Math = Love: June 2019

## Friday, June 28, 2019

### Is it Possible? Divisibility Puzzle

I'm making the most of the \$2 I spent on this recent Goodwill find. The Giant Book of Hard-to-Solve Mind Puzzles (affiliate link) is out-of-print which makes used copies from Amazon VERY expensive. If you happen upon a copy of this book at a thrift store or used book shop, it's definitely worth picking up a copy! This is the third puzzle I've created for my classroom based on this book.

I've already shared the 12 Envelopes Puzzle and 9 Squares Puzzle which also came from this book.

When I ran across this divisibility puzzle, I knew that it would make a lovely magnetic puzzle to post on my dry erase board for the upcoming year. I'm making it my goal to post a new puzzle on the board each week. I don't have space for a puzzle table like I had in the past at my old school (that's what happens when you have 30 students crammed into a classroom), so I've found that the best way to engage students in puzzles is to make them vertical by posting them on the dry erase board. The board is magnetic, and I've found I get the most engagement from students when the puzzles involve magnetic pieces that can be manipulated.

Here's the task. Is it possible to use the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 to construct a ten-digit number divisible (without a remainder) by all the numbers from 2 to 18?

I plan on putting magnets on the back of each digit. My magnets are currently locked away in my classroom, so that will probably have to wait until August.

Want to play along at home or with your own students? I've uploaded the file for this puzzle here as an editable Publisher file and PDF.

## Thursday, June 27, 2019

### Summer Block Project #1: Genius Blocks

Last summer, I ran across several craft ideas on twitter involving wooden blocks. So I promptly went on Amazon and bought a bag of 100 one inch wooden cubes (affiliate link).

They arrived at the beginning of August at the same time I was setting up my new classroom at my new school. Add this to the fact that we were still in the middle of unpacking boxes and settling into our new house we had recently purchased. Though I had ever intention of creating activities galore to use with my new students, the blocks ended up sitting on the shelf by our television for the entire school year.

This past week, I decided to finally do something with them. Because let's face it. A plastic bag of wooden blocks doesn't make the most attractive decoration for your living room.

My first block project I want to share with you is inspired by twitter, of course!

I somehow ran across this ancient tweet from 2015 last year about Genius Blocks. Curious, I asked for more details.

Fred Harwood replied with instructions about how to make my own set.

Fred shared the origin of the puzzle:

Inspired, I typed up the instructions and created a set of printable squares to glue on the wooden blocks to create my own set to use as a puzzle with my high school classes. The goal of the puzzle is to arrange the six blocks so that the sum of the numbers on top of each cube totals one of the targets below. The targets are arranged so that you are first tasked with making sums that take around 2 minutes on average to figure out. Eventually, you work toward the sum of 1 that supposedly takes around 24 hours to find. I can't vouch for the times because I haven't set down and solved all of the target sums yet myself.

Then, because I was so busy, the file just sat abandoned on my computer. When I ran across it earlier this week, I knew I had to make things happen.

After building my first cube and realizing that my idea wasn't totally crazy, I decided to take some pictures to document my progress. Yes, I realize that I could have just written on the cubes with a marker. But, I'm way too much of a perfectionist for that. I would rather painstakingly glue small squares of paper to each side of a cube. The process actually ended up going much faster than I expected.

Each row on the template makes one of the six cubes needed for a set of Genius Blocks.

Next, I cut out the six squares to be glued on the wooden cube.

I squirted a bit of craft glue onto one of the faces of the cube. I think Elmers school glue would work just fine, but all my Elmers glue is in my classroom. I was too impatient to drive up and get it, so I just used the craft glue that was in my craft supplies.

I used a cheap paint brush to spread out the glue to cover the entire face of the cube as well as possible.

Press the square piece of paper onto the glue.

Repeat the process for the other five sides. I found that I needed to wash the glue out of my paint brush in between each side.

Here's the finished product:

Actually, I still have one more step. I plan to brush each cube with Modge Podge (affiliate link) to make sure the corners of the paper stay adhered to the cube. I figure this will also make them just that much more durable since students will be handling them.

If I decide to make more sets in the future, I plan on printing the squares on different colors of paper to help tell them apart.

Inspired to create a set (or ten) for your own classroom? I've uploaded the file I created here as an editable Publisher file and PDF.

Keep an eye out on the blog for more of my wooden block activities coming soon!

## Sunday, June 23, 2019

### Nine Squares Puzzle

A few days ago, Shelli tweeted about needing more puzzles for next year since her advisory students will have already seen the ones she has used previously. This reminded me that I too will have this problem because my Pre-Calc classes will be made almost entirely of students I had this past year for Algebra 2. I remembered seeing a puzzle I wanted to recreate a few weeks ago when I was typing up the Twelve Envelopes Puzzle that I plan on using for the first day of school. This was just the push I needed to type it up!

I picked up a copy of Giant Book of Hard-to-Solve Mind Puzzles (affiliate link) about a month ago at Goodwill for two dollars. It's out-of-print which makes used copies from Amazon VERY expensive. If you happen upon a copy of this book at a thrift store or used book shop, it's definitely worth picking a copy up, though!

The book calls this puzzle "Nine Circles," but I've renamed it "Nine Squares" because squares are much easier to cut out than circles!

The goal of the puzzle is to place the numbers 1 through 9 in the 9 provided squares so that the number in any square in the upper row is equal to the sum of the numbers in the two squares immediately below it.

For example, I could place a 6 in the top row and a 4 and 2 immediately below it since 4 + 2 = 6.

It's a trickier puzzle than it first seems. I thought I was on a roll with this next attempt at solving the puzzle. 9 = 5 + 4. 7 = 4 + 3. None of my remaining numbers were three apart, so I had to scrap this attempt and try again.

With a lot of perseverance and a bit of teamwork in puzzle solving from my husband, we succeeded in finding a solution. I'm not sure if there is a single solution or multiple solutions. The books answer key might shed some light on this, but I try not to reference the answer section in a puzzle book because I always end up accidentally seeing the answer to another puzzle which I can't unsee!

I'm excited about putting this puzzle out with my students to tackle. This year, I want to do a much better job at changing out my puzzles on a weekly basis. I typed up two slightly different versions of this puzzle to share. The first version, as featured above, is meant to be solved on a table. My second version features larger squares and is meant to be solved simply using the squares without placing them on the outline on the puzzle board. I will be attaching magnets to each of the nine squares and using them on my dry erase board. The magnetic puzzles I did this past year included Double Letters, Equilateral Triangle Puzzle, Four Aces, and Matador Dominoes. My goal for this upcoming school year is to post one magnetic puzzle each week. This means I have a LOT of puzzle preparation to do this summer!

## Saturday, June 22, 2019

### Powers of i Open Middle Task

Yesterday, after spending a bit of time laminating and cutting out the cards for the trig open middle task I posted about yesterday, I started thinking about what other Algebra 2 and Pre-Calc topics I could create tasks for. As I was looking through the Open Middle tasks for complex numbers, I got the idea of creating a task involving powers of imaginary numbers. I was shocked at first that this didn't already exist. Then, I remembered why. Oh, yes, Oklahoma had to go and get rid of Common Core and write its own standards.

After throwing together a mock-up of the activity in Paint and realizing that it was solveable, I typed up the puzzle in Microsoft Publisher. The task is to use the digits 1-9, at most one time each, to fill in the boxes to create four true statements involving powers of i.

I also created some 1-9 cards to fit exactly in the exponent boxes. This helps ensure that students use each number at most once. Plus, I just like puzzles with moveable pieces!

A major perk of having a math teacher husband is that he is always glad to test out any of my creations.

Sadly, I was too slow to take a picture of my husband solving the puzzle. By the time I snapped my picture, he had solved the entire thing. I try my best to not post pictures of solutions here on my blog because I know that my creations are easily googleable by students!

I'm not entirely happy with this puzzle at the moment. I was able to find a solution very quickly as was my husband. But, I'm conflicted. Were we able to find solutions so quickly because the puzzle is too easy? Or are we finding solutions so quickly because we both have math degrees? How long would it take Algebra 2 or Pre-Calc students to tackle this task? I'm not entirely sure. But, I'm still looking forward to finding out. This is not the sort of task that I would make an entire lesson out of. It's not meaty enough for that. But, I do think that this task is perfect for a semi-quick lesson opener or closer. Or, it could be used as a station activity that students rotate between.

If you are looking to up the challenge of the puzzle, I would suggest challenging students to solve the puzzle in such a way that the exponents are in increasing order as you move down the page. It's still a very solveable puzzle, but it did require us to do quite a bit more fiddling with the numbers to make it work. If you have a group of students finish the original puzzle way too quickly, this could make a nice extension.

I'm also open to hearing constructive criticism about how to make this task better.

You can download the file for this activity here as an editable Publisher file and PDF.

## Friday, June 21, 2019

### Trig Ratio Open Middle Task with Moveable Pieces

I'm currently using part of my summer to create some activities for my Pre-Calculus classes for this upcoming year. Last year, I felt like I definitely spent more of my time creating things for my Algebra 2 classes than my Pre-Calc classes. This was probably because I had 4 sections of Algebra 2 and only 2 sections of Pre-Calc. This next year is looking like it will bring 3 sections of each. This has me super excited, and I'm especially looking forward to teaching Pre-Calc to classes of which most had me for Algebra 2!

Last year, I started Pre-Calc with a review of Algebra 2. This was necessary because the teacher I replaced had retired early the year before, and many of my students did not get a full year of Algebra 2 as a result. This review was necessary, but we kinda ended up getting bogged down in reviewing concepts that they should have already known.  (I must admit that my Algebra 2 students this past year didn't end up getting a full year of algebra instruction either as I ended up going on maternity leave at the beginning of May. Sorry for keeping my pregnancy a secret here on the blog. If you noticed a lack of blog posts this school year, that was why. I need to write a life update post soon and tell you all about our sweet, seven week old baby boy!)

For this upcoming year, I've decided to skip the review and jump straight into our units on trigonometry. So, I've been on the lookout for some great trig tasks to use with my students.

As soon as I saw this Open Middle task from Bryan Anderson, I know I needed to recreate it with moveable pieces. You could also use this for a geometry class as well!

 Image Source: https://www.openmiddle.com/trig-ratios/
First, I set out to recreate the table in Microsoft Publisher. I went through four or five iterations of how to label which way the table should be increasing before I found a way that was visually pleasing enough for me.

Next, I typed up the eight trig ratios to be printed out and placed on the template.

Once I got everything typed up and printed out, I set out to solve the puzzle by myself without a calculator or anything to write with. I've struggled since high school with doing trig in my head, so this was definitely a challenge for me. I can do trig problems just fine if I draw out the triangles and label the sides, but picturing the triangles in my head and working out the answers without a pen or pencil in my hand is a real stretch for me. But, I persevered and was able to figure it out myself.

I did arrive at a different answer than the solution provided on Open Middle. So, do be aware that this task has multiple solutions.

I look forward to watching my students tackle this task. They, of course, won't be restricted from using a calculator or writing utensil. I've already got a copy printed, laminated, and cut for each group so they are ready to go when school starts back!

Want the printable files to try this out in your own classroom? I've uploaded them here as both editable Publisher files and PDFs. I did make two versions - a large group sized version that prints on 11 x 17 paper and a smaller letter sized version. Thanks Bryan for sharing your awesome task!

## Monday, June 17, 2019

### Monday Must Reads: Volume 58

It's already Monday once again. This summer is flying by crazy fast. At this rate, I'm afraid I will blink and it will be August 12th and time to report back. As I continue to think ahead to next school year and the ideas I want to try out, I turn once again to my twitter likes. I try to go through these on a semi-regular basis and compile my favorite ideas in a volume of Monday Must Reads to share with you all. I find that the compilation process helps me remember these great ideas and increases the likelihood that I will actually implement some of them in my own classroom.

I hope you can find some inspiring ideas in this compilation to use in your own classroom!

Rob Maddock shares an amazing lesson that combines spaghetti, probability, and triangles.

Color-coded quadrilateral projects from Timikia Ramsey. Amazing work! Almost makes me wish I taught geometry...

Laura Vogel compiled her pre-calc students' ABC list of topics covered into a picture book for her 11 month old. How cool!

Launching water balloons sounds like a fun way to practice modeling quadratics to me! Great idea, Holly Olmscheid!

Looking for a way to figure out how to focus test review on what students really need help with? Check out this tally method from Annie Giercyk.

Have any jumbo playing cards laying around? Check out this Card Sharks game idea from Jennifer Fairbanks!

Also, check out Jennifer's cool coloring station in her classroom.

Laura Montgomery takes the usual Desmos art assignment to another level with laser cutting the designs in wood for end of year gifts.

Chelsea Cleveland shares an easy way to boost students' positive thinking.

Also, check out this Guess Who game for quadrilaterals!

It doesn't have anything to do with math, but I love this school tradition that Mandy shared.

Joel Bezaire shares a peek into his awesome Linear Olympics! Read his full blog post here.

Callie Hughes Gray shows what can happen when you give students an option to "Wow me" on a project.

Check out this amazing logarithm task from Math with P. Nik.

I bet Bob Lochel's students won't forget "Scratch Off Lottery Ticket Day" in stats class!

Designing cakes in math class? Check out this lesson from Kurt Salisbury!

Elizabeth Johnson shares a real-world project for examining data of daylight from different cities.

The OMHS Math Department recommends teaching circle theorems with hula hoops. How fun!

Christina Salvatore shares an alternative to your normal end of unit test.

Nathan Vaillancourt shares a brilliant rainbow-themed equation review. I really appreciate his inclusion of equations students hadn't seen before as "pots of gold."

Silvio Lioniello shares a real-world application of finding composite areas.

Greta SalathÃ© Mills offers up a new-to-me twist on SET - how many cards can you lay out that don't form a SET?

Karen shares some amazing geometry project ideas.

Kerri Homan engages students with function aerobics.

Teaching calculus? Check out the "derivers license" that Kerri's students can earn.

Jana Stenson shares some amazing golden rectangle art projects.

Paige Sheehan inspires with a lovely logarithm question.

How creative is this volume by cross section project from Peltier Alg 2 PAP

I really like this idea of goal free problems for teaching geometry/trigonometry.  Thanks for the idea, Beth Plaw!

Ella Hereth shares a great idea for getting students to wrap their minds around opposite, adjacent, and hypotenuse in relation to right triangle trig.

Paige Friedland shares a great real-world application of trig.

Holyrood Maths is making me think that I need to get a button/badge making machine...

Jed's approach of starting his pre-calc classes with "Don't Panic!" problems is refreshing and inspiring.

My trig students really excelled at proving trig identities this year. But, when I put a question on their final that asked them to justify each step, it was like I had asked the impossible of them. So, this idea from Coach Perales really caught my eye.

I first learned to play Nim as a sixth grader in math class. I've always played with physical objects like stones, pencils, popsicle sticks, etc. So, I was super intrigued to see nim played on paper. Thanks to Donna Buckley for the idea! Plus, they look like cute little Christmas trees!

I think we could all learn something from this approach by Sam Aguiar of giving students a quadratics problem on their assessment that they had never seen before.

This dot to dot approach from Math with P Nik could be applied to so many different math topics!

Alice Aspinall takes angle practice to a whole new level.

I'm super inspired by these unit circle medals from Janene Ward

Nat Banting shares a brilliant use of Desmos for giving students "just enough" information and asking them to figure out the rest.