Old Math Guy

Last week we gave the PSAT to all the 10th and 11th graders at our school. The seniors had a special assembly and freshmen reported to their homeroom class. The homerooms are assigned by building alphabetically, so the students in our homeroom are usually not in any of our classes. I happened to have a sophomore homeroom this year, so I spent the morning proctoring the PSAT. [I swear three minutes sometimes seems like an eternity when you waiting for the session to end.] Needless to say, it was a long day. So testing ate up the first four hours of the day, then I saw my Geometry class and then one of my five algebra classes for only an hour (classes are usually 90 minutes). By the end of that day, everyone was fried - my students had either spent the morning testing or sitting in their homeroom bored.  But I do not ever give free days, so I knew I wanted to do something that will help them with the linear functions unit we were working on, but a standard lesson was not going to hold their attention today.

My friend, Amanda, at Free to Discover, has an awesome set of products called, "Old Math Guy," that I have been wanting to try out, and this was the perfect opportunity. I decided on Matching Linear Graphs to Equations in Slope Intercept Form.  I asked the kids if anyone knew how to play "Old Maid," and a few said they did. I had a few kids tag-team explaining the rules of "Old Maid." Then one of my students said, "Did you bring in cards for us to play Old Maid?" I nodded. Then he said, "Wait, these are going to have math problems on them, aren't they?" I said, "Of course they are!" The rules are the same as Old Maid - they look for matches and lay them down and they draw from their neighbors hand until all the cards are out and someone ends up with the Old Math Guy.

My students had a lot of fun with this activity, and I overheard some great conversations about what made a "match." The students would watch each other like hawks to make sure their equations really matched their graphs (attend to precision!). Some students had good poker faces with Old Math Guy and some didn't. They all had fun, and it was a great brain break for the end of a long, off-schedule day.

I think this is a great engaging activity that I cannot wait to use again! With the holidays coming up, we need a lot of tricks up our sleeve, and this one kept their attention and allowed for great practice in a unique way.

Amanda even has a freebie in her store to try out with your kiddos: Old Math Guy Translating Algebraic Expressions 

Math-y Door Decor

Last week is annual "Jacksonville Goes to College Week," so our guidance counselors challenged us to a door decorating contest. I typically write those off as, "Ain't nobody got time for that," but I had such luck with my Christmas Door Decorations that I wanted to give it a try. Just like when I did my Christmas door, I also did not want to lose any instruction time. Scaffolded Math and Science had the perfect solution for me - a Slope Tree, which fit right into our Linear Functions unit.

I gave each student a leaf and they found the slope between two points and then decorated it. It was a nice exit ticket for our class on slope. We put them all together to make a tree.

The idea for my "pun-ny" sign actually came a student who said, "If this is an exit ticket, can we 'leaf' when we finish it." I took that and said, "We are ready for college when we 'leaf' ACHS." Then one of my students added some color to it when she finished a test early.

I think it turned out great - a perfect fall decoration! And best of all - no instructional time was lost in the making of this awesome math-y door decor!
P.S. If you are looking for those awesome Welcome sign letters, they are from Math=Love here 

Hurricane Matthew: From Inside the Cone of Uncertainty

I grew up in the Midwest and left 10 years ago, trading the brutal winters for year-round sunshine. Although we have had a few near-hurricanes and tropical storms in my time as a Floridian, nothing has hit close to home like Hurricane Matthew. I live in Jacksonville, Florida about five miles from the coast, where we can afford a house but can also have our toes in the sand in 10 minutes flat, with my husband (also a teacher and a native Floridian) and our two children, 4 and 1.

On Monday, my husband texted me this picture and we talked vaguely about what would happen if the hurricane actually came near us in Jacksonville, but we didn't make any real plans.

On Tuesday, the clouds over my school looked a little ominous in the morning. The storm path hadn't changed much, so I stopped at the grocery store after school to stock up on water, snacks, and batteries and I filled my gas tank with a short wait.

By Wednesday, the mood around campus was that of uncertainly - Matthew had already torn through Haiti and Cuba and its strength was undeniable. The forecast path brought it closer to home. The students minds were filled with "What ifs" and I must have been asked if school would be canceled at least 50 times. Imagine teaching the day before a holiday break and multiply it by 10, that's how distracted these students' minds were, and mine was too. I was filled with uncertainty of what the weather would bring for me and my family and what decisions I should be making. I had a quiz scheduled (the end of the 1st quarter is nearing next week), but everyone was so preoccupied that I decided to make it open notes. I tried to make my lesson on slope as low-key as possible, we watched the Adventures of Slope Dude, took some notes and practiced with a Versatiles activity. I found that the kids needed the distraction as much as I did as the rain outside beat against the windows.
By the end of the last period of the day, the principal announced that school was canceled for Thursday and Friday and everyone, teachers included, needed to be off campus by 2:30. Leaving was so nerve-racking, not knowing what I would come back to. I unplugged everything, took a few pictures of my possessions, and headed out.
The few times I get to leave school at 2:30, I usually zip home and have free reign over all the stores. Today traffic was already building on the highways, and the line at the gas station stretched out onto the road with at least 10 cars waiting in each direction. I was happy to have already taken care of these stops earlier. When I got home, the news now projected this path:
Being a math teacher, I like making decisions based on odds and probability of events occurring, but it seemed like every time I looked at the news, the odds were changing. The meteorologists were giving the hurricane a 15 percent chance of making landfall in Jacksonville as a Category 4 storm. As I tried to go to bed that night - I began to truly understand the term "Cone of Uncertainty." Did it make sense for our family to leave town? Where would we go - we have family near Orlando and Tampa, but would the weather be just as bad there? And what would traffic be like as we went there and returned home after the storm? What if the storm did significant damage to our house and no one was there to protect it because we had left? What is the storm did significant damage to our house and we were there with our two babies? What would it be like to have two small children without power in our house? Would I be able to remain calm if a true category 4 hurricane came through? 

I decided to pack a bag with clothes for everyone for five days, snacks and water, and all my hard drives of family photos, and sleep on the decision. I woke to find this on my phone: 
The uncertainty was too much, and I knew staying and waiting would make me a nervous wreck for the next few days, which I knew would have a 100% chance of negatively impacting my parenting skills. My husband decided to stay back and board up the house and deal with any damages or issues, and I buckled the kids in their car seats and hit the road for Grandma's house. My mother-in-law lives just south of Orlando and their weather forecast called for 35 mph winds and rain, which sounded much better than the 100 mph winds that could be possible in Jacksonville. I decided that the worst-case scenario of evacuating would be a traffic jam, and the worse-case scenario of staying was being huddled into the bathroom with my two little ones as a tree crashed through our roof. 

My husband weathered the storm at home without ever losing power. The wind was fierce and the rain was relentless, but our house escaped unscathed, except for some downed tree branches and mud puddles in our backyard. Many of my friends and neighbors were not so lucky.

Today my husband asked me, "If you had this to do over again, would you do it the same?" Again comes that "Cone of Uncertainty," did I make the right decision? Did I over-react by leaving? Was it overkill to board up our windows?  As a math teacher, my brain is trained to be analytical, but Mother Nature cannot be tied down with logic and reason. I do know that as this storm shifted countless times with different trajectories, I was happy to be watching from a safe distance away. 

How a hole puncher saved the day: Proving Lines Parallel Proof Activity

Even in the 7th week of school, Geometry proofs still strike fear into my little freshmen. For today's lesson on proving lines parallel, I knew I wanted them to do proofs. I found this great cut and paste activity from Amazing Mathematics. I chose to print the version that has the statements filled in and students only have to come up with the reasons for each step. By the time we get to triangle congruence, they will be writing both sides, but I was OK with giving them the outline today.

We reviewed all the theorems and converses and theorems and did a few examples together in their interactive notebooks, and then I set them lose on the proofs. I have my students grouped in threes, which is plenty of brain power to figure out these proofs. I gave each group a strip of paper and had them write the numbers 1-6 on it. Each group started with a proof (I only used 1-4 in the first round because they get increasingly more difficult). They worked together to correctly place the reasons in the proof. When the group agreed, they called me over for a check.

If it was right, I took my blue marker and scribbled off the number of the proof they finished. Then I saw a student look the other blue markers in my supply box with a gleam in his eye. And I realized with this system, there is no way I would be able to keep them from cheating. I changed the scribble to my initials, and then I had a better idea... I dug into the depths of my desk drawer and I got out my single hole puncher and punched a hole over the number when they completed it. The students LOVED it! It's amazing how something so simple totally changes the game. Then they wanted to use the hole puncher - and they would fight over whose turn it was to make the punch. The click of the puncher and the creation of the hole was as satisfying as correctly completing the proof. After I (or they) punched the number, they scrambled up the pieces and took it to the middle table and exchanged it for another proof. They kept doing this until they finished all six proofs.

Typically telling students they would be completing six Geometry proofs to prove lines parallel would be met with moans and groans, but my students were very engaged and motivated to finish the problems. I definitely see my hole puncher making future appearances in class!

Next they are going to try out this Proving Lines Parallel Crossword Puzzle. The outline of the proof is still there, but they have to come up with some missing statements and reasons. They still get the self-checking benefit of the crossword puzzle though.

Connecting Inequalities to Domain and Range

There are some concepts that I know I do a great job of explaining and others that I struggle with. At the end of the school year, I made a list of things I want to do better, and a few topics from the functions unit were on there: domain and range, using the term f(x), understanding linear translations, and focusing on parent functions. As we finished up the unit on Inequalities, I knew that I wanted to start the functions unit with domain and range so that I can refer to domain and range throughout the entire unit. As I was preparing my notes, I had a "A-Ha" moment that I could present it as a compound inequality. I loved the lesson I found on compound inequalities and my students had a good understanding of writing and graphing them.

First we talked about the vocabulary for domain and range. I told them I remember that range is for y because both the g in range and y are descender, which means they dip below the writing line. I told them to pick two colored markers and color-code the words domain and range everywhere they saw them on the page. (I also made a point to tell them to pick two colors that will look different on salmon colored paper, after a student picked red and pink and couldn't tell the difference.)

The first two examples are pretty straight forward. It's when we get to the graph that things get fun. I tried the method of making the smallest possible box around the function, but several students got confused, so I changed it to finding the farthest left and right point and drawing a line to the x-axis. I then shaded the x-axis between these two values and asked, "Who can write an inequality that describes this?" I told them because this was tricky, I was offering a "Dum-Dum" to anyone will to take a risk and try it. I don't break out the candy often - it's week 7 and this was the first candy-sighting in my room, but I knew this concept was difficult. Students were fighting over trying the inequality for y.

Then I presented these three problems and asked students to talk about how they were similar and different. They pointed out that the first graph has only points, the next has endpoints, and the last has arrows, meaning it continues forever. I did the domain for the first problem and had students come up to do the range and domain and range for the middle function. For the last one, we shaded the whole x-axis and I reminded them about problems where every number is a solution and connected that idea to the domain of all real numbers. Then I asked for the maximum, which students identified at 4, so I shaded the whole y-axis below 4. Students easily saw that as y<4. Yay!

Next it was time for some scaffolded practice. I LOVE this sorting activity. I kept the cards together (they print 4 per page) and cut apart the slips for domain and range. I find that sometimes less moving pieces helps students to focus. I loved the variety of  these 20 problems and the great conversations I overheard. Students struggled most with the circles and the line, but these led to more great discussions and opportunities for me to relate them to problems they have seen. By week 7, my students are learning that I will not give them the answer, but I will ask them questions to help them come to the answer on their own [Give a man a fish, and he eats for a day. Teach a man to fish, and he will eat for a lifetime.]

As they finished, I gave them pennant problems to practice on their own. On Wednesday, we followed an early release schedule, so each student did one problem. My students on Thursday did three each. Following the gradual release, this was a great way to end because students had to come up with the domain and range on their own. And they could! They learned so much, we ran out of room on the yarn! On to more functions fun next week!

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