One of the most common questions teachers ask me is, what is the best way to launch the year? Should we start with getting to know you icebreakers, or a syllabus review, or just dive right into content? Or maybe we should do an out-of-the box, non-routine math problem, a la Jo Boaler. Is there a happy medium between all of these ideas?
While I certainly don’t claim to have the definitive answer to this tricky question, over the years I have concluded the following:
- I like to start with content quickly. As in, no more than 2 days on other stuff.
- It is critical to explicitly state your behavioral and academic expectations on the first day. Even if it seems boring or strict. You can be a little boring and strict on the first day or two, to make sure your students understand that this is a serious class with high expectations. You will show your lighter side quickly. Don’t be mean or anything, but make sure you aren’t too casual either. It’s always easier to loosen the reins than to tighten up.
- Trying to front load the authentic experience of you and your students getting to know each other into the first few days of school is awkward and ineffective. The best way for kids to get to know each other is to work together. So better to get them to work, and make sure you mix up the groups and give them structured roles and discussion points to get the conversation flowing.
- Starting the new year with unit to review the previous year’s content is a mistake. It will only make your struggling students feel that they are already behind, and encourage them to adopt a negative mindset from the start. Furthermore, the review time is almost always too slow for kids who are caught up and too fast for students who are behind. Instead, let the year begin with new content, and gradually spiral in review as needed. This lets all kids start the year on equal footing. It will keep your top students on their toes, and encourage students who struggled last year to treat your class as a new opportunity to shine.
So with all this in mind, how do I start Algebra 1?
Last year, I decided to devote my entire first week of 9th grade Honors Algebra to teaching my students how to use graphing calculators. Coming up from middle school, where they are not allowed, most of my students had never even turned one on.
Here’s exactly what we did:
- Day 1: Calculator Basics + Evaluating a function
- Day 2: Graphing a function
- Day 3: Finding equivalent expressions
- Day 4: Determining if a point falls on a graph/is a solution to an equation
- Day 5: Quiz
Why calculator skills? Three reasons:
EQUITY I have taught in one the wealthiest zip codes in America and one of the poorest. One thing I noticed was that students who owned their own graphing calculators tended to know how to use them better than students who had to borrow one in class and return it at the end of the period. This confers advantages on all kinds of tests, most importantly the SAT and ACT. Therefore, I am committed to helping my students who only have access to a shared graphing calculator for 45 minutes a day learn to use them with ease and sophistication. I hope this will minimize the effects of a specific technological gap on the larger achievement gap.
JO BOALER Reading Mathematical Mindsets rocked my world. One of the many lessons I took from Boaler’s seminal work is that being a mathematician is not about computing mental math with ease. We need to redefine mathematical skill to encompass conceptual understanding, analytical skill, and problem solving. Reimagining mathematical skill in this way, using a calculator can actually strengthen one’s mathematical understandings.
PRACTICALITY My school tends to have a lot of schedule changes and new admits during the first week of school. Starting with a mini unit on calculator use allows me to stall the start of my first “real” unit – functions – while still teaching my students something impactful. A student can walk in halfway through this week and be okay, whereas starting in the middle of the first week on Functions would be really difficult.
Here is exactly what I did each day.
I passed out the class set of calculators and then gave students 10 minutes to complete the Calculator Skills checklist. I didn’t tell them anything at all about how to use them, I just gave them time to play around and try to figure it out on their own. They were immediately engaged and chatting with each other about some of the more complicated tasks. Then, I shared the answer key and made sure students knew all of the basics.
Then, we started the real lesson. Below is our day 1 worksheet. I intentionally started out with an open-ended, “what do you think” question to encourage exploration and participation. Some students knew to substitute in 3, others had no idea. I was careful not to react with more excitement when the kids knew the answer than the kids who did not. This is crucial to creating the classroom environment I crave — one where students feel safe to take intellectual risks, to admit what they don’t know, and to participate freely.
After we discussed what f(3) meant, and I briefly explained the concept of a function, I shared with them the 4 methods of using the calculator to find the value of f(3). I referred them to the directions on the page, shown below, and let them work in their groups to figure out how to do each method. I circulated and monitored their work, assisting as needed.
When they were done, I asked each group to decide which method they preferred. I then let the groups share their preferred methods and challenged the class to come to a consensus. This method of guided discussion is inspired by the work of Rhonda Bondie. She was my professor at Fordham, and then ten years later I attended an amazing PD she gave through Math For America. I highly recommend looking her up if you’re not familiar with her work. It’s pretty amazing.
On Day 2, we transitioned into graphing. I gave students a quick mini lesson on how to use Y= and then put them to work graphing a variety of functions. But first, I taught them a routine called Noticings and Wonderings. Basically, students record what they notice and what they wonder. That’s it! A simple way to engage every learner. It worked perfectly for our intro to graphing.
Day 3 was all about equivalent expressions. Students can check if two expressions, like x2 + 7x + 10 and (x+5)(x+2), are equivalent by typing each into Y1 and Y2, and then comparing the tables. It’s a trick I’ve seen students use to answer all kinds of multiple choice questions, and I used to hate it. But over the years I’ve realized that this is actually a powerful way to make sure students understand that processes like factoring do not actually change the value of an expression, just how it looks. This helps reinforce that oh so tricky Common Core standard Seeing Structure in Expressions. To help my students practice this, I created a set of 19 expressions that they cut up into small strips and then tried to match up into groups of equivalent expressions. It was pretty difficult because the groups were unequal sizes. One expression had no equivalent expressions at all, forming its own solo group. One group had 2 expressions, 1 had 3, and 3 groups had 4 expressions. Because my class was Honors level and because they were using the calculators to assist, I liked this extra challenge. This activity could easily be simplified by creating simple pairs, or groups of the same size. My kids really enjoyed the cutting and pasting, and having the ability to move the pieces around as they tried to figure out the groups was really helpful.
Day 4 was about the relationship between solutions to equations and points on the graph. We played 2 truths and a lie. First I modeled it with my own statements, as sort of a getting to know you activity. Then, the students did the same with a partner. Finally, I shared a sheet with 7 functions and 3 points listed under each. 2 points were “truths” – they fell on the graph of the function – and one was a “lie” that did not. I told the students to use everything they had learned about their calculators that week to figure out the lie and correct it. I blew up each problem and posted them around the room, and sent the students around the room to complete them. It had been a long first week of school and giving them the chance to move around the room helped keep the energy up.
This was such a hit. Students came up with so many interesting ways to figure out if a point was on a graph. Some of them used the table feature, but when it came to decimal x-values realized they had to change the table from auto to ask in order to check those values. I didn’t teach this explicitly, but rather by giving those decimal values set up a situation for my students to face this problem and find a solution on their own. Other students just stuck with tried and true plugging in x-values on the home screen. A few used TRACE, typing in each x-value and seeing what y-value appeared on the graph. It was a great way to end the week because it allowed students to apply their calculator skills to connect equations and graphs.
I hope this helps inspire you to consider how you use the graphing calculator in class. Reach out if you have any questions via email or DM.
If you are interested in the materials I used for these lessons, I posted all of them to my TPT store – worksheets, Google docs, Google slides, and the end of week quiz. Purchase one at a time, or grab the full bundle of all four lessons plus the start of week Calculator Skill Checklist and end of week quiz.
- Evaluate a function using the graphing calculator
- Graph any function using the graphing calculator
- Identify equivalent expressions using the graphing calculator
- Identify points on a graph using the graphing calculator
- Graphing calculator skills quizzes + expectations
- BUNDLE of 4 calculator skills lessons + quiz