Whenever I run across a great math idea online but not on twitter, I often tweet an image of the resource and share a link to the resource. I realize, though, that a lot of my readers aren't on twitter. Even if they are, it's so easy to miss a resource that's tweeted out since your twitter timeline can move so quickly. When I was pregnant this past school year, I would sometimes go weeks without looking at twitter, and I always had this feeling when I returned that I had missed out on something important but I would never know what it was. The fear of missing out is real, y'all.
My goal for this new, semi-regular blog feature I'm calling "Highlights" is to give these resources that I share out on twitter a permanent home on my blog for math teachers to peruse on their own time and at their own pace. To start with, I'll go through my twitter timeline and pull out my most recent shared resources. Then, hopefully, I will compile a new volume ever few months or so.
It's Monday which means it's once again time to look through all my twitter likes for the past week. I find that I'm much more likely to actually implement the amazing ideas I find if I take a bit of time each week to look through these tweets, share them with the world, and write a short summary of each one. I frequently find myself searching through my old volumes of Monday Must Reads for tweets to use, and I hope that you find these posts inspirational and useful in your own classroom.
By the way, can you believe that this is my 60th compilation of math teacher twitter awesomeness? It seems like I just started putting these together a few months ago!
Dorinda shares a comical graph she plans on using with her Algebra students. How fun would it be to give the students the graph and the categories and have students try to match each category with a curve on the graph. I think this could lead to some awesome discussions!
This summer, I'm on a mission to make as many puzzles as possible for my classroom from a bag of 100 wooden blocks (affiliate link) that I purchased from Amazon.
So far, I have used 6 of these blocks to make a set of Genius Blocks and 27 of the blocks to create a SOMA Cube. 33 blocks down - only 67 more to go!
Project #3 uses 15 more of these blocks to form a puzzle called "3 Immovable Pentablocks."
The goal of this puzzle is to place the three pentablocks within a 7 x 7 tray so that it is not possible to slide any of the pieces in any direction.
This puzzle is from The Big, Big, Big Book of Brainteasers (affiliate link) by The Grabarchuk Family. 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.
I began my project by joining my one-inch wooden blocks (affiliate link) with wood glue to form the five puzzle pieces.
I don't own any clamps to properly hold the blocks together while they are drying, so I once again turned to my trusty hair bands to do the job for me!
Once the glue was dry, I had to figure out how to make a tray to place the puzzle pieces in.
Since my blocks are one-inch cubes, I created a 7 x 7 table where each cell was a one-inch square to correspond with the blocks.
I cut slits from each corner of the paper to each corner of the grid.
With these slits cut, I started folding up the sides of the paper along the edge of the grid.
Once all the sides were folded up, I folded the small triangles over so the sides could be easily glued together.
Here's what a corner looks like once it's been glued.
Now, it's starting to actually look like a tray!
To make the tray sturdier (and hopefully stand up to the abuse of teenagers!), I started cutting pieces of cardstock to glue around the sides of my paper tray.
I folded each piece of cardstock in half.
Then, I folded one of the halves in half again.
These folds make the cardstock fit exactly over the side of the tray with a large overlap on the bottom of the tray to make it sturdier.
Here's what the bottom looks like after gluing on the cardstock:
Now, repeat this process three more times.
I glued an extra scrap of cardstock on the bottom of the tray to finish it off.
A finished tray! It's not absolutely perfect because one of my sides ended up slightly taller than the other three, but I'm still really proud of it.
At this point, I decided it was time to actually attempt to solve this puzzle. Remember, the goal of the puzzle is to place the three pieces in such a way that none of them can move within the tray.
That's when I discovered that this puzzle is VERY tricky. After trying arrangement after arrangement, I took a break. My husband, of course, came over and solved the puzzle in just a minute or so as I kept my eyes closed so the puzzle wouldn't be spoiled.
Once I knew that it could indeed be solved, I went at the puzzle with a new vengeance. (Of course, I never actually doubted that the puzzle could be solved. It did come from a published puzzle book, after all...)
One thing that I found frustrating in my attempts at this puzzle was that it was sometimes hard to tell where one puzzle piece stopped and the next began.
I got out my newly purchased collection of Apple Barrel paint (affiliate link) and several paper plates and got to work to fix this issue.
It worked! The puzzle pieces are now easy to distinguish from one another.
I was pretty excited when I figured out how to make the pieces fit all the way across the grid - until I realized that the entire column of pieces could be slid across the tray.
I won't spoil the puzzle for you, but I will reassure you that it can be solved! There's great satisfaction to be had from shaking the tray and watching the puzzle pieces that you created stay in place!
Want to create a copy of this puzzle for your own classroom? I've uploaded the files here.
The last time I taught Algebra 1, I used Naoki Inaba's Step Puzzles to introduce the idea of arithmetic sequences. I tweeted about it, but in the craziness of packing up my classroom and house to move last summer they never made it up on my blog.
I was first introduced to the amazing logic puzzles of Naoki Inaba in 2016 when I discovered his area maze puzzles (affiliate link) which have become quite popular.
On his website (which is entirely in Japanese...), Inaba shares a collection of logic puzzles that are PERFECT for the math classroom. I ended up writing a series of blog posts highlighting these puzzles and their potential for use in class in 2016. If you're interested, be sure to check out Volume 1, Volume 2, Volume 3, and Volume 4.
Since then, I've slowly been in the process of translating these puzzles and putting them into a more user friendly format for use in the classroom. So far, I've blogged about Angle Mazes, Zukei Puzzles, and Kazu Sagashi Puzzles.
At the beginning of this month, Simon Gregg tweeted me to ask if I had reformatted Inaba's Step Puzzles to fit more to a page than the original PDF. I had, and this tweet reminded me that I was over a year late in blogging about this!
I like to introduce step puzzles to students by showing them a puzzle and its solution and asking them to figure out the rules of the puzzle.
Because of this problem-solving based introduction to step puzzles, I have not typed out the instructions on the puzzle sheet that I give to students. I have another reason for this. These puzzles are accessible for students as young as elementary school. They are still engaging for middle school and high school students. But, with these age groups, students can be instructed to place numbers in each circle so that each line forms an "arithmetic sequence." This proper vocabulary would likely intimidate an elementary student who could easily tackle these puzzles with an age appropriate introduction.
The puzzles start out quite simply.
Sometimes my students have used the first puzzle to make an incorrect assumption about how the puzzles work. They assume that 1, 2, 3 is the answer to the first puzzle because 1 + 2 = 3. When really, it is 1, 2, 3 because 1 + 1 = 2 and 2 + 1 = 3. You can check student understanding of this by having them solve the second step puzzle 3, 5, ___. The correct answer is 7. Students with the prior misunderstanding would answer 8.
I've found that once I set students straight from this misunderstanding that they seem to be good to start tackling the puzzles on their own.
The puzzles quickly progress in difficulty. Soon students have to start figuring out where to start solving the puzzle. If students start in the wrong place, the puzzle will seem impossible.
You can download Inaba's original Japanese version of these puzzles here. I've uploaded my paper-saving version here. I'm looking forward to using them with my Algebra 2 students in this upcoming year in our sequences and series unit!
Before I close out this blog post, check out how Simon Gregg combined WODB (Which One Doesn't Belong) with Step Puzzles!
For years, I've had it in the back of my mind and on many a to do list to create a typed version of my naming polynomial speed dating cards to share!
My first set was created with index cards. I wrote the polynomials on the front of the index cards with magic marker.
On the back, I used pencil to lightly write the name of the polynomial. I did this in pencil to make it harder for students who might try to look through the card and read the answer!
This specific set of cards made their debut way back when NPR came to visit my classroom. NPR even captured photos and audio of my students doing the polynomial speed dating activity if you want to take a listen!
So, what is speed dating? You might know it by its more traditional name of "Quiz Quiz Trade." It's one of my favorite activities for building students' fluency with concepts that require very little calculation. To do a speed dating activity, you need a deck of cards with questions written on one side and answers written on the back.
In this case, the "questions" are polynomials, and the "answers" are the corresponding names of the polynomials. I always start my speed dating activities by passing one card out to each student question side up. I instruct them to work out the problem on their card and check their answer by flipping the card over. Usually at this point in our polynomials unit, we've only done a handful of examples in class. For some students, this might be their first attempt at naming a polynomial all by themselves.
Once all my students have had a chance to work out their own problem and check their answer, I then explain the rules of the activity.
The goal of speed dating is to get to know something about the other person as fast as possible and to exchange information in case you later decide you want to get to know them better. The goal of this activity is to figure out the name of the other person's polynomial as fast as possible, to exchange information (trade cards), and find a new partner to get more practice.
Usually, at this point, I model the activity with a student. Then, I have all my students stand up and pair up. In each pair, students hold their cards up to each other with the question side facing out and the answer facing them. Students take turns naming each other's polynomial. If a student messes up, the other student often gives a hint or shows them the answer and helps them figure out where they went wrong. After both polynomials have been successfully named, students trade cards and go off in search of a new partner.
There are several things I LOVE about this activity.
1. Students are up and moving around. This automatically increases student engagement. 2. Students are interacting with students from all over the classroom - not just the students they normally sit by. 3. Students get immediate feedback. Plus, it's peer feedback. If a student is struggling, hearing a peer re-teach part of the lesson can be a powerful thing. Students need to sometimes be reminded that I'm not the only teacher in the classroom. We can all learn from one another. 4. On top of getting immediate feedback, students also immediately get another chance to test out their new-found polynomial naming skills. 5. It's one of the easiest activities for me to jump in as a teacher and participate alongside my students. If I have an odd number of students, I often participate myself just so there's no excuse for a student to be standing and doing nothing while waiting for a partner. When I do this, I use it as an opportunity to retire some of the cards from the game and introduce new cards that students have not yet seen. 6. The amount of time that the activity lasts for is super flexible. I can use it as a five-minute activity or a two-minute activity, whatever fits what a specific class needs.
In fact, I love this activity so much, I want to be able to not only share the idea with you but make it easier for you to implement it in your own classroom by providing a printable file!
A few years ago, I started using printable business cards (affiliate link) to create my speed dating activities. This is a huge time-saver because it completely cuts out the laminating and cutting steps. If you bend the business cards a certain way, they just pop apart. It's actually kinda fun!
If you don't have access to these business cards, don't worry. Just print on normal letter sized paper and trim off the excess margins before cutting the cards apart!
My biggest class this past year was 30, so I created 30 different polynomials for students to practice naming.
Here's what a finished speed dating card looks like.
And, my favorite thing to share: action shots. I have a policy of never posting pictures with student faces on my blog to maintain student privacy. Students are always so engaged in speed dating activities, that it makes me so sad to have to cover up their faces. I want the world to know just how engaged students can look in math class! I guess you'll just have to try it in your own classroom so you can see it for yourself!
I have uploaded the file for this activity here as an editable Word Document and non-editable PDF. Remember, these are formatted to fit printable business cards (affiliate link), but you could easily print them on regular letter sized paper and cut off the excess margins before cutting the cards apart.
Even though it's now the middle of summer, I'm just now getting around to blogging about an activity that we did in January. Yes, that pretty much sums up how this year's blogging is going. I feel like almost every post starts with an apology of how late the post is. So, without further apology, I want to share with you the 2019 Challenge. We've still got a few months of 2019 left, so I guess the post isn't too tardy yet.
Kicking off the spring semester with a challenge based on the new calendar year has become a bit of a tradition in my classroom. Let's take a bit of a trip down memory lane.
I fully had plans to put up the 2019 Challenge as a bulletin board before we went on Christmas Break. That did not happen. Then, our first day back from Christmas was cancelled due to ice. This meant our normal two day week to welcome us back to the second semester was now a one day week. There was no way that I was starting new content on a one day week, so I decided to take the 2019 Challenge I had planned to put up as a sort of puzzle for early finishers and turn it into an entire class activity.
Note: I usually use this as a "Welcome to the new semester!" activity, but you could just as easily use this as a "Welcome to the new school year!" activity in August/September.
If you're not familiar with the challenge, the goal is to use the digits in 2019 (2, 0, 1, and 9) exactly one time each along with any mathematical symbol or operation of your choosing to create expressions equivalent to the numbers between 1 and 100.
I gave them a list of some of the possible mathematical operators to get their brains moving.
I love to use this challenge to introduce students to one of my favorite words: concatenation.
Concatenation means that 2 and 0 can be combined to make the number 20.
My students have yet to be introduced the concept of factorial yet, so I gave a quick tutorial on what it looks like and what it means. We started by trying to complete this chart.
We started by trying to complete this chart as a class on the dry erase board. It was interesting to hear students' theories evolve as each new answer was revealed.
In the past, I would post the challenge, introduce it to my students, and let them fill out as many solutions as possible. As the first day would progress, the challenge would get more and more difficult as the easier numbers that could be achieved by simple addition and subtraction with maybe a little multiplication thrown in were already claimed.
I needed to keep six entire classes of students engaged, so I decided to have each class start the challenge from the beginning. That's when I got the idea to pull out my 100 number chart (affiliate link) that I purchased last year from Amazon.
Then, I spent some quality time with the paper chopper and some cardstock to cut out a different colored set of squares for each of the six groups that my desks are arranged in. I sized these squares to be the same size as the 1-100 cards that fit in my pocket chart.
Groups would work together to find as many expressions as possible to equal numbers between 1 and 100. When a group found an expression for an unclaimed number, they would bring their solution up to get it verified. If it was correct, they would place one of their squares of cardstock on top of the number to "claim" it for their team.
The small numbers always seemed to go first.
By the end of the 50 minute period, the board would look something like this:
Or this one from one of my pre-calculus classes.
In some ways, this activity structure was better than my bulletin boards of the past. And, it also left some attributes to be desired. Let me try to reflect.
Adjusting this to a group-based competition did have some unintended consequences.
Some groups were WAY more hyper-competitive than I expected. One group had one of their team members permanently stand next to the 100 number chart so that as soon as they figured out a number and got their solution checked they could mark it with the color for their team. This meant that this student was not doing any math at all which was not my intention.
I attempted to combat this by requiring in another class period that only one person from each group was allowed out of their seat. This solved the prior issue but created another. One student from the group would tend to spend the entire time running answers up to my desk and getting them checked before marking off their numbers on the chart. This meant that there was still a student who was primarily doing no math at all.
Still yet another downside to the competitive team nature of this activity was that some groups tended to give up entirely as they realized JUST how far they were behind the other teams. Some students started trying to play games on their phones instead of participating in the activity because they knew that their group was NOT going to win.
To combat this in the future, I might have students remove the cards from the chart after solving them and have them place them in a small box or basket for each team. This way, everyone can still see what numbers remain unsolved, but they can't easily see how far ahead or behind they are from the other teams.
I really appreciated the fact that making this into a group activity ended up engaging a vastly larger percentage of my students than my previous use of the activity with early finishers.
However, a trade-off was that my students weren't necessarily learning from one another as much as they have in the past. This was because previously, students would write their solutions to each number on the bulletin board. Often, students would take a solution for one number and end up tweaking it slightly to create a different number. Usually, this would involve adding a factorial symbol to a 0 to produce a 1 or something similar to that.
Frequently, students would see a solution written on the board and ask a question about it, thinking it was incorrect. This made a great teaching moment.
If I do this again, I might write 1-100 on the dry erase board and have students write their solutions next to each number as a step in the process. This keeps the competitive aspect while still encouraging students to learn from one another. It's also easily erasable between classes.
I've got lots to think about before I decide how I want to proceed with the 2020 Challenge. My main concern isn't the structure of the activity but what to do about the fact that we only have two 2's and two 0's to use. If you have any ideas, I'd love to hear them!
I'll close this rather long rambly blog post with one of my favorite solutions to the 2019 Challenge.
Students are given paper cut-outs of the letters C, E, and L. They are tasked with using all 3 letters (no overlapping allowed) to create a new letter E.
This can be achieved without flipping any of the pieces over, so this will make a perfect magnetic puzzle to put up on my classroom's dry erase board.
The author of the book poses this as a way to have students practice the problem-solving strategy of "Change Your Perspective." Because the book poses the question and immediately shares the solution (I guess it is a teacher's guide...), I didn't get a chance to attempt to solve this puzzle on my own.
I did give the puzzle to my husband to tackle to see how he would handle it. He tried many different configurations with little success. I ended up having to give him a hint. Once I did this, he immediately found the answer.
You can download the file to recreate this puzzle here as both an editable Publisher file and non-editable PDF.
Normally, I never post puzzle answers on my blog, but I think I will make an exception for this one since the linked PDF gives the answer away as well. I've posted a picture of the solution at the link above in a folder titled SOLUTION.
If you're going to use this with students, I would definitely recommend solving it yourself or taking a look at the solution before presenting it in class!
A week or so ago, I shared the first of many wooden block projects I have planned for this summer. Those Genius Blocks were actually my second project of the summer, but they were the first project to be entirely finished and ready to be blogged about.
Yesterday, I finally finished up the wooden block project that first caught my eye last summer - SOMA Cube Blocks.
One of my goals for this summer is to make as many projects as I can for my classroom from a bag of 100 one inch wooden cubes (affiliate link) that I bought from Amazon LAST summer and never got around to using. This project requires 27 wooden blocks.
The SOMA puzzle was created in the 1930s by Piet Hein. SOMA is a set of seven polycubes that can be combined to create a cube and other geometric figures. If you're interested in the history of this puzzle, I recommend this excellent website with an overwhelming amount of information about the origins of SOMA!
I loved that the above website shared scans of the original patents for the SOMA Puzzle. I printed off one of the patent images and used it to build my own set of SOMA puzzle pieces using 27 wooden blocks and wood glue.
I didn't have any clamps to hold my blocks together like the wood glue (affiliate link) suggested, so I ended up using hair ties to hold the blocks together as they dried. Elegant? No. But, it worked!
I used one inch wooden blocks (affiliate link) for this, but you could really use any size. Just make sure that the blocks are a consistent size.
To make sure I hadn't made any mistakes, I challenged my husband to do the traditional SOMA puzzle - create a cube using the 7 SOMA pieces.
I plan on putting this out in my classroom as an on-going puzzle for students to tackle. I would like to post a new SOMA challenge every week or so. The blocks have been done for almost two weeks now. The challenges for students to complete, however, have been lurking on my to do list.
I used the snipping tool to grab images of some of the different arrangements that can be made with the set of 7 SOMA pieces. Then, I compiled them into a file to print and post in my classroom. I ended up with 31 different challenges to post which should keep my students busy for almost the entire school year.
I plan on attaching a sheet protector to the wall above where the SOMA pieces will live in my classroom. Then, I can just easily change the challenge out on a weekly basis.
Want the set of 31 challenges to print and post in your own classroom? I've uploaded them here as an editable Publisher file and non-editable PDF.
If you don't want to post the challenges on the wall in a sheet protector and change them out on a regular basis, you could easily print them 4 to a page. Then, cut them apart, hole punch them in the corner, and make a small ring of puzzles to keep near your SOMA pieces.
As I've been prepping for my classes for next year, I continually finding myself referencing previous volumes of Monday Must Reads. This is just the inspiration I need to keep compiling these volumes in an attempt to capture the awesome ideas of math teachers on twitter! I hope you find an idea to use in your own classroom and at least one new math teacher to follow.
Last year, I had such a hard time learning student names at my new school. After working at the same small school for six years, I was used to only having to learn the names of my new freshmen each year. So, the job of learning almost 140 new names all at once was more than a bit overwhelming. I love this flashcard idea from Richard Jones. I'm sad I won't be able to use it this year because we don't get access to class lists until the day before classes start.
Usually, the ideas I share on these Monday Must Reads posts are all-mathy. But sometimes, I can't resist sharing a science idea since I have taught sections of both physical science and chemistry in the past. This covalent bonding activity with tracing paper from Mr Shah is just too good not to share!
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.
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.