#phonespockets First attempt: quick reflections



So I am jumping on the #phonespockets bandwagon. I just hit record on the voice recording app on my phone, stuck it in my pocket, and then went about teaching. That was yesterday. Today, I listened to the recording (~10 minutes). Here are a few quick noticings:

1.) I was a little self conscious at first, but after a few minutes I forgot I was recording. I set a timer to remind me when 10 minutes was up so I could stop recording. It didn’t interfere with the class in the way that video recording sometimes does.

2.)  Background noise was not as bad as I thought it would be. I constantly worry that the room is too loud, making it hard to concentrate. But I want kids talking to each other (learning is social and all) so I have to resist the urge to quiet everyone down. Listening to the recording, the room doesn’t seem too loud really. I can clearly hear not only my own voice but also the voice of the student I’m talking to at the time. It’ll be interesting to see if this holds for other classes as well, in particular my big class later today.

3.) I only talked to 4  kids the whole 10 minutes. This is something I’ve also been thinking a lot about; how do I make sure to have authentic, useful conversations with students but also be fair about getting to everyone? Talking to 4 kids in 10 minutes means I averaged 2.5 min/kid. So in a class of 27, I would need 68 minutes to get to everyone. Some days that’s doable (I’ve got 90 minute blocks), but I suppose I don’t need to reach every kid every day. But in that case, I need to think more about tracking these convos so that I don’t always end up helping the same students and ignoring others.

4.) I am pretty good about using wait time after asking a question, but I could stand to add a few seconds to my usual wait time. I also need to utilize follow up questions better. For situations like this:

Me: “What are you going to do next?”

S: “I don’t know”

Me: <makes a suggestion>



Thoughts on Teaching Engineering Practices


I am teaching Engineering this year. In this class, I really do feel like a mentor in the room, a partner in learning. I think the big difference is that the class really is project based. I haven’t quite figured out how to assess appropriately just yet, but I am sticking to the “here’s a problem, GO!” mentality. Our most recent one looks like this:

And here are some students working on it:

(note: Not staged. And I assigned no roles, just the problem.)

The kid on the left is modeling a plastic holder for a magnet that will have a name embossed on the side. He’s learning and practicing  skills in Autodesk Inventor (our 3D CAD software). He chose this role in the group as he is passionate about 3D modeling and printing.

The kid in the middle is measuring the magnets with a dial caliper. He is learning about precision in measurements and asked some excellent questions about significant digits.

The kid on the right is documenting the process in her engineering notebook. She has assigned herself this role because she is thorough and has a good eye for detail. She also keeps the group on track by doing this.

All three of them are learning and practicing communication and collaboration skills to solve this problem. They had to clearly define the problem and then brainstorm solutions before getting to this point. And now that they’ve arrived at their potential solution, they are working together to develop it.

So, I think they are hitting NGSS Practices 6 and 8 in particular:

6. Designing solutions in engineering

8. Obtaining, evaluating, and communicating information

But do I want a “Teamwork” section on my rubric? If so, what exactly makes a high score in “Teamwork”? Clearly, these three kids are rocking it. But what about another team that has a different dynamic? It’ll be hard to judge, but does mean I can’t? Not sure.

So here’s my rubric for now. My plan is to have the teams assess themselves with this rubric and then turn it in as part of their project portfolio.

iPad Formative Assessment


So, I’ve been using my ipad pretty much every day. I mainly use it as a sort of mobile document camera, snapping pictures as I walk around. I usually then project the work on the board and ask students to explain it for the class. This gives me a chance to ask some good questions like: “Why did you multiply by 99 instead of 100?” “Is there really a force pushing on he ball?” “If your rule is +2 every step, how many will there be in the 73rd step?” Sometimes we spot mistakes, sometimes I purposefully get two pics to compare, sometimes we are surprised by different methods, always good learning happens! I’ve got hundreds of these now:










Function Notation Can Wait


It has been way too long since I’ve blogged, but from what I’ve been reading lately I am not alone on this.  Like many others, I have been feeling a little overwhelmed this year.  It is tough trying to keep up with new curricula in Algebra and Physics, and I’m basically constructing my textbook as I go too.  </whine>  So far, I’m happy with the way things are going in both classes.  In Algebra, I’m using the learning targets that I wrote over the summer (modifying as I go of course) and I’ve been using a bunch of the handouts from Connecticut’s model Alg 1 curriculum (click “CSDE” then “Mathematics” then “CT Common Core Alg 1”, thanks to Jen Silverman for sharing that resource with me!).  If you teach Algebra I or MS Math, I’d give them a look at least. (Edit: guest password is CSDE.)

I’ve also been writing a class blog to keep in touch with students and parents.  That blog also serves as a model for my students when they finally start their blogs (we have them set up but haven’t started posting yet).  I’m thinking maybe we should do an Explore-MTBoS-style series of missions! Gotta get to work on that with all my free planning time. 😉

A highlight for me this year has been doing a lot of problem based lessons.  Some I got from the CT curriculum, but mostly from online sources like MARS, 101qs.com, or the twitterblogosphere in general.  I’ve really been enjoying this type of lesson and I think most of my kids have too.  Many parents told me at back to school night that their kids were enjoying the class.  However, I’ve found that many kids are struggling to make the connection between the lesson and the assessment (I have the same problem with modeling instruction in physics).  My worry is that if I don’t come up with some fixes for this problem, I’ll revert to old ways and abandon the problem based course design (which I think is going well otherwise).  Anyway, here’s an example of my assessment scheme:

First, the lesson handout:

So, we did this handout.  As a class, we noticed that the cost would depend on whether or not the dog needed a bath each visit.  We decided that it was a dirty dog, so yes it did need a bath every time.  Then, we wondered which would be the better deal and decided that it would depend on how many times you visit the place.  With some guiding questions, groups of kids modeled the scenario, made some nice TI and Desmos graphs and most decided that they should go with  Super Dog Delight because it would be cheaper in the long run.


Ok, so one of the skills I am looking to assess after this activity is solving equations with variables on both sides.  Here’s how I did that:

1.  Formatively assess during the activity.  Notice the different methods for writing and solving equations, point them out to the whole class.  Have students demonstrate their methods.  Celebrate mistakes!

2.  Multiple choice summative quiz.  5 questions, randomly generated by Socratic Brain (according to my specifications).  Students must get 5/5 twice (on different days) for full credit.  They can take the quiz as many times as they need to.  Questions look like this:


3.  Screencast!  Our school got an iPad cart (20), so I checked it out and had students make screencasts explaining their solutions to a particular equation.  Here’s an example of one.  He made some nice mistakes in there.  I gave feedback, but I’d love to work out a system where they view and critique each other’s screencasts (working on it!).  We also used Infuse Learning to practice literal equations:

photo (2)

4.  The Exam.  So, to assess this skill one more time, I have a scenario similar to the Dog Spa problem on their quarter exam.  My strategy on the Algebra exam is inspired by a History teacher I had in high school who would give us essays on every test, but let us know the topics beforehand so that we could prepare.  I decided to try something similar by giving the students the scenarios, but not the questions.  Here’s what I showed them:

And here’s the questions I asked:

And I gave them some class time to prepare for them.  I told them to think of questions they have and how they might go about answering those questions.  I also told them to think about what questions I might ask and how they would answer those.  Feelings about the exam were mixed.  Some students were excited that I was giving them a peek at the exam, but others were confused as to how to proceed because of the lack of questions.  I think the latter group of kids is the group I referred to earlier.  They’re the ones who are not making the connections between the activities we do in class and the skills required for the assessments.  Like maybe they participate in the group activity by making a graph, but then never learn about writing an equation (“my part’s done here”).  Now that I’m thinking about it though, it seems like the solution might be more problem solving activities, not less.  That would mean more chances for that kid to write some equations, right?

So why the title “Function notation can wait”?  Well, I started the year with my Unit 1 called “Modeling with Functions”.   But, I found that my students were thrown off by the notation and it was hurting the learning process.  For instance, we did the checkerboard border problem 3-act-style (thanks to Dan Meyer for the fancy graphics).   Here’s a few examples of what they came up with:

photo (3) photo

They explained how they saw the pattern very well and then also used function notation in their equations.  But when I asked them to explain why they wrote the equation that way, I got “Because that’s how you did it”, and that’s not what I want!  They should use function notation because it’s useful as a labeling tool, not because I said so.  Other groups wrote the equation as (# of blue tiles) = 4*(width of smaller square) + 8, which I like much better anyway.  I don’t want to confuse anyone when they clearly get the idea conceptually.

So, new title for Unit 1: Patterns and Modeling.  Function notation can wait.

What I Learned at Camp


More specifically, Twitter Math Camp 2013!  Here’s what I got:

(note: these are just some highlights, I learned way too much to capture in one post)

First and foremost, I learned about how to teach math better.  That was definitely the focus of the conference.  And it wasn’t just obvious to us classroom teachers, see Eli’s take on it (from Team Desmos):


So, the “big picture” takeaway for me was definitely Max Ray’s “I notice, I wonder”.  I just love the wording of that!  It’s so inviting; everyone can notice something, and everyone wonders about things.   The basic idea is that when you present the students with the scenario you want them to analyze, first ask them what they notice, then what they wonder (and give credit to all ideas).  Simple, brilliant!  And when I really thought about it, I noticed that I had been trying to ask these questions of my students all along (in both my physics and algebra classes), but I had been fumbling the wording. 😦  I would say things like “so how does this work?” or “what’s going on here?”.  Duh, Mr. Owen, if they knew what was going on already, then they wouldn’t need the lesson.  In Max’s session, I noticed that after we had done a few minutes of noticing, some people started throwing out things that they wondered too.  I wonder if it’ll be that easy with students, I hope so.

I also learned about what makes for a good group work task and how to implement one.  Thanks to Anna (@Borschtwithanna) and Jessica (@algebrainiac1) for that one.  Main takeaway from their session was that to be a good group task, there need to be multiple obvious ways to solve it.  What a great way to get kids talking about math, have them solve the same problem and then debate who did it the “best” way!  That may not have been the main point of the session, but that’s what I got out of it.

While that session was on the topic of group dynamics, I also attended a great session on building a class community.  It was Sadie’s (@wahedahbug) session on Counting Circles.  A counting circle is a classroom routine that builds number sense.  It’s pretty much what you would think a counting circle is.  Sadie suggests chapter 4 of this book to get started (I have not had a chance to check it out yet, but will soon).  The book is for K-3, but the concept is totally scale-able.  It’s not just about counting!  For instance, let’s say we’re going around the circle counting up by 1/2s, then I stop and ask “what number will Suzie be?” (Suzie is 7 kids from where we stopped).  Some of my kids will go straight to a linear function to solve that, some won’t.  But that’s just it, the methods will all be on the table so we can share and learn.  But I think the biggest reason I’m gonna use it is for the confidence building.  As we started the counting circle with a group of math teachers, several of us commented that we were nervous.  Imagine how the kids will feel!  The thing is, we’re all in it together.  I felt like a part of a mini community in our session and that was after doing it once.  If I make this part of my class routine, my hope is that the kids will feel that same sense of community.  This should make them more confident and less afraid to share out, and that’s in addition to the numeracy skills we’re building.

It was also great having Team Mathalicious there.  I had already planned on utilizing some of their lessons, so having them explain their thought process really helped me out.  I feel that after attending their sessions, I’ll be not only better at implemented their lessons, but also better at writing my own real world lessons, based on my own and my students specific interests.  It didn’t hurt that Steve Leinwand  and Ann Lawrence were both in my lesson writing session, throwing out ideas and asking good questions.

I also learned way too much to type by just talking to people.  The importance of these face to face encounters cannot be overstated.  I think that was the best thing about the camp.  Every conversation I had was amazing!  Some were not math related (which is a good thing!), but a lot of them were.  And it was super obvious that everyone there has a passion for what they do.  Specifically though, I saw a passion for math (or maths for our British friends) in many of the attendees.  What I mean is that they were in one way or another involved in doing mathematics, not just teaching it.  In his Mathematicians Lament, Lockhart talks about how we don’t get music teachers that don’t play music.  The implication is that we do have math teachers that don’t “play math”.  And that has definitely been true of me.  It’s not that I don’t like math (especially to play with), but I haven’t been doing it, really.

So I had a few conversations with Edmund Harriss (@Gelada) and he totally convinced me that I need to.  Not because I’m a terrible teacher if I don’t play with math and constantly work at new problems, but rather because it is fun.  For example, he asked me if I had heard of the 3x+1 problem.  It goes: take a number, if even —> take half, if odd —> 3x+1 it, then repeat till you get to a loop.  Try it with 3:  3 – 10 – 5 – 16 – 8 – 4 – 2 – 5.  And bam! there’s the loop!  Now try 23.  Have fun!  But where it really gets interesting is in the mathematical art.  Check out some of Edmund’s stuff, amazing!  And after seeing the things he did with Desmos after only a few days of playing around with it, I’m convinced that I need to play around with math more.  Of course, kids like to play too, I just need to give them some toys!

So, there it is.  Teach math better, play with math more.

I had an awesome year, but…


Next year will be so much better!! I learned so much this year and I love my job more than ever. Im gonna punch next year in the face.

Here’s a few things I’ll keep and a few things I’ll change:

Flipclass: Some parts I liked, some parts not so much. I found that taking the lecture out of the classroom and moving it to the home environment was not effective. Now, I’m not saying that direct instruction doesn’t have its place. The videos I made did get watched and they were helpful to many students. It’s just that I had them at the wrong point in the learning process. The awesome thing is that the kids showed me this by how they used them. I had intended for them to watch a video on a particular topic, then come in to class ready to discuss and dive into activities. But hardly anyone was watching them (they didn’t know why they needed those skills yet).  So we’d do our activities, then have some sort of assessment.  The kids who weren’t making the right connections between the activities and the problems or tasks on the assessment did poorly on those assessments.  But then, they used the videos to get some help before they reassessed on that topic (and really these were the kids who I made the videos for in the first place).  Seeing this, I kept making the videos, but with this purpose in mind. Which leads to my next topic:

Homework: As I started the year having students watch videos for homework, I had a bit of a dilemma after scrapping that idea. Should I go back to p.342 #1-30 even? Should I give just a few problems (a la Dan Meyer)? Or do I just not assign homework at all? I ended up doing some of each, and while I preferred no homework, I found it hard to get everything done in class. So I’m giving homework problems again next year. But i think I’m gonna like it because I’ll be using SocraticBrain.com, which tracks homework progress automatically. I plan to put certain skills in there throughout the year to make sure that we are keeping them fresh. Which leads to my next topic:

Spiraling skills: I feel like this was my main problem this year. I didn’t do a good job of keeping skills coming back throughout the year. One place I failed was not reassessing enough. This is another place where SocraticBrain.com will help out. When I make a rubric, I can include whatever skills I want on it. That way, all skills can be tracked all year. So lets say I give a task where they need to solve a system of equations by graphing it, and a student makes a mistake with slope. I can enter a new score for slope in the gradebook, so that I and the student both know that even though they may have had it at some point, slope needs some work now.  I also am planning to implement some “Algebra Skillz” after talking to a colleague about it. He does a set of basic skills each week with different sorts of incentives for getting them done. They can work on them whenever they have time, and they check each others work. This way they’re constantly keeping tabs on any basic skills that may need work. Which leads to my next topic:

Standards based assessment and reporting: Love it. Not a fad. Gonna keep doing it. Just changing systems. I used ActiveGrade this year and it worked great, I definitely recommend it if you’re looking for a SBG system. I think it’s even linked with Haiku LMS now too, so check it out. But the benefits of teaching next door to the creator of your system are too many to pass up. My friend and colleague Stephen (@socraticbrain on the twitter) has put quite a lot of work into making SocraticBrain.com and next year I’ll be using it for Physics and Algebra!! If you can’t tell, I’m pretty excited about that because it’s awesome. It has algorithm generated questions for homework and quizzes, rubrics for graded tasks, ClassDojo style assessment of discussions, and all of it is automatically entered into a standards based gradebook. It’s kinda hard to describe out of context, but look out for plenty of posts next year about it. Speaking of awesomeness:

Inquiry learning: Sometimes it went well, sometimes not, but I always learned something. One major reflection from this year is that questions are extremely important and that they should come from the students whenever possible. I found that our physics lab discussions were not successful because we did not always have a clear goal in mind. I knew what types of questions the kids would be able to answer as a result of the lab, but they didn’t. So the plan next year is to start all labs with “what types of questions should we be able to answer using this model?” For instance we could watch a video of a bowling ball and a tennis ball being dropped from a window. The students will probably want to know which one is going to land first (and hopefully some other stuff too).  So then we could bust out some carts and tracks and start to develop a model for accelerated motion.

I think that I did a decent job of coming up with and/or finding some good inquiry activities in algebra. I even got a shoutout on Dan Meyer’s blog for some of the cool activities we did (and also got linked to from Frank Noschese’s blog, dropping the big names here) 😉 So I’m doing something right I guess! That said, I know I have a lot to learn about executing a good 3act. I’ll be watching Dan and Andrew to get better at those (and you should too).

What are you planning to get better at next year?  Can I join you?  Anything I can do to help?

Collaboration is Key


I do not consider myself a master teacher. But I feel like I have brought myself closer to that goal this year than in my previous 5 years combined. And collaboration has been the key. My advice to all teachers who care to listen:

Get on Twitter and find some like minded people there.

Here’s just a few examples of how my Twitterings have helped me and my students this year (there are like a bajillion of these too!).

Example 1:


I follow Danny (college physics) and he posed the question “What is a model?”. You can see my reply and explanation there in the pic. What’s awesome is that this collaboration went from the classroom to twitter, then back again. Literally the next day in class, I used the analogy of a model being like a tool. We were in a circle holding up our whiteboards to show what we had learned from a lab. I told students to think about digging a hole. What would they do first? (Get a shovel) Then I said “the board you are holding is your shovel!”. Some of them were holding spoons we decided, and since it’s pretty hard to dig a hole with a spoon, we better figure out how to make those boards better.

Example 2:



Then this:


Example 3:

I think it is very important that HS teachers begin talking more with college professors so that we can figure out where there may be gaps in kids’ knowledge between our classrooms. And so we can share ideas on best practices in teaching and learning. Guess where we all are?


Example 4:

The best idea in collaboration since the mathtwitterblogosphere: the CCSSM Draft! Last night, a small group of teachers decided to NFL-style draft their two favorite common core standards from grade 8, along with one math practice standard, and then create a lesson with them. Here’s the story of how the whole thing shaped up over the course of a few hours on a Friday night (it’s a little long, but give it a chance!).

What I especially love about this is that it feels like our version of Genius Hour (a sort of free for all learning time). I would love, love, love for my students to have Genius Hour in my class next year and so the chance to model what it looks like and what you can get out of it is awesome! Bonus: the link I provided up there for Genius Hour also shows how powerful Twitter can be as a collaboration tool.

Man, do I feel like the major underdog on that list for the CCSS Draft! I better bring my A game. 😉 And that’s the point, right? Give kids some time to work on something they care about, and they’ll bring their A game too.

An Attempt at Mistake Analysis


First of all, if you somehow read my blog, but not Andrew Stadel’s, stop here and subscribe to his blog.  He’s been doing awesome work with 3 Act videos, his estimation site, and recently analyzing math mistakes.  Then, as Mr. Stadel said in a recent blog, you gotta check out Michael Pershan’s Math Mistakes page as well.

Ok, so here’s my contribution to the mistakes conversation.  I had students do this activity (it’s a functions matching activity) that I got from Mrs Reilly’s blog.  It went pretty well and I was pleased with the results in general.  Then, as an extension I gave each group a whiteboard with a quadratic equation on it.

That’s it. No real instructions.

They naturally decided to make a table, a graph, and a sentence for their equation.  This ability to go right to work creating different representations is something that we’ve been working hard on in physics and algebra, and I was pretty proud of them for just doing it without explicit instructions.

The results in one of my classes were not so great though.  Their boards were riddled with mistakes and we ran out of time in class to do any real work on fixing them.

But the next day (different classes), I had a spur of the moment idea.  I had a hunch that this class was going to do a little better on them in general, so I thought “Why don’t I give them the same problems and then have them compare their boards to the boards with the mistakes?” And then that turned into the students writing notes to the other class to help them out.  Here’s the boards with mistakes and the notes (some are more helpful than others):


I love the idea, but it didn’t work exactly as planned.  The students were not really thinking about the specific mistakes made by their peers.  They were mostly just pointing out that something was wrong.

I like that the mistakes weren’t obvious necessarily, but that did make it harder for students to spot them.  I think I can build up to this activity by using the mistakes game more frequently in class (basically, they insert a mistake on purpose and the rest of the class tries to find it).  By getting good at finding these purposeful mistakes (which should be easier to spot), they should be better prepared to spot accidental mistakes and even misconceptions.

Real World Factoring


I got asked today “is there a real world connection to factoring?”. I hadn’t heard that one in a while and I think it’s because I’ve been doing a good job of “starting at the end” like this awesome teacher. Factoring though, that one had me thinking I’d better just stick with what I know. So I showed them the area model for multiplying two binomials, then we worked that backwards and called it factoring. We even did some whiteboards earlier today. I told them a new student was coming and they would need to teach them the skills they just learned using only one whiteboard. Here’s what they came up with:

Not too bad. I also asked them plenty of questions to make sure each group member could explain what was on their board. And there were a few mistakes (some still in there), but that was ok because we fixed them as a group! So, clearly they’ve got this skill now. But the question still came up “is there a connection?”. Dammit.

I think that my techniques here were good because they can factor a trinomial now. And we also have made connections between quadratic equations and real world projectiles:

basketball shot

The constructed response portion of our last exam even had a real world connection:



But where I failed was connecting these events.

So I think what I should’ve done was start the unit with a video of a projectile.  Then get the students asking questions like “how high will it go” or “where will it land”. Then when I show them factoring (using the same method I just did) they won’t ask “where’s the connection?”, they’ll just proceed to answer their own questions using this handy new skill they learned (plus maybe a few others).

Modeling in Algebra I: An example


The modeling method I’ve been using to teach physics has really made me think about way I teach Algebra.  Here’s a good example:

The topic:  Exponential Functions

The way I taught it last year:

Step 1: Introduce the topic with some notes and some example problems.  I used a PPT presentation to show the students the equation y = a*b^x and explain what all the parts mean.  Then we looked at some example problems.

Step 2: Explore the topic with an activity.  We did the classic M&M’s activity to explore a “real world” example of exponential growth.

Step 3: Practice.  We used problems from the text, most of which did not have a context.

Step 4: Assess.  We had a test after about a week or so.  Done.

The way I taught it this year (modeling):

Step 1:  Explore the topic starting with this clip from the movie Contagion.  I got the idea from Leslie Macfarlane on 101 Questions.  I used this handout with it.  We started by discussing what factors would effect the spread of a virus.  We came up with a bunch, but most importantly: the type of virus (R-0 in the video clip) and the number of people who currently carry it.  Here’s what their handouts looked like filled in:

Photo Jan 13, 3 54 15 PM

Step 2:  The kids figured out on their own (in groups) that the flu virus doubles each cycle and the smallpox virus quadruples each cycle.  They also were able (with a little help) to figure out that the cycle # (x) needed to be the exponent in the function.  Then, it wasn’t hard to get them to write the function like this:

(total # of people infected) = (starting number of people) * (mutiplier)^x

Step 3:  Generalize it!  We then discussed a general form for the equation.  They needed to make a connection between the R-0 number from the video and the multiplier they used to generate their charts.  As soon as I brought up the question, they noticed that it was just (1 + R).  At this point, my head almost exploded from awesomeness.  Now, they understood that the “multiplier” they used was given by one plus the growth rate.  How did that happen?!  I didn’t “teach” it to them!!  So now they’ve got y = a * b^x, they know what the “b” means, and since we graphed each initial scenario, it was simple for them to see that “a” is the y-intercept.

Step 4:  Expand the generalization to new scenarios (exponential decay).  We used this handout to figure out that if you are losing a certain percentage each cycle, then it’s just (1 – R) instead.

Step 5: Practice.  I gave them 3 or 4 scenarios of each type to practice.  For each scenario, they made a chart and a graph (using Desmos or by hand).  The answer to any questions asked was secondary to showing me that they could analyze the situation using the exponential model.

Step 6: Assess.  Two short multiple choice quizzes, some questions with contexts, some without.  Then an open ended task in which they had to explain to me the differences between two functions.  Retakes are available on all three assessments as needed.  They also take the assessments when they are ready.

Why is this new way better?

I have students now who are willing to try figuring things out on their own.  They see that it can be done.  Especially in Step 4, I saw a bunch of students working to find a function that defined an exponential decay scenario.  They didn’t say “Mr. Owen, what’s the formula?” or “I don’t know how to do this because you didn’t teach us this yet.”  Check out the example below.  This girl decided that (hmw * .10) = y  and that the next value in the table was given by (original amount – y).  I just had to suggest using substitution to combine those two expressions.  From there, it wasn’t too hard for her to see that to do that 10 times, you just raise the expression to the tenth power.

Photo Jan 10, 9 26 28 AMHere’s an example of a practice quiz done by a student (this one has no context):

Photo Jan 11, 11 57 23 AM