Math = Love: 2019

Friday, June 14, 2019

Kazu Sagashi Puzzles from Naoki Inaba

Recently, I was scrolling through pictures I had taken on my phone, and I realized that I never got around to blogging about the Kazu Sagashi Puzzles I used with my students back in April. I was introduced to this logic puzzle in 2016 when I discovered the amazing puzzles of Naoki Inaba. Inaba is best known for his area maze puzzles which have become quite popular.


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Discovering these puzzles led me to his website (which is entirely in Japanese, by the way) and a treasure trove of other puzzles with great applications in the math classroom. I ended up writing a series of 4 blog posts in 2016 highlighting Inaba's puzzles and their possibilities for use in the math classroom. Click here to check out Volume 1, Volume 2, Volume 3, and Volume 4.

Since then, I have translated several of these puzzles into English to use with my students. As a result, I have shared the files here on my blog. You may remember my posts on Angle Mazes and Zukei Puzzles. Recently, I went looking for a new puzzle to use with my students, and I settled on the Kazu Sagashi puzzle to translate.


Though, I prefer to think of these as Apple and Orange puzzles. I like that these puzzles take on several different variations as you progress through the different levels. When I used these with my students, I only gave them the first four levels. Each of these levels has a very similar set of instructions.


These puzzles are in no way my own creation. All credit goes to Naoki Inaba. I have simply retyped them up to make them easier to use in an English speaking classroom. You can download the original puzzles here.

Image Source: http://inabapuzzle.com/study/kazu_q.pdf
Let's take a look at the different puzzle variations.


In Level 1, students are presented with a set of squares. Some squares contain an apple. Other squares do not. The goal is to identify a 2 x 2 square which holds the specified number of apples. The first puzzle has a 1 beside it. This means the goal is to find a 2 x 2 square that only contains a single apple. Do you see it?



Let's progress to Level 2.


It's the same set-up as before, but this time we are looking for a 3 x 3 square.

With Level 3, we're back to 2 x 2 squares with the added twist that some of the individual squares now contain more than one apple.


Level 4 continues the trend of multiple apples with a larger, 3 x 3 square.


I've only used these four levels with students. My Algebra 2 classes had a bit of difficulty wrapping their minds around the instructions to get started, but my Pre-Calculus classes jumped right into solving the puzzles without any help or clarification from me. The students really enjoyed the puzzles. A few days after we did these, a student asked if we could do more of those apple puzzles instead of the lesson I had planned for the day!

We had quite a few days of interrupted instruction in April where I only ended up seeing half of my classes due to standardized testing in the morning, and I found these were the perfect task to give students to keep their minds working on a day that might have been wasted otherwise. These did not take anywhere near the entire class period. But, that was okay because many of my students used the extra time to retake quizzes, complete missing work, or work on assignments for another class.

If you've been wondering why I like to refer to these as Apple and Orange Puzzles when so far the puzzles have only contained apples, you are about to find out!

Level 5 tasks you with finding a 2 x 2 square which meets a specified requirement instead of a specific number of apples as before. In the first problem for this level, you need to find a 2 x 2 square that contains an equal number of apples and oranges. For the second problem, the square needs to contain more oranges than apples.


Level 6 continues this new trend but with 3 x 3 squares.


Level 7 changes things up once again by specifying what the difference between the number of apples and oranges must be.


If you would like to download my English version of these puzzles, I have uploaded them here as an editable Publisher file and a PDF.

Thursday, June 13, 2019

Twelve Envelopes Puzzle - FREE DOWNLOAD!

I've finally reached a point in the summer where my brain has started thinking about ideas for the new school year. Actually, I've been thinking about next year since around February or March, but I've finally stopped *just* thinking about next year and started creating resources. It's been a number of months since I've had a chance to just sit down and create resources without any time pressure, and I've forgotten how rewarding the process can be.

Two days ago, I typed up a poster that I will be hanging up in my classroom with the Google Classroom code for each period of the day. This past year was my first year in a 1:1 environment and my first year using Google Classroom. Every time I got a new student this past year or had a student switch from one period to another, I had to remember to go and look up the Google Classroom code so they could join the class to get assignments and announcements. I can't tell you how many times I had to drop everything and look up a code for a student at an inopportune time. This next year, I will be posting the codes on a poster so that I can point students to the poster whenever a classroom code is needed. 


Yesterday, I started working on my plans for the first day of school. Last year, I had my favorite first day ever with the Twos to Nines Challenges. I absolutely loved being able to engage my students in mathematical thinking and problem solving from Day 1. Listening to their conversations gave me great insight into my students' attitudes toward math.



The activity went so well that I would be tempted to do the same activity again this year, but half of my classes will be made up of students who I taught this year. Next year, I will be teaching 3 sections of Trig/Pre-Calculus (students I taught this past year in Algebra 2) and 3 sections of Algebra 2 (students I have never taught before). This calls for a new first day of school math task.

Last week, I was feeling a bit bored from staying home so much this summer, so my husband and I spent the better part of a day visiting thrift stores as an excuse to get out of the house. At Goodwill, I picked up a new puzzle book, Giant Book of Hard-to-Solve Mind Puzzles (affiliate link), for the bargain price of $2.


It's currently out of print, but you can still pick up a few used copies for relatively cheap on Amazon.

In this book, I ran across a puzzle involving twelve envelopes. I posed the problem to my husband, and we reasoned through it together. We arrived at a lovely, unique solution, and I decided that it would make the perfect puzzle for this year's first day of school. I appreciate the fact that this puzzle is solveable with only basic arithmetic. It's an interesting puzzle but not so complicated that it should take our entire 50 minute class period. After all, I still need to leave myself time on the first day to take roll, go over basic syllabus information (particularly the supplies that students will need to purchase), answer student questions, and take care of the sort of housekeeping items that always seem to pop up during the first week of school. 

Yesterday I typed up the activity and sent out a quick tweet about it. I've been absolutely blown away by the number of likes and retweets, so I figured I should blog about the activity now instead of waiting until after school starts in August.

Shaun and I ended up working through the puzzle in the opposite way than the book's original wording suggested, so I made a couple very slight changes to the wording of the puzzle to reflect this since we figured students would also benefit from taking this approach. Basically, the book had the envelopes numbered 1 through 12 and the cards numbered 110-121. We reversed this.

The puzzle now reads: "I have twelve envelopes numbered 110 through 121 and twelve cards numbered 1 through 12. Can you place one card inside each envelope so that the number on the envelope is divisible by the number in the envelope?"

I typed up the puzzle, and Shaun taught me a new Publisher trick to add a white outline to my words to make them more readable over the image of the envelope in the background. I didn't even know that was possible! 


Then, I made 1-12 number cards to place inside each envelope.


I actually considered using actual envelopes for this activity, but I ended up deciding against that since having to open every single envelope to check students' work would be a hassle. Ultimately, I decided to find a clip art image of an envelope and created my "envelopes" that way. This way, students could just lay the card on top of the "envelope" to make for easy checking.


Originally, I had planned on cutting apart the twelve envelopes, but then I realized that I could just leave them connected and laminate them that way. This means the activity has fewer pieces to be cleaned up. Plus, it should make the checking process simpler since the envelopes will not be in a random order.


Students must match each card with an envelope that is evenly divisible by that card. For example, the 5 card could be matched with the 115 envelope since 115 is divisible by 5. But, the 5 card could also be matched with 110 or 120. Students will need to use mathematical reasoning and the process of elimination to figure out exactly where to place the 5.


Similarly, 3 could be placed with 120. 3 could also be matched with 111, 114, or 117.


I haven't used this puzzle with students yet, so I have no idea how long it will take. I plan on making a set of cards/envelopes for each table group on the first day. I will print each set of cards/instructions on a different color of paper to make it easier to return lost pieces to their home. It can't just be my students who seem to lose the single random card to the floor without realizing it, right? 

I'm planning on using this as a first day puzzler at the high school level, but it could easily be used during a unit focusing on divisibility rules for younger grade levels. I will be restricting my students from any calculator or technology usage during this activity. It is my hope that this will force students to use mathematical reasoning throughout the activity instead of simply plugging numbers in a calculator or attempting to google for an answer. 

I will definitely post an update to this blog when I finally get to use this in my classroom come August. But, if anyone uses it with students before then, I would love to hear how it goes! I have uploaded the files for this activity here as a PDF and Publisher file. If you choose to download the editable Publisher file, you will need to download the free font, Fredoka One.

Monday, June 10, 2019

Monday Must Reads: Volume 57

This summer, I've been doing lots of thinking about how I want to structure my 3 Algebra 2 and 3 Pre-Calculus classes for next year. One way I've been doing this is reading through my previous volumes of Monday Must Reads and looking for which ideas match my courses I will be teaching and look like something worth implementing. Seeing how useful I have found these previous compiled volumes of Monday Must Reads has encouraged me to put together another volume as I continue to think about what I want my classroom to look like this coming year.

Hopefully you can find some ideas for your own classroom in this post!



Ginger Richey shares a great culminating project that combines synthesizing the year's learning with a fun arts and crafts project.

Image Source: https://twitter.com/GingerRichey1/status/1128813722586292225
Check out these awesome hands-on projects shared by the SBA Mathematics Department.

Image Source: https://twitter.com/DepartmentSba/status/1104396633826099201
Image Source: https://twitter.com/DepartmentSba/status/1135643415008423936
Stephanie Worthington inspires with her giant triangle based lessons.

Image Source: https://twitter.com/stephworthy249/status/857627149297213443
Leslie Byrd shares several creative ideas for using radian and degree cards in the classroom.

Image Source: https://twitter.com/MrsLeslieByrd/status/985979259645825025
Stats teachers, check out this idea for hypothesis testing from Mary Ollier.

Image Source: https://twitter.com/mom_ollier/status/827975745012170757
This problem shared by Dan Rodriguez-Clark really caught my eye.

Image Source: https://twitter.com/InteractMaths/status/1136359217433124864
David Butler shares an excellent post he wrote about teaching people to play SET. As someone who really struggled to wrap my mind around this game for quite awhile, I love this well thought-out approach. Also - check out how he has modified the game so that color blind people can play!

Image Source: https://twitter.com/DavidKButlerUoA/status/1135781808535064576
Check out this awesome mathematical artwork created by the students of Ashley Tewes!

Image Source: https://twitter.com/ashleyanntewes/status/1135597085498249217
Ashley's project was inspired by previous projects by Stephanie Woldum. Check out Stephanie's newest project.

Image Source: https://twitter.com/mrswoldum/status/1135680154133549056https://twitter.com/mrswoldum/status/1135680154133549056

Image Source: https://twitter.com/mrswoldum/status/1137137123746811905
Marilyn Burns shares some photos of a math classroom in 1968. I absolute love the peg board for graphing!

Image Source: https://twitter.com/mburnsmath/status/1135299466376802304
Kristy Jacob inspires with her positive post cards.

Image Source: https://twitter.com/KristyJacob26/status/1134911839807188992
What a cool idea to host a Polar-Parametric-Coolness-Desmos-Graph-Off. Amazing idea, Mr. Flory!

Image Source: https://twitter.com/ADHSPreCalFlory/status/537224431060656128
Looking for a data collection project? Rebecca Goodman had her students build straw rockets after watching October Sky. Check out a video here of the rockets in action.

Image Source: https://twitter.com/goodmansclass/status/1127278051480543232
Jourdan Hager shares an inspiring project that involves studying blueprints and creating a full size drawing of a WW2 plane. What a memorable lesson!

Image Source: https://twitter.com/hypotemooose/status/1132734519063252992
Check out this post from James Tanton on "tempting errors."

Image Source: https://twitter.com/jamestanton/status/1130116920001191936
Julia Anker gives us an inside look into the creation of the awesome unit circle projects that I always admire whenever I see pictures of her classroom!

Image Source: https://twitter.com/AnkerMath/status/1132397827374477312
 Shelby Guillory shares some lovely responses to an end-of-year reflection prompt.

Image Source: https://twitter.com/ShelbyGuillory1/status/1132138261567102976
Want to make quiz/test grading more fun? Check out these clever questions that Ms. Clifford adds to her assessments.

Image Source: https://twitter.com/MsClifford3/status/674787167420456960
Image Source: https://twitter.com/MsClifford3/status/600358976765751297
Image Source: https://twitter.com/MsClifford3/status/473446145046642689
I'm teaching three sections of trig/pre-calculus next year, so I've been on the lookout for creative project ideas. Check out this arc length and area sector project idea from Jennie Mayola-Galay.

Image Source: https://twitter.com/MsJG19/status/1105604616111063041
Check out these other trig projects, too.

Image Source: https://twitter.com/MsJG19/status/1126623534929862658
Image Source: https://twitter.com/MsJG19/status/1128786694763945986
Henry Thompson shares a yummy way to introduce radians using Twizzlers.

Image Source: https://twitter.com/JCHSCoachT/status/1085995805645959168
John Golden shares the brilliant idea of finding your birthday in radians.

Image Source: https://twitter.com/mathhombre/status/1101240988062961665
Katrine shares an open middle problem for conic sections.

Image Source: https://twitter.com/KatrineBryan/status/671915251604971520
Christee Joesten shares a vacation-based conic section project that looks like a lot of fun.

Image Source: https://twitter.com/ChristeeJoesten/status/982226957160013826
 Kristi Stephens makes learning about parabolas and conic sections with s'more making.

Image Source: https://twitter.com/KristiMStephens/status/996485704598409218
I'm not entirely sure how it works, but Paul Naanou's game of "Marco Polar" sounds like a lot of fun!

Image Source: https://twitter.com/PNaanou/status/1070118790212579328
Mrs. G's Parabolic Curve project looks like a lot of fun!

Image Source: https://twitter.com/kgerdeshhs/status/1039873026173661184
Check out this inspiring art from Amy McNabb!

Image Source: https://twitter.com/amcnabb3/status/1132024964176130048
Paul Jorgens shares the brilliant idea of solving puzzles which lead to locker combinations and more clues/puzzles. How fun!

Image Source: https://twitter.com/pejorgens/status/1131723032936894465
How awesome does "Extreme Makeover: Clock Edition" sound? Check out this project from Anna Pfeiffer.

Image Source: https://twitter.com/makinginmath/status/1131739663088021504
Looking to spread positivity with some encouraging notes? Check out this daily practice from Emily DeLuca.

Image Source: https://twitter.com/DeLucaPSD/status/1111709939121209346
Patricia Pinder shares the results of a Unit Circle Flower Project.

Image Source: https://twitter.com/trishmollo/status/1123202173410660352
I really like this sticky note prompt from Mrs. Csoke: which method are you still unsure about?

Image Source: https://twitter.com/csokemath/status/1113906167992942592
And, check out these unit circle projects!

Image Source: https://twitter.com/csokemath/status/1123745239922036737
These literal equation posters from Mr. Perez's students look amazing!

Image Source: https://twitter.com/SrPerezMath/status/1068488788027027457
Until next time, keep sharing your awesome ideas!