoS tweets by turning an activity into a worksheet.¬†Does it help if I told you they work on this in groups? Please don’t kick me out of the MTBoS; my TMC16 airfare is non-refundable!! ¬†I mean,¬†check out the directions…they still have to choose which 5 to use the quadratic formula on! There’s thinking, not just rote practice! ¬†I promise!

Unit 2 4

(file) Hey, you know what this chapter needs? Some radical equations!

(No file). Ok if there is one thing my Algebra II students left knowing this year it’s that (x – 5)^2 means (x – 5)(x – 5). A few dramatic gasps and some fake tears over the dead puppies the first few times someone tries to distribute the exponent and they seemed to have remembered it. Of course, I’ve done the same thing in other years and it never worked, so YMMV.

You know, I think we may need some more group speed dating:

Unit 2 6

(file here AND it included answers!) Then¬†it’s finally study guide time!!

Unit 2 5

(file) And if you’d like to hear the beautiful sound of my voice explaining 31 different quadratic problems, here are the showme videos of the study guide: #1-11 #12-27 #28-31.

Whew! ¬†That’s a lot of quadratics, my friend. Hope you found something useful! As always, feel free to leave a comment or tweet me if you have any questions or found a matho!

Category: Alg II | Tags: ,

Alg II Files: Equations Grab Bag!

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On September 12 of last year I posted about the first half of first unit of my Algebra II course redesign with the cliffhanger of “more to come later.” And technically, today is later!

To catch up: I tried pivoting Alg II a la Jonathon, but I’m not as awesome as he is at this long-term-everything-connects thinking so basically I just redid the first semester order. These are the materials I used for the first chapter, solving equations. I REALLY liked putting all of the equations together into an equations grab bag. I wish I would have slowed down here and spent more time on inverses and flowcharts. (Also see Julie’s better¬†take on this).

Also, in case you’re new to my blog and/or just reading it in a blog reader, be sure to check out all of my Algebra II posts–organized here for all of your graphic organizer/homework/study guide needs. (I have them for Precal and Geometry, too! [Geometry is still a work in progress])

Also also, here is the google doc I use to post all of my notes and homework for the students. It may also be helpful to you for planning.

Ok, so we last left off at solving linear and literal equations. ¬†We took a small quiz on that, then jumped into “let’s throw all the different equations together and see what happens!” Starting with absolute value:

 

(Blank file here) Nothing fancy, except for the fabulous flowchart action. To “unabsolute value” you have to make two equations! Here’s the homework for the next few sections:

Unit 1 1

(File here). Now should probably be the time I mention that I tried really hard to correct typos/mathos as I found them, but don’t be surprised if there’s still a few here and there. Please let me know if you find any so I can correct the file!

Then it’s time for powers!

(file here) I especially liked having square roots and cube roots together so we could discuss when we did or did not need two answers. Also look at that #10 just begging to be brought up again if you want to use completing the square to solve quadratics!

And if you’re going to talk about powers, you should probably talk about roots!

(file) What’s that you say? This would have been a perfect time to bring in some radical equations that didn’t work, and you could tie it in to yesterday? ¬†That sounds like a great idea. But remember I had a wide range of abilities and this was still the first month of school. Sometimes you have to pick your battles.

We played a round of group speed dating, which you can read about (and get the file for) here.

Then study guide:

Unit 1 2

(file) While I still have some blogging mojo left, I’m going to try to get another unit up today!

 

Category: Alg II