Math = Love: September 2019

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!

https://amzn.to/2JQpjkp

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!



Puzzles.com 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!