Math = Love: April 2020

Thursday, April 30, 2020

Transformations of Functions Word Search

Yesterday, I got the urge to create something. Creation is one of my favorite parts of my job. I love to put in some time and effort to create an activity for my students to use. I find not only the process of creation to be re-energizing but also the act of seeing students all over the world getting to experience the activity I created through the remarkable power and nature of social media.

So, what did I create? First, I baked a yummy batch of chocolate chip cookies (Shaun got to choose the type of cookie) from Magnolia Table (affiliate link). They have become my go-to chocolate chip cookie recipe, and they always receive rave reviews. Well, except for the time that I was in a hurry and accidentally used white sugar instead of brown sugar.  They were still edible, but let's just say I didn't take them to church with me as planned...

While waiting for my trays of cookies to bake, I started flipping through this year's Algebra 2 binder. I was looking for inspiration for something to create. Ahhh...yes...transformations. It's such a crucial topic in Algebra 2 and plays a huge role in Shaun's Algebra 2 Notes which I am currently using to based my Algebra 2 curriculum on. It's definitely one of the areas where I had the most need for improvement. As the year progressed and we performed transformations on the different parent functions we encountered, I found that my instruction got better and better.

 Image Source: https://primefactorisation.com/blog/2020/03/25/algebra-2-class-notes-v-0-3/
But, what about those first lesson of the year on transformations where we don't know our parent functions yet? How could I give my students some much-needed practice with this concept? Last year's practice (or I guess I should say this year's practice since we still have 1.2 weeks of distance learning left for the year) consisted of way too unstructured dry erase practice where I told students to check their answers with Desmos. Students struggled to figure out if their sketched graphs *really* matched up with the Desmos graph. And, I ran around the room for the entire hour like a chicken with my head cut off trying to answer question after question while also redirecting groups who seemed to be using their Chromebooks for things that weren't Desmos. Yeah, it wasn't my best lesson.

So, I needed something self-checking. Something where students knew without a doubt whether their sketch of the transformation was correct. And, I wanted something technology free so I could better monitor groups to see that they were on-task. This has all been a VERY long-winded way to say I made a word search.

No, not that type of word search.

I know what you're thinking.

We won't be staring at an array of scrambled letters until our eyes bleed looking for the letters that spell out REFLECTION and TRANSLATION. Maybe those type of word searches have a proper educational use in some circumstances, but my own memories of school equate word searches with busy work. And, I've got too many important math concepts to teach to give my students busy work.

It's a totally new type of word search, and I'm super excited to get to try it out in my Algebra 2 classroom come August or whenever we get to teach in classrooms again.
Students are provided with a graph that features a function, f(x), which is defined by a dashed line, and an assortment of letters of the alphabet spread around the coordinate plane.

There are fifteen different transformations of f(x) which when graphed join together four of the letters on the coordinate plane. When these four letters are unscrambled, they form a common school-appropriate four-letter word.

For example, if you were to sketch f(x + 6) + 2, you would get something that looks like this:

The transformed graph joins together the letters N, T, W, and A which can be unscrambled to spell WANT.

If students don't get a graph that joins four letters together or if the four letters they do find don't spell a word, they will know that they have done something wrong. Self-checking activity for the win!

Because I like to overcomplicate things, I made several versions.  All the versions currently use the same letters and transformations. If this activity proves to be popular, I might make different versions in the future to focus more specifically on certain types of transformations or levels of difficulty.
If you want to give students the fifteen transformations to sketch all at once, I have formatted it as a sort of worksheet. You definitely won't want to print it double-sided, though. Print one copy of the graph for each student, and print one copy of the worksheet for students to record their answers on for each student.

Even if you do elect to take the worksheet route, may I recommend placing the graph in a dry erase pocket (affiliate link)? It will make your students' lives SO MUCH EASIER. All of my dry erase pockets are at school, so you will have to settle for a picture of my graph in a sheet protector. By the way, sheet protectors work completely fine for this. But, I prefer the sturdiness and improved erasability you get from a bit more high end product like a dry erase pocket (also known as shop ticket holders.)

I hesitate to use the activity in this form in my own classroom because I fear it would lead to the same result I get when I try to use one of those clever joke worksheets. One student works diligently to figure out the puzzle, and then can't contain themselves from shouting the answer out to the ENTIRE CLASSROOM. Is that just my students?!?

Most likely, this will be featured in my classroom as a small group activity where students are probably arranged in pairs. They will be given one challenge at a time. After completing each challenge, they will bring it back to my desk. I will check their answers and give them a new challenge.

To facilitate this small group version of this activity, I decided to make cards with each of the transformations written on them. And, because I couldn't help myself, I made two different versions of the cards, 5 to a page and 15 to a page. The 5 to a page cards look nicer and each feature the instructions, but I realize copy limits are a reality in many districts. If you hate cutting and laminating, you'll definitely want to go for the 15 to a page version.

This small group version also called for a small edit to the dry erase template.

Check out those boxes at the bottom for students to write in the word they found so that you can check their work!

I've done quite a few of this style of activity in my classroom. One things my students always struggle with is keeping track of which challenges they have completed. To help them in this regard, I usually try to provide students with a small slip of paper to track their progress. You can use this in several ways. Students can track their own progress. If you have a highly motivated group of students, you could take yourself out of the equation and not require students to check their solutions with you. They would just mark off their completed challenge on their tracking sheet and grab a new challenge from the table.

If you students need a bit more external motivation, you can use a stamp to mark their sheets as they finish each challenge. Initials work fine for this as well. I also sometimes break out my trusty single hole punch to mark which challenges students have completed. I often use these tracking sheets to give a participation grade of sorts for activities. I decide on a number of challenges that students must complete to receive "full credit." If groups exceed this number of challenges, I give them a minor amount of extra credit.

Another perk of doing this as a small-group activity instead of just a worksheet is that it gives the teacher more control over the challenge. Maybe horizontal stretches and compressions are outside of the content of your course. Just pick out the transformations that you want to use with your students and ignore the rest. There will be letters on the coordinate plane that your students never use, but that's completely fine.

Or maybe you want to do this a whole class activity. Give each student a copy of the graph in a dry erase pocket. Project a transformation on the screen. Then every student can attempt it at the same time.

I love that each teacher can put their own sort of spin on this activity to try and meet their students' specific needs. I can't wait to see what you guys come up with!

One last thing. I have included a blank answer key in the file for this activity. I have intentionally NOT included the answers on the key. I have two reasons for doing so. First, my students are master googlers. I've lost count of the number of times students have discovered I have a blog because they have gone searching for the answers to an activity I created. Even more importantly, I don't think any teacher should be using this activity in their classroom if they haven't worked through it themselves. So, print off the blank answer key, and give the activity a try yourself. Enjoy!

Monday, April 27, 2020

Last week, I sat down to compile a new volume of Monday Must Reads. Then, I realized it was a Tuesday that just *felt* like a Monday. And, with that realization, all my motivation went right out the window. I'm 97% sure that it's Monday, so let's delve into the world of my recent twitter likes. This is my semi-regular attempt at capturing the amazing ideas of math teacher twitter. I hope you find an inspiring idea or two!

Howie Hua has been on a roll lately with his clever mathematical memes and tweets. Need more entertainment and inspiration in your life? I'd definitely recommend giving him a follow on twitter!

This are some lovely Open Middle Tasks from Dana Harrington. They're perfect for the Algebra 2/Pre-Calculus classroom!

@druinok shares an excellent teacher hack for these times of distance learning.

Thanks to HSE Physics, I now know of the existence of Autodraw.com. And, now you do, too. I tried it out, and I have to say I'm impressed.

Check out this beautiful origami display from Clarissa Grandi.

Sara VanDerWerf shares a thought-provoking image for your geometry classes to ponder.

If you haven't seen this bad graph floating around social media, zoom in and give the y-axis a nice view. Thanks for sharing, Marek Gierlinski!

Dan Anderson shares a brilliant way to have students open up about ways you can up your teacher game to be a more effective educator.

Teaching graphing angles in standard position? Check out this game from Bowman Dickson.

Until next time, keep sharing your awesome ideas!

Friday, April 24, 2020

Connect the Dots Puzzle from Puzzle Box, Volume 2

Today I want to share a lovely puzzle with you courtesy of Erich Friedman in Puzzle Box, Volume 2 (affiliate link). If you love puzzles like this, you should definitely check out Erich's Puzzle Palace which is chock-full of amazing puzzles.

All three of the books in this series (affiliate link) have been a lovely addition to my classroom. I highly recommend them!

This puzzle is absolutely perfect for placing in a dry erase pocket. Want dry erase pockets for your classroom but don't want to pay a premium? Here's a little shopping tip for you. Search for "shop ticket holders" instead of "dry erase pockets." They are the exact same thing, but since they are marketed towards car repair shops to keep their invoices clean, they are often SO MUCH CHEAPER.

Students are given a square full of dots and the following instructions. Connect the dots below into a collection of triangles. The triangles should not touch or overlap, and each triangle should have three different edge lengths.

Grab your dry erase marker so we can give this a try. Our first triangle. Check. Remember to make sure that the three side lengths are all different. Check.

And, we can conveniently use the three dots to the right to make our second triangle.

Oh no! It's an isosceles triangle which means two of the side lengths are the same. It looks like we are going to have to start all over.

And start over, I did. Things were going well until I realized I had a leftover dot in the bottom left corner.

I guess it's up to you to try and solve the puzzle! You can download a printable version to use this puzzle in your classroom here. And, in this day and age of distance learning, I can also see importing this into a Desmos Activity Builder and having students use the sketch feature to solve it!

Thursday, April 23, 2020

Combining Sets Challenge

My brain has finally started letting me think about next school year. Of course, I'm not thinking about it TOO much yet. For one thing, this school year is still ongoing, at least for a couple more weeks. Due to COVID-19, our students' last day is May 8th. We started distance learning on April 8th. It doesn't feel like real teaching, though, because I'm so limited in the scope of what I can do. Then, there's also the fact that I don't know exactly 100% what I'm teaching next year. I don't want to get too enthused with planning and end up creating resources for a course I'm not teaching.

I'm pretty sure I'll still be teaching Algebra 2 next year, though, so I've been flipping through what we did this year to get my mind thinking about what worked and what could use some major tweaking. This year, I used the fill-in-the-blank Algebra 2 notes that my husband wrote last summer that are 100% aligned to the Oklahoma Standards. (Because OK decided to trash common core before ever actually teaching common core, it's hard to find things that actually align to what the state says we're supposed to be teaching. Don't get me started on the textbooks my district adopted that claimed to be Oklahoma aligned...)

Sadly, I didn't get to teach all the way through Shaun's Algebra 2 notes. But, I loved the lessons that my students did get to experience. This set of notes is incredibly cohesive and well-thought-out. I feel like I understand mathematics more deeply as a result of working through them. And, this is coming from someone with a degree in mathematics. I've always looked at Algebra 2 as a very choppy subject. It's always felt like a mish-mash of all the topics that we want to fit in while students are still in high school. This year (my sixth year teaching Algebra 2) was the first time I've ever really felt like I was teaching a well-rounded subject and not a thrown together at the last minute course.

That was the good. The not so good? Shaun's Algebra 2 Notes/Curriculum is quite unlike most other curriculum resources you can find here in the United States. (I guess that's what happens when you take someone who was educated in Australia where maths class looks entirely different from the US and let him put his own spin on the Oklahoma Algebra 2 standards.) It was hard to find practice assignments and activities that were of the same rigor as the notes.  And, it was a year-long frustrating experience trying to write satisfactory assessments. Ideally, I would have unlimited time to write my own assessments (with five different versions and five different answer keys). Sadly, I still haven't figured out that unlimited time aspect. So I did my best to find pre-written questions that matched up in the test banks I have access to. Each assessment, though, left me feeling completely unsatisfied and wanting to rip it to shreds and start over. As a result, I feel like quality assessment is an area that I really dropped the ball in this year.

I ended up making a few new activities here and there, but this was hard to do with a baby at home. Again, how amazing it would be to have unlimited time... What few activities I did make, I never got around to blogging about. That's what I'm here to try and start remedying today. Then, I can hopefully start making some new activities for next year!

Instead of beginning Algebra 2 with the traditional Algebra 1 review, Shaun takes a different approach and jumps straight into some basic set theory. We learned enough new symbols to boggle my students' brains for a few days.

We tackled element/not an element notation.

 Source: https://primefactorisation.com/blog/2020/03/25/algebra-2-class-notes-v-0-3/

We discussed the subsets of the Real Number System and their fun symbols.

 Source: https://primefactorisation.com/blog/2020/03/25/algebra-2-class-notes-v-0-3/

And, we found the intersection, union, and difference of various sets.

 Source: https://primefactorisation.com/blog/2020/03/25/algebra-2-class-notes-v-0-3/
I knew at this point that my students were going to be in definite need of some practice with all these new symbols. This led to the creation of my Combining Sets Challenge.

This group activity involves nine separate challenges were students must figure out how to combine the given sets A, B, C, D, and E using intersection, union, and set difference symbols to create nine new sets of numbers.

Each group is given a laminated sheet of paper defining sets A through E.

Each of the nine challenges is printed on a separate card.

I also gave each group a strip of paper to write the names of their group members on. Then, as each group completed a challenge, I would initial the box of the challenge they had completed or use a hole punch to punch a hole in the appropriate box.

Let's take a look at an example challenge. We'll tackle Challenge 3 which is pictured above. Students must find a way to combine the provided sets (A - E) to produce the set {4, 5}. I notice that 4 and 5 are included in both sets A and C. And, conveniently, 4 and 5 are the only numbers included in both sets. Therefore, I can write {4, 5} as A C. (The intersection of A and C.)

Some of the challenges have exactly one way to solve them. Others can be solved in several different ways. I am intentionally NOT posting an answer key to these nine challenges here because I know from my own students how google-happy they can be when presented with a challenging task.

I highly, highly, highly recommend that you work through ALL nine challenges yourself before using this activity with students.

My students really enjoyed this activity. They might have been a little frustrated at the fact that one of the challenges required them to combine THREE different sets. GASP.