Math = Love: November 2017

Tuesday, November 28, 2017

Color Square Puzzle from Puzzle Box, Volume 1

Today's post will probably be short because I'm currently battling a sore throat. I've got my fingers crossed that this is due to allergies and not an impending cold.  

Yesterday, I put out this week's new puzzle. I have a table at the front of my room that is designated as the "Puzzle Table." Every Monday, I put out a different puzzle for students to tackle over the span of the week during spare class time.

This week's puzzle has been incredibly popular after only two days, so I'm excited to share it with you here on the blog.

First, I think I need to tell you how I ran across this puzzle in the first place. Just a note: this post does contain affiliate links. If you purchase the items mentioned in this post, I will receive a small percentage of your purchase price. This helps support this site without costing you any extra!

The Grabarchuk Family reached out to me via Twitter to ask if I would be interested in reviewing their new Strimko puzzle book.

I had never heard of Strimko puzzles before, but I jumped at the chance to try out a new-to-me puzzle. It turns out they're super awesome, but that's the topic of an upcoming blog post. Today, I want to tell you about a puzzle that I learned about as a result of learning about the Strimko puzzle books.

After getting Strimko Book 1 in the mail and being super impressed by the quality, I went to look at what other books I could get from the Grabarchuk Family. This search led me to discover Puzzle Box, Volume 1 which was edited by part of the Grabarchuk Family.

It was in this book that I ran across Puzzle #7 by Richard Candy. Using 8 given tiles, create a 5 x 5 square where no piece is allowed to touch a piece of the same color - not even at a corner! This "not even at a corner" part is what gives the puzzle its trickiness.

Lucky for us, you can see this puzzle as part of the "Look Inside" preview feature on Amazon. This book is full of awesome, math-y puzzles, and I would recommend it for any math teacher who loves incorporating puzzles into their classes. The puzzle below is just the tip of the ice berg when it comes to the potential this book has to play an important role in your classroom.

Immediately, I saw potential for this puzzle to appear on my puzzle table. So, I set about creating a grid and set of pieces for my students to manipulate.

I designed the grid to print on 11 x 17 cardstock because I believe bigger is always better when it comes to puzzles for student use. If you don't have access to 11 x 17 paper, you can choose the option in Adobe to print on multiple sheets of letter sized paper and glue/tape them together. Or, you can scale it to fit on letter sized paper. Keep in mind that you will also need to scale the tiles so they are the same size!

Then, I designed the tiles to fit perfectly on the grid. The tiles must be printed on three different colors of letter sized paper. I used Astrobrights paper to make them extra bright and colorful.

After printing out the puzzle pieces, I started to think that this puzzle was going to be too easy. Then, I sat down in the floor of my living room and began to try and solve the puzzle myself. I tried and tried and tried and tried. Nope. This puzzle is definitely not too easy. It was actually kinda frustrating. So frustrating, in fact, that eventually I whined enough about how hard it was that my husband temporarily abandoned his computer game to help me solve it. That, ladies and gents, is true love! Even then, it probably still took at least thirty minutes between my husband and myself to find a solution.

Since it's been out on the puzzle table, my students have been working in groups to attempt and solve this puzzle for themselves. Usually, it starts with one student attempting it. Soon, another student (who usually hasn't read the instructions!) offers a helpful (or not so helpful) hint. This leads to a discussion of the rules, and just like that another student gets sucked into the puzzle. At one point, I had five chemistry students gathered around the puzzle at one time today.

One chemistry student refused to leave the puzzle table today to take our notes over dimensional analysis because he thought he was that close to solving the puzzle. A student in my math concepts class has been especially drawn in by this puzzle. I had to drag him away from the puzzle yesterday because he needed to do his quiz over solving two-step equations. Today, he persisted until he became the first student (so far) to solve the puzzle.

There has been a bit of debate on twitter over how many possible solutions there are to this puzzle. I snapped a picture of the solution my husband and I came up with to compare it to the solutions my students come up with this week. So far, we have found two different possible solutions. I'm looking forward to collecting data to help determine if there are more!

Want to try out this fun/frustrating puzzle with your own students?

I've uploaded the files I created to make a classroom version of this puzzle here. Special thanks to Richard Candy for publishing this puzzle in Puzzle Box, Volume One. I look forward to trying more of the puzzles from this book in my classroom in the future!

Monday, November 27, 2017

Monday Must Reads: Volume 20

Happy Monday! Things have been pretty quiet here on the blog since last Monday's Must Reads post because I decided to take full advantage of the opportunity to rest during our 9 days off for Thanksgiving. Today was our first day back, and I'm excited about what's ahead for all of my classes as we sprint towards Christmas Break.

I hope you enjoy this week's "Must Reads."

I'm a huge fan of Quarter the Cross, so I'm super excited about this new puzzle: how many ways can you shade a third of the large triangle? Thanks to Michael Jacobs for sharing! 

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John Rowe offers up a new Open Middle Problem that will be a perfect addition to your unit on linear equations. Keep procrastinating, John. We all appreciate the fruit of your procrastination!

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I love Sarah DiMaria's approach to displaying the norms created by each class. The idea of having each student sign the norms is brilliant.

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I had my first experience with Prime Climb (affiliate link) at a meeting of the Tulsa Math Teachers' Circle. David Butler shares a simple but brilliant tweak to make playing a life sized game of Prime Climb even easier: colored sashes to represent teams.

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Charlotte Anne combines food with proof. Now, I want to do my own research. Are Doritos consistently sized?

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Toni Madison shares an inspiring Christmas-themed project that could be used in pretty much any math class: vocab ornaments. Be sure to check out Toni's blog post with more details about this project and other awesome Christmas ideas for the math classroom!

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Thanksgiving may be over, but I can't help but share this awesome angle finding activity from Ms. Grove.

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I've used Skyscraper puzzles in the past with linking cubes (affiliate link), but Danny Whittaker has opened my eyes to a different approach: dice!

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Janice Mejia shows off a student example of a social media project. Love how this type of activity can bring out student creativity!

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Until next week, keep sharing!

Monday, November 20, 2017

Monday Must Reads: Volume 19

Happy Monday! It's a very happy Monday here in the Carter house because it is the first official day of Thanksgiving Break! I think the stress of this school year has been getting to me a bit. This weekend, I cried at least twice. My first tears came when I opened the refrigerator to find that the previous night I had placed the ice cream carton there instead of the freezer. My second bout of tears came while trying to do a physics problem that didn't have a corresponding example in the book. So, here's to a week of relaxing and not thinking about school as much as possible.

But, first, let's talk about this week's Must Reads. Then, I'm off to do dishes and make a new batch of soup.

Sean Corey shares some posters which create a great visual for the 4 C's of math questioning.

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 Looking for a fun thanksgiving activity? Elizabeth Carney shares a creative turkey puzzler.

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Kent Haines challenges his students with an interesting task. I need to take some time and think this one through myself!

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Mr. Coster inspires with a fun looking escape room activity. This looks like a blast!

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Bob Lochel poses an interesting puzzle that will most likely be showing up soon on my puzzle table.

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Jennifer Williams shares easy-to-implement data collection activities. I will definitely be stealing the time to complete a puzzle idea! 

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Shelby Roth shares a photo of some awesome posters in her classroom that represent each different subset of the number system.

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Primary Maths shares a website that has great potential for writing future math problems!

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Greta Bergman shares two new open middle style problems she has recently created. These look fab!

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Mary Williams helped her students get in the Thanksgiving Spirit by creating a beautiful bulletin board to show off their gratitude.

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Jae Ess is an expert when it comes to creating thoughtful and creative interactive notebook pages.

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Miss Baird makes atomic structure come to life by combining two simple supplies: paper and string. I look forward to using this in chemistry!

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Until next week, keep up the awesome sharing!

Friday, November 17, 2017

Five Things Friday: Volume 4

It's Friday! And, it's a VERY happy Friday for me because now that the school day is over it means that Thanksgiving Break is here! This is a much needed break, and I'm looking forward to having an entire week off to catch up on the parts of life that tend to get neglected during the school year.

Every Friday, I do a quick post of five things I deem shareable but not worthy of an entire post on their own. Without further ado, let's get to it!

1.  In chemistry, we did a density challenge this week. Students had to calculate the maximum amount of sand that could be placed in a film canister so that it still floated. We tested our canisters today, and every canister floated! I ordered a set of 24 film canisters from Amazon (affiliate link) especially for this lab. The lids were a bit hard to get on/off, but they worked perfectly for this activity.

2. We wrote thank you notes today after our Algebra 1 quiz. Students had to choose one of the thank you cards I printed on colored paper, fold it in half, and write a thank you note to someone at our school. I chose to let students write letters to teachers, support staff, or other students. Some wrote silly notes. Others took it seriously. One student's note brought her friend to tears during first period. This is the power of just saying thanks. Interested in downloading the thank you card templates I created? You can find them here.

3. My study of physics is continuing. I've started creating an interactive notebook of sorts to contain my physics notes and worked practice problems. There's something about doing my study in a notebook that makes my learning feel more real. Since starting to keep my worked problems in a notebook, the amount of problems I've been working has been increasing. So, that's a win!

4. Last year, my husband taught a middle school computer science class using the curriculum. One of the activities involved having students build boats from aluminum foil. Students were challenged to create a boat design that would hold the most pennies. We took a trip to the bank one day and got several dollars worth of pennies. This year, I've been getting my own mileage out of this bowl of pennies. We did the aluminum foil boat activity during the first week. Then, we used the pennies to determine how many drops of water will fit on a face of a penny. Students practiced using the scientific method to make a hypothesis regarding how different liquids would compare to water when it comes to drops fitting on the face of a penny. Finally, we used them recently to calculate the density of pre-1982 pennies and post-1982 pennies. Students used these densities to test their hypothesis regarding the composition of pre-1982 and post-1982 pennies.

5. I got some UTA goodies in the mail this past week. The President of UTA heard that I was a finalist for Oklahoma Teacher of the Year, so he decided to send me a gift of a UTA Pennant and Scarf. I did my Masters Degree in Curriculum and Instruction through UTA online. I have a TU flag in my classroom from my undergraduate days, so I'm excited to have something to hang up in my room to represent my time in grad school.

Thursday, November 16, 2017

Volume 51: Things Teenagers Say

It's already time again for another volume of Things Teenagers Say. Either my students have been saying more interesting things lately, or I've just been better at writing them down. I'm not sure!

Check out previous issues of Things Teenagers Say:

How am I not supposed to worry when your ones look like twos?


Student: Mrs. Carter, can you eat butter since you're a vegan?
Me: I'm not a vegan. I'm a vegetarian.
Student: What's the difference?
Me: Vegans don't eat any eggs or dairy products. They don't even eat honey.
Student: Why?
Me: Honey comes from bees.
Student: Woah.
Me: They also don't wear leather since it comes from cows.
Student: Do they wear anything?


Student 1: Why do students keep saying you are pregnant?
Me: That rumor has been going around for the entire six years I have worked here.
Student 2: Yeah. Someone said it must be twins because you've been pregnant for so long.
Me: What?
Student 2: Can you believe that some students at our school think you have to be pregnant for 18 months to have twins?


Don't leave me with these heathens.


They treat us like slaves in this school. I don't come to school to be told what to do. I come to see my friends and play sports. I'm not learning anything.


Food and cats. Aren't those the same thing?


He'd never survive in a gunfight. They'd tell him to take ten paces. He would take five and turn around and shoot. Then, he'd be an outlaw.


Do trees shrink when they get older?


Student 1: Mrs. Carter, it's 12 days until our birthday!
Me: I know! I'm excited.
Student 2: You're going to have a birthday?
Me: Yes. I'll be 28.
Student 1: 28? You look like a mom!
Student 3: A cat mom.


Me: What do we use to measure time?
Student: A ruler.


What would you do if Mr. Carter ever left you? A cat would always be there for you.


Student 1: The cat I want is like $3000.
Student 2: Is it a tiger?


Student 1: We need to do the quiz on Thursday because I might not be here on Friday.
Me: Why?
Student 1: My puppy died.
Student 2: Today is Tuesday. If your puppy died, why would you be gone on Friday?
Student 1: We're going to have its funeral on Friday.


Me: When I was in school, I learned "My very excellent mother just served us nine pizzas" to remember the planets. But, now that Pluto is no longer a planet, I'm not sure how they are teaching it in school.
Student: Didn't Pluto get blown up?


Student: Mrs. Carter, do you know what the best way to eat bananas is?
Me: No.
Student: Trash.


One freshman student to another: You look old. You look like a grown woman. Your face looks like that of a 40 year old.


Student 1: Can we name the tree Bob?
Student 2: The tree can't be named Bob. We already had a problem with Bob emptying out his swimming pool.
Student 1: So why can't our tree also be named Bob?
Student 2: Trees can't empty out pools or even swim in them in the first place.


Student 1: We don't have school next week.
Student 2: That's how Thanksgiving Break normally works.
Student 1: Rude! What would you say if I said I was dying?
Student 2: I would say, "Of course you are dying. I can see the blood stain on the carpet."


Me: What is special about mapping diagrams that will help us with finding domain and range?
Student: Mapping diagrams show love to the oval shape.


Instead of writing "It passes the vertical line test," I'm going to write VLT-Approved.


One time I sneezed back in Vietnam...


It reeks in here. It smells like rabbit.


Wednesday, November 15, 2017

Algebra 1 Solving Equations and Inequalities (Unit 2) INB Pages 2017-2018

We are currently working on relations and functions in Algebra 1 which is by far my favorite unit of the year. This means I can finally share our solving equations and inequalities unit with the internet!

This is my second year teaching Algebra 1 under the new Oklahoma Academic Standards. And, I'll be honest; I'm still trying to wrap my mind around what exactly the standards entail and how best to go about teaching them. This year's unit on solving equations went 100 times better than last year. Having said that, I still have so many changes I would like to implement in the future. I'm proud of what we did this year, but I know that I can still do more. Next year, I want to implement more application problems.

Every unit starts out with a divider. One side of the divider has a place for students to list the "Top Ten Things to Remember" from this unit. At the end of each unit, students get a grade for completing this as part of their notebook checks. Some students keep a running list as we go through the unit. Other students wait until right before the notebook check to write their list. Still others leave it blank. I can't win every battle.

The opposite side of the divider has places for students to record their quiz scores for each skill.

You can find out more about these dividers and download a template here.

Before beginning to solve equations and inequalities, we did a quick review of inverse operations.

We followed this up with an inequalities investigation that was inspired by an activity from Discovering Algebra (affiliate link) called "Toe the Line."  The goal of this activity is to remind students that we need to flip the inequality symbol whenever we multiply or divide both sides of the inequality by a negative number.

Up Next: A summary of steps for solving equations/inequalities with variables on one side.

Next, we did a quick review of how to graph solutions on a number line. For my students, this is all a review except for graphing "not equals to."

In the past, I did this without the equal sign. I'm SO thankful I finally found time to add the equal sign this year.

We did six practice problems in our notebook over solving equations/inequalities with variables on one side. Students stapled these problems together and glued them on a single page. Some students even chose to staple their paper with the steps on top of the practice problems to condense things even further. I kinda like this approach!

At the end of our first unit, students were really struggling with translating between words and algebra. So, I decided to continue giving my students practice translating by giving them every single equation and inequality in WORDS instead of ALGEBRA. Was this the right decision? I'm not really sure. But, I can say that half way through this unit on solving equations/inequalities, my students started translating between words and algebra like bosses! The continued practice did end up paying off. What it prevented, however, was the chance to look at different types of application problems. I would like to combine these two approaches when I teach this again.

Here are close-ups of each:

Next time, I do want to make a few changes to this template. I want to switch around steps 7 and 8. By having my students check their solutions before they graphed them, some of my students became confused and started putting the results they got from checking their work on the number line instead of the solution they found.

To introduce the idea of solving equations with variables on both sides, I gave them a set of scale puzzles that I downloaded from Sarah Rubin at Everybody is a Genius. I love giving these puzzles to my students and giving them 3 minutes to solve them. There are only two rules:

1. Both sides of the scale must balance.
2. Whatever number is placed in one box on the scale must be placed in every box on that scale.

Students have a hard time following rule #2. Of course, the reason they want to break rule #2 is that the some of the problems they are trying to solve are actually impossible.

Our next foldable was also inspired by Sarah Rubin.

As a twist, I had my students create their own equations.

A New Set of Steps: Solving Equations/Inequalities with Variables on BOTH Sides

Practice Problems:

Here are close-ups of each:

I reused a foldable I made last year for compound inequalities. I'm still not happy with how well my students understand the differences between "AND" inequalities and "OR" inequalities. I need to rethink my approach to this in the future.

We only did four practice problems in our notebooks for compound inequalities. I think we should have done more.

Here are close-ups of each:

Steps for Solving Absolute Value Equations

Practice problems are next.

Close-ups of each problem are below.

Steps for Solving Absolute Value Inequalities

Practice Problems:

Our last skill for the unit is solving equations for a specific variable. This is also known as solving literal equations or changing the subject of the equation.

I let my students choose between two methods of solving: flowchart method and the more traditional algorithm for solving equations.

We did four practice problems twice each.

You can download the files for this unit here.