Math = Love

Sunday, September 29, 2019

Tangram Challenge Binder

This school year, I'm taking two approaches to incorporating puzzles into my classroom on a regular basis. Every Monday, I put a new magnetic puzzle up on the dry erase board. For example, last week we tackled the Domino Effect Puzzle.

I also have a table that I have designated as the "Puzzle Table." These puzzles tend to be more hands-on puzzles with lots of different challenges using the same set of hands-on pieces. For the first month and a half of school, my students really enjoyed the SOMA Challenges I shared about this past summer.

This week, the SOMA blocks are going back in the cabinet and being traded out for TANGRAMS!

After my first year of teaching, I invested in a class set of tangrams (affiliate link). I love using tangrams as a growth mindset puzzle at the beginning of the year by asking students to create a square using all 7 tangrams. Don't need 30 tangram sets? Amazon also sells four sets for just a couple of dollars!

With the SOMA Challenges, my students really enjoyed being able to flip through the binder of puzzles and choose a challenge to work on. So I decided to give my students the same binder full of challenges to complete with the Tangrams.

I got the tangram pictures from my favorite clipart website - Clipart ETC. The website is chock-full of educational clipart that can be used by teachers 100% for FREE. My most-used section of their website is their collection of coordinate plane clipart. They have an entire section of Tangram Clipart that made putting together this binder super easy.

I love that there is a great variety of images. Hopefully, my students will all be able to find some Tangram Challenges that capture their interest. There are 97 different challenges which should keep my students busy for a very long while.

If you don't want to put out all the challenges at once, you could also put one up each day/week/etc with magnets.

To save you the work of copying and pasting the tangram clipart yourself, I've shared the file of tangram challenges here.

Saturday, September 28, 2019

Domino Effect Puzzle

When I shared a photo of this week's magnetic puzzle of the week on twitter, someone was quick to point out that I need to share the file on my blog. This week, we tackled a puzzle called Domino Effect from Classic Brainteasers: 195 Puzzles to Keep You Sharp! (affiliate link)

Students are given 8 dominoes. The goal of the puzzle is to arrange these 8 dominoes to form a 4 x 4 square in which the number of pips in each row and each column is the same.

I put magnets on the back of my dominoes and posted the puzzle on the dry erase board.

But, I also made a tabletop version with smaller dominoes and a template to set them on top of. 

I had a handful of students give this puzzle a try this week, but there was much less participation than usual. I'm not sure why...

Want to try this with your own students? I've uploaded the files here.

Tuesday, September 10, 2019

A+ Puzzle

Mondays are quickly becoming a day that my students look forward to. Yesterday, I overheard one student excitedly tell another that they were excited to see what this week's joke was. Then, they raced to read it and check out the answer.

Ready for it? According to another one of my students, this week's joke is a good one!

Want more math jokes? Check out my math joke of the week collection here.

Monday is also the day of the week when I switch out our weekly magnetic puzzle.

Last week, we tackled the Nine Squares Puzzle that I posted this summer.

This week we're testing out a brand new puzzle called the A+ Puzzle from The World's Biggest Book of Brainteasers & Logic Puzzles (affiliate link). This book is massive at around 700 pages, but I was a bit disappointed in the fact that it had very few puzzles of the sort that I like to use in my classroom with moving pieces.

The puzzle gives you five shapes which must be arranged into a plus sign. Yes, it is possible.

No, this does not count as a plus sign. 

Yes, this will drive both students and teachers crazy. I included this in a presentation I did this summer, and I had some teachers rather frustrated with this puzzle for quite some time. The look on their faces when they finally figured it out was priceless.

Download a copy of the puzzle and join the fun in your own classroom here

Saturday, September 7, 2019

20 x 9 Challenge

Last summer, I picked up a copy of Pierre Berloquin's 100 Numerical Games (affiliate link) at Goodwill for a couple of dollars. It's turned out to be a good investment because it has served as inspiration for several fun classroom challenges.

Want to see if the book has anything you could use in your own classroom? If you have an Amazon account, you can use Amazon's "Look Inside" feature to read some of the puzzles/games for free. Just keep clicking "Surprise Me!" to see more puzzles!

I turned several of the puzzles in this book into the Twos to Nines Challenge which I ended up using last year on the first day of school.  So many of you readers have used the challenge this year with your students already, and I have loved seeing all the pictures!

Another puzzle in this book caught my eye recently, and I decided to turn it into a classroom challenge as well.

Here's the puzzle (or game as the book calls it) as originally written:

I have dubbed this the 20 x 9 Challenge since it requires you to find 9 different ways to write an expression that equals 20. Sounds easy, right? The challenge is complicated by the fact that each expression can only use a single digit, and that digit can be used no more than six times.

Here's the template I ended up creating to give to my students.

Yesterday was the first Friday of the month which meant it was Early Release Day. As a result, classes were shortened from the usual 50 minutes to 40 minutes. My students had a short ACT bellwork quiz to take at the beginning of the class period, so we only had 35ish minutes left afterwards. This was fine with my Algebra 2 classes, because we were able to use the time to do some dry erase practice with sketching transformations.

My Pre-Calc students, on the other hand, needed to start a new section which required a full review of special right triangles from geometry. I did not want to tackle this on shortened Friday schedule that also happened to be a Friday where quite a few students were gone and the first football game of the year. And, that's the story of how my Pre-Calc students ended up being the testers for this activity. In reality, it's suitable for students in much younger grades. All students really need to tackle this challenge is some knowledge of the order of operations and some persistence.

They were super engaged by the activity, and I really didn't even have to do much explaining at all. For the most part, students picked up the challenge, read the instructions, and just dived in. The main questions I ended up answering were in relation to whether certain things were allowed. The instructions don't specify what mathematical operators that students are able to use.

Many students wanted to use exponents. I allowed this as long as the exponent was the specified digit AND the exponent counted as one of their digits. For example 3^3 was fine, but that counted as using two threes. I also had students using square root signs and decimal points. One group even ended up using a vinculum for a repeating decimal which I found to be quite an interesting approach. Of course, one could argue that this meant they were actually using infinite digits...

When I posted the challenge on twitter, many people were using factorials in their solutions. Factorials don't show up anywhere in the Oklahoma standards, so none of my students ended up taking this approach.

I also allowed concatenation, and I believe that you have to allow this for this puzzle to be possible. For example, two 2s could be put together to form 22.

Really, it's up to you to make up your own rules for what you want students using and not using in this challenge. As part of the process in writing this blog post, I took a look at the solutions provided by the book's author. Each solution is possible WITHOUT any factorials, square roots, exponents, or decimal points. (Okay, the author does post a solution involving an exponent, but most of my students found a simpler solution for that number which did not use an exponent.) Each solution is possible using only concatenation, addition, multiplication, and division. Oh, and parentheses, of course!

I'm intentionally NOT posting my students' answers to this blog post because I already had one group of students go googling for this challenge on their chromebooks in search of the solutions. I know it can't just be my students that do that...

You can download your own copy of the 20 x 9 Challenge here.

Monday, September 2, 2019

3 Hares Puzzle (and Other Puzzles of Late)

We're a few weeks into school now, and SO much puzzling has been going on in my classroom. It makes my teacher heart so happy to watch students delving into these different puzzles and coming back day after day with persistence and joy in problem-solving.

I've made it my goal this year to put up one puzzle each week on the dry erase board using magnets. Last year, I discovered that presenting puzzles vertically (on the board) drew in different students than those puzzles presented horizontally (on the puzzle table). So, this year, I made space in my classroom for both.

My first magnetic puzzle of the school year was the 3 Hares Puzzle from The Big, Big, Big Book of Brainteasers by The Grabarchuk Family (affiliate link). The goal of this puzzle is to arrange the six pieces in such a way that every hare has exactly two ears. Since my pieces have magnets on them, it's super easy for students to try out different arrangements.

It's out of print which makes the used copies on Amazon a bit pricier sometimes than I would prefer. If you can pick up a used copy for a good price, DO IT! This is one of my favorite puzzle books. It has such a variety of different puzzles and SO many of them!

You can still access quite a few of the puzzles for free, though. Amazon's Look Inside Feature lets you look at quite a few of the puzzles for free. Just keep clicking "Surprise Me!" on the left pane to see a different page of puzzles.

Back to the puzzle! Here's a student attempt at the puzzle that ended up not working out.

The art teacher who teaches right next door to me has been so captivated by this puzzle. Almost every time she walked through my room during our PD days, it would her eye. She intentionally had to make herself not stay and solve it so she could get back to her room and get her classroom set up! has a small printable PDF version of this puzzle on their website. Of course, I had to super-size the pieces to make them more appropriate for hanging on the dry erase board. You can download my jumbo sized pieces here.

Now, let's talk about some of the other puzzles we've tackled recently.

On the puzzle table this month, I've had my SOMA Cube Challenges. Students have LOVED playing with these cubes SO much! I made my pieces by gluing one inch wooden cubes together, but several people on twitter have pointed out that you can buy already created SOMA sets on Amazon (affiliate links). Once you have your blocks, all you need to do is print the challenges from this blog post. I put each challenge in a sheet protector and placed them in a binder that lives on the puzzle table. Students just flip to a new challenge each time they complete a challenge or get too frustrated by one of the puzzles. 

 Sometimes they even take the blocks off the puzzle table and take them to their desk to play with.

These continue to get more and more play even though I've never actually mentioned them in class. All I did was set them out on a table and watch to see what students did.

For the first few days, it was only really students that I taught last year that paid any attention to the puzzle table. But lately, I see students from all of my classes making a beeline to the puzzle table as soon as they walk in the door or finish their assignment for the day. 

For the second week of school, I switched out the 3 Hares Puzzle with the Equilateral Triangle Puzzle. This was a favorite magnetic puzzle from last year. The goal of the puzzle is to arrange the six pieces so that they form an equilateral triangle. This part is pretty simple. The hard part is making sure that no pieces of the same color touch - not even at a corner!

Students that I had last year have still been enjoying this puzzle even though they have seen it previously. Apparently a full year is plenty of time to forget the solution! 

Looking for more puzzles for your classroom? Be sure to check out my puzzle page!

Saturday, August 24, 2019

Math Joke of the Week Posters and Binder

This is a project I started putting together at the end of last school year. I'm super excited about how it turned out. I put the finishing touch on it this week, so I'm finally ready to share it with you guys.

Image Source:
I saw an idea on twitter a year or so ago (yes, I realize it's a tweet from 2015, but I didn't see it until 2018) where a teacher posted a daily joke for students in their classroom. It was actually featured in Monday Must Reads Volume 45. I decided I wanted to do the same thing with math jokes. But, I wanted to do it on a weekly basis. I also knew if I didn't pre-plan what all the jokes were going to be and prepare them all in advance that it would quickly become the "math joke of the month" or "math joke of the semester."

I started collecting math jokes from various websites and typing them up in Google Slides.

After I had almost 40 jokes, I printed them off and placed them in sheet protectors.

I printed the answers 4 to a page and cut them apart so they could be inserted in the sheet protector behind the joke. 

Then, I assembled all of the sheet protectors with the jokes and answers in my new "Math Joke of the Week Binder." 

Now, I can easily pull out a new joke each week and place the old joke back into the binder.

I have a chalkboard coordinate plane in my classroom that I don't use because I also have a smaller dry erase coordinate plane.

Last year, I just hung some posters on top of the chalk board and sort of used it as a bulletin board. It worked, but it didn't look the nicest. This summer I got some bulletin board paper and taped over the coordinate plane. Then, I used some colored tape I had in the cabinet to make a border around the edge. It doesn't look perfect up close, but it looks so much nicer than it did last year.

Since it's still magnetic, I'm planning on using this board to hang various things using magnets such as announcements, information from the office that I'm required to post, upcoming ACT dates, my math joke of the week, and whatever else I can think of.

I bought a set of 16 magnetic clips from Amazon (affiliate link) to use to make it super easy to hang stuff on the board. They're super strong, and I think they're going to make it easy to change out stuff as necessary.

Once I had my first joke of the week hung up, I decided it was missing something. So I decided to design a sign to hang above it that says "Math Joke of the Week." It also gives students instructions about how to find out the answer to the joke.

As you can see, students flip up the bottom of the sheet protector to reveal the joke's answer. 

Here's next week's joke.

It was super easy to grab the binder, take out the next sheet protector, switch the magnetic clips to the new sheet protector, and place the old joke in the back of the binder for next year.

You could even make it a student job to switch out the joke each week!

Interested in posting a math joke of the week in your own classroom? I've posted the jokes as Google Slides here. If you'd rather have a PDF to print, you can find PDF versions of the jokes here. This link also includes links to the poster that says "Math Joke of the Week" and the binder cover.

Have a favorite math joke I didn't include? Leave it in the comments, and I'll type them up and add them to the files at a later date! Some of the jokes I included are definitely targeted towards a high school audience (making mention of trig functions), so I'd like to add some more jokes so that there is a full year's worth for elementary and middle school teachers as well!

Monday, August 19, 2019

Teaching the Train Game

I've got so much I want to blog about and so little time to actually make it happen. I want to talk about the first day of school and the second day of school and my new plan for bellwork and my new systems for cell phones and dry erase markers and my classroom decorations and my puzzle table and my thoughts on being a working mom and I guess you get the idea...

I guess I'll start by blogging about an activity I *should* have blogged about last year. For the past two years, the Train Game has been my go-to 2nd day of school activity. I've mentioned it on my blog before, but I've never written an entire blog post explaining it fully.

The game isn't actually called the "Train Game." It's actually 20 Express (affiliate link) by Blue Orange Games. But, years ago, my students dubbed it the "Train Game," and the name stuck.

I received this game as a Christmas present in 2014 from my sister. In fact, it was one of the very first board games that Shaun and I played together. I'm pretty sure he's won almost every time we've ever played...  

Sadly, the game is discontinued. But, Blue Orange still has printable game sheets on their website for people to download and print. So, all you have to make to create your own game set is a set of tiles to draw from.

The first time I tried explaining this game to students, I really struggled to get them to understand the rules. So, over the years, I've created a way to explain them with the help of some visuals and teacher moves. For the past two years, I've turned these visuals into a set of Google Slides that I think explain the game pretty well.

I love this game because it is the perfect mix of strategy and luck. It can be played by any number of people. Plus, it's super low prep!

I start my explanation by going over some basic rules. I have my students use dry erase markers, so the "no erasing" rule is super important.

Whenever I tell students that longer trains are worth more points, they always look at me with confusion. This leads to my next slide where I ask "What is a train?" Instead of telling students what a train is, I give them two columns. The sequences on the left are trains. The sequences on the right are not trains. Then, I challenge students to figure out what makes a train a train.

I didn't intend it this way, but students often come up with the misconception that a train is a sequence that follows a pattern. They notice that 1, 4, 7 involves adding 3 each time and 20, 21, 22 involves adding 1 each time. Usually, they voice this before they read as far as the third example of a train. The 8, 15, 15, 30 throws a wrench into this theory.

After a bit of discussion, students eventually arrive at the realization that a train is a sequence of numbers where each subsequent value is GREATER THAN OR EQUAL TO the previous values.

Next, I try to aid students in solidifying this new knowledge by challenging them to find the trains in a set of numbers. Students often make a mistake of identifying the last train as 9, 8, 11, 15, 40 instead of seeing two trains of 9 by itself and 8, 11, 15, 40. When students do this, they are almost always called out by their fellow students. I barely have to do anything!

I color code the trains just to re-emphasize what creates a train of numbers. Students cannot understand the rest of the game without understanding what a train is. 

At this point, I tell the class that I have a bucket of numbers that I will be drawing from during the game, and it is to their advantage to know what numbers I could possibly draw.

I project a list of the numbers on the screen and ask students what they notice about the contents of my bucket.

The most important things for students to realize are that the numbers in the bucket range from 1 to 30. The numbers 11-19 appear twice. And, there is one wild card (denoted by an asterisk). This wild can be placed in any position on the game board. At the end of the game, it can be considered to be any number of your choosing when calculating your score. 

At this point, I introduce students to the game board.Pro tip: Don't hand out the dry erase markers until you've explained ALL the rules. My students, at least, can't resist the urge to doodle!

I used to laminate the game boards, but I found students had a really hard time erasing the dry erase marker from the laminated plastic. Now, I use dry erase pockets (affiliate link) for this activity. They erase SO much better. Blue Orange has a free download of the game boards on their website

During the game, students write each number as it is called in one of the 20 train cars around the edge of the gameboard. The goal is to create trains that are as long as possible. The longer a train is, the more points it is worth.

At this point, I introduce students to the scoring chart that is printed on the gameboard. A train that contains 5 numbers is worth 7 points. A train that contains 11 numbers is worth 30 points.

I've found that the best way to get students to wrap their mind around scoring and game play is to share a sample game board and ask students to calculate the student's score. 

 As a class, we identify each train and use the score chart to figure out how many points it is worth. 1, 3, 5, 7 contains 4 values, so it is worth 5 points. 2, 9, 11, 11, 14, 18, 19, 20, 22, 23, 25, 26, 30 contains 13 values, so it is worth 40 points. 13 is in a train by itself. This doesn't do us any good because it's worth 0 points. 8, 29 is worth 1 point.

Then, I challenge students to see if they can beat this sample student's score of 46. 

Let's see if I can summarize the rules of game play. 20 numbers will be drawn. After each number is drawn, the number must be written in one of the train cars on the game board. Numbers cannot be moved or erased once they are written down. Each number must be written down before the next number is called. Try to arrange the numbers in the train cars so that sequences are formed where each number is greater than or equal to the numbers that come before it. Longer sequences are worth more points than shorter sequences. Highest score wins!

The first game that we play as a class is definitely a learning experience for students. It's often about halfway through this first round that the rules/strategy of the game finally click for ~25% of students.

I love to watch students' strategies grow and develop as we play subsequent rounds. This game truly is a student favorite. I hope your students enjoy it as much as mine!

As for time required, I was able to talk through the explanation of the rules, play 3-4 rounds of the game, and we still had 10-15 minutes left of our 50 minute period. One thing to be aware of. If your principal walks in your classroom while you are playing this game, they will assume that you are playing bingo!

After many requests, I have uploaded a copy of the game card and template to cut out your own pieces here. You can access the Google Slides I created here.