Author Archives: quantgal

About quantgal

Laurie has an MS in Education and an MA in Economics. She teaches high school math at Sir Francis Drake High School in San Anselmo and has credentials in mathematics and economics. She has also taught middle school math and she's taught business and statistics at College of Marin. Laurie and her husband, Doug have raised two daughters who are now in college. You can email her at

Unit 1 Planning: Get them engaged on Day One!

(8/21) I will have my first day with my Algebra 2 students on Thursday (8/24). Here I sit, thinking about what to start with. Last year, we learned how to write numbers in different bases. Kids enjoyed it and asked to do more with it. But, we didn’t have a lot of time for it and it did not show up on the first test. It’s not part of the Algebra 2 curriculum. However, I remember learning about different bases somewhere in my high school math classes. It’s disappeared from the curriculum. Or, maybe it’s reappearing somewhere else.

Having kids learn to write the number 25 in base 5  (looks like 100), 7 in base 7 (looks like 10), 12 in base 4 (looks like 30), really is interesting for them. Their little neurons start firing. They say things like “Whoa!” and “That’s so cool!”

We also spent time issuing texts, getting kids signed up on Remind , and doing getting to know you activities. We went over some expectations, etc. But, I knew I had won them over. Then I started teaching.

This year, I want to do that again. And get them on Desmos quickly – download the app, etc. Play Marbleslides: Lines, etc.

(8/23) I make a plan often based on all of the great ideas and inspiration I get from Twitter math teachers (#mtbos #iteachmath), Jo Boaler, Dan Meyer and many others. I recently read a great article about not grading students in the first month (or some time frame like that) and I thought, “Wow, what a great way to build culture and address equity issues.”

So, I’m thinking about that right now.

I feel that the most important things I can do as a teacher is invite students to be curious, let them know they are an important part of the class, and teach them mathematical concepts. After meeting with my excellent colleagues, I’ve come up the following plan:

We are going to see if those iPads work. If they do (fingers crossed) I want to get students to do a card sort activity, and hopefully play some marbleslides and then get into some vocab around linear functions and translations. We will get signed up on Remind and learn about a few classroom expectations. Seriously kids, no phones and limit your bathroom breaks.  Be nice. That’s really it. However, when working with teens, there is always a need to discuss these things, come to an agreement and then move forward. They will test these agreements. We will need community building. I look forward to that.

I’m really excited to get going. I’ll be working some great activities and mathematical ideas into my lessons. We’ll explore some history, look at different bases, play games on Desmos, be creative, and have another great year!

Excellent Summer PD: Desmos Summer Institute

This summer I went to a two day Desmos training in sunny San Diego that was completely dedicated to improving student learning through activity builder.   Dan Meyer, their CEO, kicked off the training with his typical charismatic, humorous and collaborative way of learning about us and generating the goals and plans for the next two days. There were about 25 teachers and a group of Desmos staff and Desmos Teacher Fellows. So, we were surrounded with amazing support, creativity and collaboration.

The Desmos staff said we can share the materials from the workshop. I love that attitude of sharing. In that spirit, I’d like to share with you one of the great shares of Day 1, the Desmos scavenger hunt. The Hunt provides tasks and solutions so you can test your skills and learn new ones. We had great fun with that.

Using the activities or making your own requires you go to I recommend you get started by watching the one minute video and then create an account. You can login and start searching existing activities.

I recommend starting with searching the existing activities and activity bundles. There are individual activities or bundles of activities by topic (there is a list on the sidebar to the left of the screen). For instance, in Algebra 2, there is a bundle for exponential functions. There are currently seven activities. By doing a quick preview of each activity, you can decide which ones you want to use and when to use them during your unit. As you preview the activity, you’ll see a green pop-up that gives teacher tips. They are really helpful.

To make your own activities, I recommend using the materials provided by the Desmos team to help you build a great activity. To build your own, use this link to get started Or, sign in to, and click ‘Custom’ under ‘Your Activities’ on the left side bar. You can click ‘New Activity’ on the right and then click the ‘Get Started Here!’ link to take you to, to see helpful videos and examples. I also really recommend that you use the Teacher Guide when creating your activity. Each activity has a printable guide to help you build your activity and lesson plan. [FYI, the link to the Teacher Guide is an example, you will get one that corresponds to your activity]

I love the activities in Desmos and have had great success with them. Students work and I am freed up to circulate and help as needed. At a glance, I can see where every student is from the teacher dashboard. I can use the teacher tools to anonymize student names and project individual student work or entire class screen overlays so students can see multiple ways of solving problems. Students get instant feedback on their work. Pacing is individualized and many activities get more difficult as you progress, which challenges every student. Students naturally start to ask each other questions. I can partner students as needed. I can even pause an activity – which always leads to groans and the question, “Why did you stop it?!?” You can read about my marbleslides experience What’s great about marbleslides, if you want more details on a specific activity.

My takeaways:

  1. There are amazing educators out there. Find them and stick with them. Then, find more. Share your ideas. Share your lessons. Build better lessons together.
  2. There are great activities for Algebra 2 already built in Desmos. I’m not sure I want to build any myself. It’s not easy to do and more are being added all the time. There are teachers all over the country adding to the bank of activities.
  3. The activities are varied and can be used in many ways – introducing a topic, vocabulary builders, practice, and formative assessment. So far, the ones I’ve used have all provided differentiation for students.
  4. I will build some activities for my AP Economics classes, which I will be teaching for the first time and am very excited about. I’m picturing supply and demand shocks as a starting place. I built my story board using post-its, as recommended, and am ready to start building!

Having the time to really delve in and learn the tools and process for building activities was a gift. There is a second training August 10-11 in San Mateo, CA. Sign up by July 21

Feeling Overwhelmed, Math Teacher?

Time for a break. The best thing to do is turn off your computer, put your books away, close your planning book and take some time to think about other things. Really, just shut it down.

I can hear you saying to yourself, “I can’t because I’m expected to have this done by…” whatever deadline you’ve set for yourself. You can shut it down, though, and you should because you are feeling overwhelmed. And, you are most likely feeling overwhelmed because you are overwhelmed.

This job can get really demanding sometimes. People generally don’t seem to understand that. How could they unless they’ve done it? And, sorry to say it, but here it is… It can even sometimes feel that your administrators don’t understand what your workload is like. You have so much to do and so many people asking you questions and needing your help, that you sometimes don’t get a chance to eat or get some water or do the things you had planned to do that day. And, because you couldn’t do them, you are not ready for tomorrow. Yikes, stress!

When you’re having these thoughts and feelings, listen to them. When things feel like they are too much, it’s because they are. So, set everything aside and go home. Nurture yourself.

Go get some coffee, take a walk, go to a movie. Let yourself get back in touch with other things that matter. Read a chapter of a book you’ve been meaning to read. Play some music and dance in your living room (or classroom). You need a break, both mentally and physically.

When you go back to work, all that stuff will feel a bit easier. You may find that some of the problems have resolved themselves. Or, because you’ve calmed down and relaxed and are feeling better, you think of easy, creative solutions. You get some ideas. Novelty returns.

Give yourself a much needed break, even while still at work.

It’s okay to find an easy activity for the day to give you a bit of recovery time. Or, work in a review day and pick some random problems from the book. Don’t give homework.

Ask students to write 5 quiz questions for the next quiz based on the assignments so far. They will be working and you can circulate to see what they are thinking. Ask for 2 easy problems, 2 medium problems and 1 tough one. You can even differentiate and ask some students to write only 3 questions, but that have multiple parts. Mix it up. Notice what kids are saying, give guidance. Ask them to make mini how-to posters on graph paper. Have them color them in. All of these activities are useful for them, help to build mastery and allow you to relax and help and not be the center of attention.

It’s okay to not reply right away to email. It’ll wait. And your reply may even be better if you give yourself some time.

It’s okay to push your schedule back a day. You made the schedule! You can change it! If you are feeling overwhelmed, your students probably are, too. Ease off the gas pedal.

And, really, no matter what people say to the contrary, it’s okay to postpone the quiz if you haven’t written it. It’s okay to give a quiz with only 5 problems instead of 20. It’s easier to grade that, too. It’s okay to not work insane hours trying to do it all. Listen to your own needs sometimes.

As teachers, we set really high standards for ourselves and sometimes we struggle to meet them. That’s okay. Rest and good health are really important components in running a marathon.

I wonder, is math more demanding to teach than other topics? Well, maybe. I can think of some arguments supporting that view. My only experience teaching another subject was at our local community college, where I taught in the Business Department. It was definitely easier. But, it was also college.

So, let’s take care of ourselves, Math Teachers. When things start to feel really intense, take a break. Let your mind and body relax. You’ll actually handle the work demands better, once you forget about it for a while.



Tough grading moments….

I’m re-blogging this post from last June. It’s a good recap for keeping grades, grading and study habits in mind as we launch into our second semester next week

Laurie Hailer

One of the toughest things about grading is when the students with 79% or 89% ask/plead/argue for the B- or the A-. I do round an 89.5% or higher, to the 90%. I think that’s just doing proper rounding, as I like to teach in my classes, as opposed to truncating the grades. [Don’t know what truncating is? You can find out here] . But then, the 89.2% kid asks for the A-, too. I would be inclined if their test scores were in the A range, but they weren’t completing all the assignments, and so homework was dragging the grade down. But, if the test scores are in the B range, and homework completion is bringing the grade up to B+, I think that’s good enough.

I have several students who’ve missed a lot of school, or have ADHD and just don’t complete every assignment, or just never are there…

View original post 809 more words

Helping Students Deal with Test Anxiety

Sixteen students and one parent just left my classroom after I hosted a math test anxiety workshop. The purpose was to provide some knowledge and insight about how to recognize the cause of their anxiety and to manage it before, during, and after a test.

We discussed what test anxiety is, the causes and symptoms, and then some techniques to manage those symptoms. I used three resources for the workshop (links at end of blog post). Most of the following is primarily from the Anxiety and Depression Association of America at this link. I used some prepared notes as we talked and had students write in causes and symptoms of anxiety, then reflect on what they were experiencing.

Here’s a play by play of the workshop:

Get ready:

First, set up the room with a seating arrangement where everyone can see each other. A circle is best, but tables pushed together to form a square works, too. Have some snacks out and ask student to pass them around and put away phones or homework.


Provide a handout and let students have space to write down the  information and reflect on their own experiences. Here’s a test-anxiety-workshop-handout with the guided notes sheet I created and a printed article from  available here. All of the links on the handout are listed at the bottom of this post (since you can’t click on the pdf links).

Encourage students to have a snack and pass the plate of mints (or other snack) around. This gets them to interact on a small (but fun) scale.

Intro: What is test anxiety?

Test anxiety is a type of performance anxiety. Much like a gymnast who has practiced her routine, she will feel nervous the day of the competition. Also, like the first day of school when we, as teachers, meet our class for the first time. We’ve prepared our greeting, have our course information organized and then suddenly get nervous as we actually start to speak. Students feel this during presentations, during competitions, and during tests. A little bit of anxiety can be a good thing. But, when it interferes with your performance, it needs to be recognized, examined and addressed.


  1. Prepared or not prepared? If you’ve prepared and feel you know the math, you’ve been successful on practice problems and you’ve completed the assignments, you’ve paid attention during class and understood the material, then you are very likely prepared for the test. However, you may not have done all those things and you may be feeling like you should have studied more. As students walk in the room, they are talking about things you are suddenly feeling unsure of. You may now be feeling unprepared for the test. This may be the source of your anxiety.
  2. Fear of failure and/or the consequences of failing. It’s possible that you have really high expectations of yourself or someone else has really high expectations of you, putting a great deal of pressure on you to perform well on the test. Maybe you think you must get an A or you will not get into that prestigious college. You don’t want to do your best, you want to do THE best.
  3. Prior bad experiences in math or on tests resulting in a negative attitude towards your performance, or the test, or school. These past bad experiences can be causing anxiety.

After discussing these causes, students were given some time to reflect on what was causing their anxiety. It could be from one, two or all of the above. We took about 5 minutes to share out. This share out allowed students to talk and hear what was causing stress for others. They could share their personal specific situations. After the share time, the mood in the room was more relaxed. People were talking to each other about what was bothering them and what they were worried about.


  1. Physical: headache, nausea, vomiting, diarrhea, sweating, shortness of breath, rapid heartbeat, light-headedness, and feeling faint. It can even lead to panic attacks which can make a person think they are having a heart attack or can’t breathe. All of these physical symptoms detract from a person’s ability to focus on other things.
  2. Emotional: People can feel feelings of anger, fear, disappointment or helplessness. All of these feeling interfere with one’s ability to concentrate. They can be a consuming. It is hard to simplify a rational expression on a test if you are dealing with these feelings.
  3. Behavioral or Cognitive: Having negative thoughts or comparing yourself to others can cause anxiety. Your concentration is lowered when you are telling yourself that you aren’t as good as others.Are you telling yourself you’re bad at math? Or that you are not a good test taker? Those are negative thoughts and they cause anxiety if you are about to take a test.

Again, give students time to write down their symptoms and share out.

Tips and techniques to manage anxiety

Before the test: (and maybe during for some)

  1. Minimize the susceptibility to anxiety by taking care of yourself. Get enough sleep. Not just the night before the test, but regularly. Eat a healthy breakfast – eggs, oatmeal, something nourishing. Drink water. Get exercise and take time to yourself on a regular basis.
  2. Make sure you’ve actually prepared. Ask your teacher for guidance. Check resources at for ideas about study skills. Studying takes place early and often. Cramming rarely results in sustained strong performance.
  3. Keep a positive attitude and remember that this test is not a measure of your worth as a person. Do your best and keep expectations reasonable. When you expect A’s and A’s only, well, that’s putting the highest expectation on yourself that you can. Would you do that to a friend? Probably not.
  4. What would you tell a friend? Tell yourself the same thing. Use positive self-talk. Remember that great 3-pointer you shot, or think about how great your boots look, or how you wrote a great poem, or paper. Think of your favorite song or book. Think of a favorite character from a favorite book and imagine what they would say or do.
  5. Have a reward planned for after the test. Give yourself something positive to look forward to. A movie after school, ice cream with friends, etc.

During the test:

  1. If you notice anxiety setting in, work to balance it. For physical symptoms, take three deep, slow breaths. Then, relax your jaw. Actually let your mouth open a bit, making sure your teeth are not touching. Wait 5 seconds. Then relax your shoulders. Pull your shoulder blades down your back and relax. Place both feet on the floor to relax your leg muscles. Jaw, shoulders, legs. Now relax your abdomen. Now your hands. Put the pencil down and rest your hands on the desk or your thighs. Take 3 deep, slow breaths.
  2. Then, tell yourself how great you are.
  3. Remember to read the directions and questions. Start with an easy problem. Scan the test before starting. Do the problems out of order. Where possible, check your answers. Always try something on every problem. Your idea is probably a great starting place.
  4. Focus on the test, not other students.
  5. Remember to look forward to your reward.

After the test, remember that you did your best. Enjoy your reward. For next time, if you need to study differently, ask your teacher for ideas. If you need more help with managing anxiety, ask the counselors for help, or check out the websites on the handout.

Give students time again to imagine which techniques they can see themselves using. Let them use some space to creat some positiev self-talk messages. Let them think of a possible reward for them selves. Ask them to share out.

Time’s up! Workshop over!


  1. ADAA: Test Anxiety
  2. : Test Anxiety Article
  3. Weber University: How to Overcome Math Anxiety

Teaching about Habits for Studying Math

This year, one of my focus areas is helping kids learn how to study math. It seems that Algebra 2 is a tough year for a lot of students. Students are combining so much of what they’ve learned – geometry, fractions, factoring, solving, graphing – and applying it to learning new and more complicated functions: polynomials of higher degree, rational functions, exponential functions, piece-wise functions, step functions, etc. The list is long!

I’m trying to teach habits that have worked for other students, using students who are successful as a model. However, a lot of the habits of successful students are those that are picked up from and reinforced by parents, teachers and friends. They are habits that they may even enjoy or at least find easy to do, and have likely been doing for years. They are the traditional obvious habits: go to class, take notes, practice in class, finish your homework, check your homework, make corrections, and find the answers to your questions. Finding the answers to your questions is important. You can check the book, online, ask a friend or the teacher during the next class.

What about some not so obvious habits? Maybe these traditional study habits are based on traditional learning styles that work well for traditional teaching environments. What about kids who’ve tried these, but need more? Well, this blog is meant to give some other ideas to try.

Here are some things to try:

  • Sometimes, just reading the question or concepts out loud helps. That’s a technique that’s not always taught. Sometimes, we just didn’t read the question and so we get the wrong answer and can’t figure out why.
  • Here’s a really helpful one that is often not used: look at the material before you come to class. The teacher will hopefully be following some sort of shared schedule and you can look at the topic ahead of time. That way, when you get to class, you have an idea about the topic and you are actually now hearing about it for the second time. This is a good idea as there are sometimes distractions during class and we don’t always have full focus every minute. This is a really helpful habit to use in college.
  • Make vocabulary flashcards.
  • Make a cheat sheet even if the teacher doesn’t let you use it.
  • Read the chapter review section and the practice test problems (back of the chapter) before the end of the unit. Look every week, not just at the end right before the test.
  • Get enough sleep.
  • Eat well.
  • Exercise.
  • Be realistic – it may not happen for you just by wishing. Do you need to put your phone in another room while you study? Are you really concentrating? Have you been avoiding thinking about math and avoiding spending time on it? Do you think you can study right before the test and do well?
  • Are you telling yourself positive things or negative things? Tell yourself you can learn, and you can succeed and do well. It takes work, and you can do it. If other people can do it, so can you!

I provide my Algebra II students with a list of habits – some traditional, some of the above – as well as a schedule. I keep getting better at presenting this. Every grading period (we have 3 per semester) I make a new one and each one is better than the first. The first time, I just put the space for them to write the topic, then I included the topics, then I included the topics and the dates. Prior to that, I had a separate calendar sheet, assignment tracker and habits checklist. Now, it’s combined. Attached is the most recent: r3-assignment-tracking-and-self-checks   The second page is the habits/topic schedule and checklist.

I really need to reinforce it, too. I want to spend more time reminding them to check the list.

What do you do that works well? Let me know!

My first #ObserveMe went poorly

Well, I was really looking forward to being observed using the #ObserveMe rubric from Robert Kaplinsky. I’ve really been consciously aware of elements from the rubric and want to make sure that in every class I am allowing time for students to work together, to ask questions, use diagrams and discuss strategies. I want them to do partner work, individual work, and participate in full class discussions.

Today, I had a colleague scheduled to visit me and do an observation for 30 minutes. I was trying to accomplish two things today:

  • Connect intercepts of a graph of polynomial functions to the factored form of the equation
  • Teach how to factor after creating a desire to use factored form

I’ve noticed that most of my students struggle with factoring. This year it seems to be that more students struggle with it than in the past. So, I don’t think they struggle, really, I think they just haven’t practiced it enough. Maybe it’s just not as emphasized as it used to be. No problem. But, for polynomial functions, factored form is pretty nice.

I’ve seen that most of my students can factor using GCF really well and they can factor quadratics really well when a is 1 and some do well when a is something other than one. They are good with the box method and the diamond method. Some are using the box method to factor higher order polynomials too (third degree, mostly). But, most struggle if they are used to the diamond method and a isn’t 1. Many also have a hard time recognizing a difference of two squares. So, lots to review and lots to learn.

Because we just finished a grading period last Friday, I spent much of the weekend grading and planning. I had some trouble finding what I was looking for for today’s actual focus. Polynomials: graphing, factored form, factoring. There’s actually a lot out there, but I can be picky and I didn’t want to create my own. I ended up purchasing a bundle on Teachers Pay Teachers. There was a good assortment of problems, note templates and it was well organized, covering all of the concepts and factoring that I was looking for.

Anyhow, for the observation, I had thought to focus our class discussion and activities on multiple representations of polynomials – equations, tables and graphs. Then, with the help of Desmos, students worked together to complete an assortment of questions. Some were lower level fill in the blank, others were more big picture, “How do you know when you are done factoring?” I’m still thinking about that. I can’t wait to see what they say.

Well, in the last 30 minutes of our 90 minute class, it was time to focus on factoring rules and patterns. Using what I thought was a pretty nice set of sample problems and a nice set of practice problems, I projected my note sheet so that we could all go through the problems together. But, suddenly it’s was 9:05. I had 5 factoring concepts to get through in 25 minutes. So, I pretty much grabbed the reigns, led/dominated the conversation and worked through the examples (too quickly), with students mostly following my lead.

First set: Factoring with GCF, difference of two squares, then together. Ideally, those were review, right? So, going quickly through those is okay, right? (No, Laurie, not right. The whole reason I was doing it was because there some people who needed to learn/relearn that.)

Next: Hurry, gotta get to the sum and difference of cubes!

We got there, and I really just told them the rule, did a couple of sample problems (which weren’t super easy) and gave them the assignment. I didn’t get to the fifth concept, so cut the assignment short. No problem, we can go over that next time. Class ends…

Observation wise, my colleague was there for the last 30 minutes – the transition, then the ‘I lead, you follow’ method of instruction. Not my finest. She gave me all zeros.

Well, as much as it hurt my pride, it was really good feedback. I’m glad that I know I don’t usually teach like that. And, my students are actually doing really well this year. Things are generally really good. That is not meant to be a deflection or me trying to give myself a pass. I took that feedback to heart and immediately tried to find better ways to teach it.

To be honest, on some of the nuts and bolts stuff, I default to direct instruction. I would have been complacent about that and never changed had it not been for that rubric. I never expected to be an all zeros teacher. I know part of the problem was getting stressed about the time. Usually, I don’t care about that. But, overall, I feel like I am behind schedule, so I was feeling pressured to get that factoring happening.

As I’ve had the day to think about it, the direct instruction was okay, the notes and practice problems were all fine. It was the way I organized the discussion that left no room for student input, problem solving, strategy analysis, practice or interactions with each other, much less with me.

I might have run my next class the same as the first had it not been for that feedback. Instead, I gave more time for the factoring, and had students suggest first steps. We tried various methods. I had students talk to each other and work on a problems together.

Time was a factor today, certainly. However, my conscious decision to organize the conversation around student input and interactions in my second class, allowed students to have more time to think and express their reasoning. More time to ask questions of each other and answer questions. Those processes lead to better retention and interest.

On the upside, I’m glad that I know where my students are with factoring and was taking steps to improve what they know and expand on it at the Algebra 2 level. I look forward to seeing my first class again in two days, to better address those concepts and get some meaningful conversations and practice happening. That’s one of the great things about teaching. You get to see them again and fix what you did wrong.

Thanks, Robert Kaplinsky for that rubric. Thanks, my dear Colleague, for your time and feedback.