Math = Love

Saturday, August 18, 2018

Twos to Nines Challenges (AKA Best First Day Activity EVER!)

Day one and two are in the books! I'll share a bit more about what I did with my classes on the first two days in a later post, but I want to go ahead and share the mathematical challenge I used with my students on the first day since I have got several questions about it on twitter.

This summer, my husband and I ran across a treasure trove of puzzle books at Goodwill. We *had* to buy them. As Shaun was driving us home, I flipped through the books and would occasionally pose puzzles for us to solve together in the car. We had a lot of fun with this, and in the process I found some puzzles that would be PERFECT for use in the classroom.

One of my favorite new puzzle books from this Goodwill trip is 100 Numerical Games by Pierre Berloquin (affiliate link). If you don't believe me that this book is awesome, just take a look at who wrote the foreword. THE Martin Gardner!

You can a free peek at some of the puzzles in this book by using the "Look Inside" feature from Amazon.

One particular set of puzzles which is sprinkled throughout the book really caught my eye.  This version was based on the number two, but the book also featured puzzles for the numbers three through nine.

The task is to use exactly four twos (or threes, fours, etc) to make each target number. Add arithmetical symbols between the numbers to make every equation true. You may use plus, minus, times, and divide symbols, as well as parentheses and brackets for grouping. 

Originally, I thought about turning this into a puzzle for my puzzle table, but I never got around to it. Fast forward to this past week. I needed an activity to do on day one, and I decided I wanted to do something a bit different than what I've done in the past. For reference on past activities, check out my post on 21 Ideas for the First Week of School!

One of the messages I communicate to my students on the first day of school is that we do math everyday. I can't just say this. I also have to give them math to do on day one.

Yes, there were some groans. We carried on anyway.

My students are arranged in six groups of five, so I decided to set up six challenges around the room. The book featured challenges using the numbers between 2 and 9, so this meant that I had not used the challenges based on the numbers 8 and 9.

To introduce the task, I threw the Eights Challenge up on the TV.  (It's going to take me a while to get used to saying TV and not SMARTBoard!)

After a quick overview of the rules, I gave them a few target numbers to work towards.

Students quickly got to work. Some grabbed paper and a writing utensil. Others got out their graphing calculator or phone calculator. Still others just sat and thought about the task.

Within a couple of minutes, a student in each period would announce that they had found the answer to 10. I asked them to read me their solution so I could write it on the board.

Almost every single time, I ended up hearing 8 + 8 / 8 + 8 = 10. So, I would tell them that we needed to check their work. This was when I asked them what the order of operations says that we need to do first. Unanimously, the class would say divide. Then, a bit of panic would set in. 8/8 is 1. So, 8 + 1 + 8 is 17, not 10.

Without me saying a word, the class would start to suggest either a different way to solve the problem OR a way to salvage this attempt. It usually wasn't long before someone would suggest that we could use PARENTHESES! So, from this, I learned that we do know our order of operations. We're just a bit rusty, but I can deal with that.

After the class found a few of the solutions for the Eights Challenges, I decided to change things up a bit. I told them that now that they understood how the puzzle's structure worked, it was time to try a

Around the room, I had marked off six four-foot sections of white board space so that each group of students could have their own space for working problems throughout the year.

At each station, I had posted a challenge based on a different number.

I typed up the instructions for each challenge. My students didn't really need this since we had done part of the eights challenge as an example, but I did see a few groups reference it. One group used their dry erase marker to actually write symbols between the numbers. Good thing I laminated them!

Then, I typed up the target numbers that students had to find. I thought about making them into magnets so the students could move the target numbers around, but I wasn't sure where all magnets were. Let's just say that moving classrooms sucks. I can't find anything right now!

I ended up just taping them to the dry erase board. This worked just fine. Most groups left the numbers stationary and just wrote their solutions next to the appropriate number. A few groups did move the numbers around. The tape stayed sticky, so they were able to change the number positions without any issues. Since this activity went SO well, I think I will definitely add magnets at some point.

Each table group chose a different number based challenge to work on. They instantly got to work, and the room was soon abuzz with awesome conversations. Students were excited and joyful as they found various solutions. Students were checking other students' ideas and pointing out any issues. Lots of parentheses were being used. Were all their answers perfect? Nope. But, it's day one, and it gave me a great snapshot of where my students are starting from.

It was the first day of school and every kid was engaged. In fact, I would say this was the most engaged my students have ever been on the first day of school. This was my favorite first day of teaching EVER.

Check out this awesome group work! 

Each group was given one dry erase marker and one graphing calculator to encourage collaboration. Every few minutes, I would announce "SWITCH!" This meant that the person holding the marker needed to pass it to another person in the group. The calculator person did the same thing.

Every once in a while, I would introduce a new twist. About five minutes into the activity, I had the groups pause and look at me. I instructed them to nominate one volunteer from each group. This person was to hold their hand up so I could ensure that I had one volunteer from EVERY group. They asked what they were volunteering for. I just said "You'll find out soon."

Once one hand was up from every group, I informed the class that these students would be rotating one group clock-wise. So, each group would lose one member and gain a different member. There were a few groans with this announcement, but students complied. I was excited to try this strategy since each group was working on the same type of challenge, but no two groups had the same problems to solve. This meant that the new group member could bring STRATEGIES from their previous group, but they could not just bring ANSWERS.

After a few times of rotating a single group member, I changed things up yet again with having the entire group rotate to the next station. I did run into a few issues that I hadn't figured out how to handle beforehand. The groups assigned to the challenges based on lower numbers (2s, 3s, and 4s especially) were sometimes able to completely finish their challenge. When this happened, I did one of two things. In my smaller classes, there was often a challenge that had not yet been started. In these classes, I sent the finished group to this untackled challenge. In my larger classes, I had the finished group split apart and join other groups.

The Sevens Challenge ended up being the most difficult for my students to tackle. Often, there would only be two or three target numbers solved by the end of the class period. 

Want to try this activity with your own students? You can find where I typed up the challenges in two different formats: Google Slides and PDF. I hope your students enjoy it as much as mine! This activity had my students finding joy in solving tricky math problems. My job is done.

Monday, August 6, 2018

Radicals Interactive Notebook Pages - Algebra 1

Radicals. I don't know why, but this is always one of my favorite units of the year to teach in Algebra 1. There's just something about watching students solve problems that they would have never thought they would be able to solve that makes my teacher heart happy.

Like with every INB unit, we start off with a unit divider. You can find more details about these dividers and a free download here.

The back of the divider lists our skills for this unit. It also gives students a place to record their progress.

I teach simplifying radicals through prime factorization because it works no matter what the index of the radical is. This means we need to do a quick review of prime factorization since it's been awhile since they've seen this.

Most of my students learned prime factorization with the factor tree method. This is how I learned it as well.

When I was student teaching, I was introduced to the birthday cake method. I find that my students make WAY less mistakes when they use this method. There's just something about the fact that the prime factors are arranged linearly that helps them make sure they didn't miss a factor.

Of course, I let my students choose which method they prefer. In each class, there are students who are devoted fans of each method. When I do problems myself, I actually find myself switching between methods depending on which seems easier for that problem.

Next, I give my students a chart for recording the prime factorization of each natural number under 100.

Students are allowed to use this chart for the rest of the radicals unit. This gives them lots and lots and lots of practice finding prime factorization.

Now, it's time to actually start dealing with radicals. I really emphasize vocabulary at this point because I think it's important for all students to be on an even footing while discussing these new looking types of problems. In the past, students have only been exposed to basic square roots.

Plus, there's the fact that I didn't even know this vocabulary when I started teaching. I remember teaching an Algebra 2 lesson on radicals where I kept referring to the little number on the top left of the radical. I had to get out a textbook and look up the word index. Vocabulary is important!

Now, it's time to simplify radicals.

Add and Subtract Radicals

Multiply Radicals

Before we start dividing and rationalizing the denominator of radicals (yes, it's in the Oklahoma standards), I try to give my students a taste of history and the WHY of what we're doing.

Rationalizing Practice

Dividing Radicals

Files for this unit are uploaded here.

Sunday, August 5, 2018

Five Things (Not Friday): Volume 21

I got the "Welcome Back!" letter in my inbox recently with all the important professional development dates, and I started setting up my new classroom this week. So, it's really starting to sink in that I'm about to start my new job!

Here's a small peek at five things I've been up to lately.

1. Classroom progress pictures! So far, I'm just hanging posters I have made in the past. I've made a bunch of new posters, but they need to be printed on 11 x 17 card stock. I'm so new at my school that I don't even know where the copy machine is. I mean, I know where it was ten years ago when I was a student there, but things change. I'm a bit scared to just go opening random doors, but I guess I will have to figure this out at some point. Also on my list of things to figure out: where in the world is the teacher's lounge? I have New Teacher Orientation on the 10th (so soon...eek!), so I'm guessing I will have a lot of my questions answered then.

SOH CAH TOA Posters | Includes/Excludes Posters

Pythagorean Triple Posters

Mistakes are... | Keep Calm and Combine Like Terms | N/O and O/K | Left and Right
A math room isn't complete (in my opinion) without a number line! 

Printable Horizontal Number Line | Positive and Negative Infinity Posters

Order of Operations Posters

My order of operations posters took a bit of a beating last year thanks to students' backpacks, so I really need to reprint A and S. But, I went ahead and hung the old ones up in case I don't get to that item on my to do list for a while. 

Math-y Welcome Banner
It's nowhere near done, but it looks like a room that I could teach class in tomorrow if I had to! 

2. Friday, I got to see Chris Shore present "Reaching and Teaching "Those Kids."" It was very thought-provoking, and I really enjoyed watching Chris execute his well thought-out teacher moves.

Chris equipped us with lots of different strategies for engaging every student every class period.

I was super-excited to get to see Clothesline Math in action!

I'll definitely be looking for ways to incorporate the clothesline into my Algebra 2 and Pre-Calc classroom! I also love the 4 digit problem. The task: make the numbers between 1-100 using exactly 4 eights and any exponent of your choosing (except 8).

3. I spent some quality time recently updating my teacher planner with some new calendar pages. Special shout-out to my husband for designing an excel file to automatically generate these pages!

Last year, it took a bit of adjusting to get used to a vertical layout. But, I discovered I LOVE it!

4. I found a bunch of safe-t compasses (affiliate link) at a garage sale. I'm super excited to use these in my classroom this year. Then, when I was cleaning out my cabinets of my new classroom, I found some giant demonstration sized safe-t compasses. I'm thinking these will come in handy teaching pre-calc!

5. My wooden cubes came in the mail! I've got big plans for these 100 one inch cubes (affiliate link)! I found at least three different puzzles online made of cubes that I will be making for my puzzle table! Now, I just have to find some time to paint them. I can't wait to share these ideas on the blog as I get them made and introduce them to my students!