Pi Day Activities

In the past, I’ve not really been a fan of Pi Day (please don’t revoke my math teacher card!). Most of the time it just seems like a party day that ends up being a waste of time that I could’ve really used as an extra instructional day (Oregon always gets a ton of snow at the end of February, which makes early March stressful). That said, I love to celebrate and have fun, so I’ve been thinking and thinking about how to have the best of both worlds! I think I’ve finally figured it out.

I plan on doing two things with my students. The first is a circle investigation that lets them discover what pi is, and then they derive the formulas for the circumference and area of a circle. My favorite part is the proof of the area formula for a circle…I think I have it laid out in a really cool way that is also very pattern-based for students. It also allows them to built upon their prior knowledge, which is fantastic!

For the record, all of my students already know the formulas for circumference and area, but I strongly doubt any of them actually know why those formulas work. Most of my students have been regurgitating those formulas for years without actually knowing one bit of the “why” behind why they work. So, from Algebra 1 to Pre-Calc, I think all of my students will really benefit from the conceptual understanding and process of deriving formulas that are introduced in this activity.

In the first investigation, students are to find and measure 5 circles using string and a yard/meter stick. I’m going to let my students go on a bit of a circle scavenger hunt around to school that way they’re not all using the same ones, but I also have 5 circles to print out for classes/students that I know might not be able to handle that amount of freedom. I plan to have my students work in groups of two or three.

After students are done with the three parts of the investigation, they get to move onto the coloring activity to apply what they’ve learned. I don’t know what it is about coloring, but all of my students LOVE to do these types of activities. Regardless of age or gender, they are all down to color. This activity is also self-checking because of the way it’s set up. There are 10 problems in total that are broken up into two columns. Each of the answers from the first column will match up with another answer from the second column. The way that the problems match up creates the color-coding key for the picture.

I would love to know what you do in your class to celebrate Pi Day. Please leave a comment below, I’d love to hear from you!
-Audrey

If you would like to use these activities in your own class, you can find them here!

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Mystery Sum Activities – The Perfect Practice Structure + FREE DOWNLOAD

This winter, I’ve been working with my first ever student teacher. One of the first things that we did was make a list of different practice structures and the benefits of each one. He had definitely heard of some of them from his MAT program, but several of them were brand new. One of the newbies, was a “Mystery Sum” activity, which happens to be one of my all-time favorites. I got to talking with the other math teachers in my department, and none of them had heard of it either!

Since Mystery Sum Group Challenge Activities are one of my favorite practice structures, I figured I’d share all of the details with you! Be forewarned, I will say it’s the most time-consuming of the practice structures if you’re making it from scratch.

To give you an example of how it works, I’ll walk you through my Solving 2-Step Equations Mystery Sum Activity (you can download it for free here, if you join my mailing list!).

Students work in teams of 4 to complete the mystery sum group challenge. The way this activity works is that there are six suits of cards (I make them with a flower, crown, star, peace sign, lightbulb, and phone but you can really use whatever). Each suit has four cards (one for each student). The cards are actually numbered. I always have it set up where the cards within each suit are differentiated as follows:

Card 1 – Basic
Cards 2 & 3 – Basic/Moderate mix
Card 4 – Moderate/Advanced mix

I do let my students know that each card is leveled so they can pick an appropriately challenging problem to work on. They’re pretty good at self-reflecting and choosing the right card.

Once students are in groups of 4, each student gets a work recording sheet, and each group gets an answer recording sheet. Finally, we’re ready to go. Also, teachers, this part is really important, this is an activity that you absolutely MUST have an answer key pre-made. Students will be checking in with you rapid-fire, so you need to be ready. I always include an answer key with my activities, so you don’t have to do any extra prep!

Now that students are in groups and they have all of their supplies, you’re ready to begin! Each group gets a suit of cards (each suit contains 4 cards). Students will take their designated number, and begin solving their problem on their personal work recording sheet. Once students get their answer, they will write it on the group answer recording sheet. After the whole group has finished their problems, they need to find the sum of all of their answers to the problems within that suit. Once the group has found the sum, they can check in with the teacher.

Now, we’re getting to the part that I LOVE so, SO much about this activity! At this point, the group should check in with you about their sum. If they’re correct, then exchange the suit of cards they’re working on for one they haven’t done yet.

If they’re incorrect, that’s where the magic happens! Don’t tell them anything other than the fact that their group has not found the correct sum. It is up to them to work collaboratively to find the error(s). This activity promotes so many things that are the best parts of math class:

  • Collaboration
  • Error analysis
  • Persistence
  • Precision
  • Effective team communication

Plus, it’s differentiated! Seriously, what else could you ask for in an activity?

Once a group has made it through all six levels, I like to have them go become helpers around the room.

It’s fantastic to see students progress over the course of the activity. They may struggle a bit initially (which is a big reason why this is a group activity so they have built-in support), but as they progress, suit through suit, they pick up speed and accuracy.

Hopefully, I’ve given you an idea of why Mystery Sum activities are one of my absolute favorite practice structures around.

If you’d like to try out an activity without having to make one yourself, you can download my Solving 2-Step Equations Mystery Sum activity, here by joining my mailing list! I promise to never spam you, and will only send updates about sales, new resources, giveaways, and the occasional tip or trick that I’ve learned.

The DIY Christmas Tree – Surprisingly Mathematical

Oh, the sweet irony of living in a town that ships Christmas trees all over the nation (seriously, they helicopter them out by the bunch), yet I don’t have room for one in my house.

A few years ago, after seeing a few ideas of DIY space-saving Christmas trees on Pinterest, I was inspired to make my own (or should I say I was inspired to enlist my dad to carry out my vision?).

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Supplies Needed:

  • 4×8 plywood
  • Hot glue and a hot glue gun
  • Tree colored garland (I think I used 2 packages of this)
  • Green, yellow, and brown paint
  • Jigsaw
  • Chalk Line
  • Measuring Tape
  • Pencil
  • Picture hanging kit (both to attach to the back of the tree and to the wall)

I bought a piece of 4×8 plywood from HomeDepot or Lowes. I think it was around $13. Again, it was several years ago so some of the details are a bit foggy.  I also got two packages of 30foot garland that looked like pine needles. It was super cheap, around $10 for both packages. I already had all of the other supplies.

Here’s a copy of the original plan I had for my dad:

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Originally, I had planned that I wanted the tree to be 6 feet tall and 3 feet wide, with a 6-inch stump at the bottom.

My dad had other plans, though. He said that we could reduce the amount of cutting we had to do if we rearranged where we put the tree on the plywood board.  This is how he suggested positioning it:

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To simplify things even further, we decided to make the side length of the tree 6 feet, instead of the original 6.18ft. This slightly reduced the height of the tree, but it made for easier measurements.  The original side lengths and heights can be compared using the Pythagorean theorem, or trig if you wanted to!

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Once my dad marked off the 6ft line on the left edge of the plywood board, he used his measuring tape to swing an arc around the cutting board, hinging from the upper left corner. Could your students figure out what the radius/diameter of this circle would be? Hint: it’s not 6 feet!

Once he drew the arc, we measured 3 feet across from the 6ft mark on the left edge. At this point, he brought out a chalked line (something I’ve never seen before!). He had me hold it from the upper left corner, and he pulled it to the 3-foot mark along the arc he just made. Once he had it taught, he pulled the string up a bit and then it snapped down on the plywood leaving a very visible, straight chalk line (burnt orange in color).

We then measured off 1.5 on the bottom of the tree, and then made another chalk line from the upper left corner down through the middle of the tree, continuing down a few inches further. Geometry vocabulary that applies: bisection!

We then were able to measure off the stump of the tree. I think I made it 3×6″ or 4×6″.

I used Microsoft Word to make a big star. I printed it, cut it out, then traced it on the plywood.

At this point, it’s time to cut out the tree and the star!

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The next thing I did was paint the tree. I happened to have a bunch of dark green spray paint left over from an old project, so I spray painted the tree. For the stump and the star, I used some old Crayola paint that my parents have had since I was a kid (seriously, they’ve had that paint since I was 7 or 8). It worked like a dream!

After the paint is dry, I started to hot-glue down the garland to the tree, in a zig-zag pattern. This is the part that took the longest, by far. It was very useful to have a second person for this.

After all that was done, I hot glued down a picture hanger to the back, and hot glued on the star to the front.

Using just regular ornament hangers, I attached two strings of LED lights and some ornaments.

Here’s the finished project:

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Also, right next to the tree I have a wax warmer going with a fir tree scent. It really brings the whole package together.

All in all, I think I spent about $25 on supplies. I love how it looks (it really does look beautiful!), and it’s super easy to store when it’s not in season–I just hang it up in my garage.

I hope you enjoyed reading about how math unexpectedly showed up in my real-world DIY Christmas tree project.

-Audrey

How to Make the Most out of the Last Day Before a Big Holiday Break + GIVEAWAY!

Keeping engagement high the last day before a big break from school (like Thanksgiving or Winter break) can be difficult. Students can barely contain their excitement, teachers are beyond exhausted, and you’ll still find yourself surprised after all these years about exactly how many families decide to begin their breaks a day early.

Here’s what I do…

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Typically, I try to end a unit before going on a large break. I really don’t like having a week (or two!) off in the middle of a unit, so I’ll always try to test before going to break. That being said, I always try to avoid doing it the very last day before break, for a couple of reasons. Firstly, the number of students who are absent the day before a big break is astounding. I don’t want to have to go through the hassle of before/after school makeups for 10+ students–plus, the odds that they’ll do as well with a week+ in between is highly unlikely. On a more personal note, I also refuse to give a big test on the last day before a big break because then that means I have to spend my break grading. Teachers deserve breaks, too! Do yourself a solid and plan to give the big assessment the second to last day before a break that way you actually have time to grade.

So, that brings us to the big question…what do you do with that last day before a big break?! I always try to use it as an opportunity to review essential past skills in a game-like format or incorporate in other activities that I normally wouldn’t be able to fit into a unit. For example, before Thanksgiving break, I like to play my Domain & Range of Continuous Functions Connect4 activity with my Algebra 1 class. Domain and range is such a critical skill for success in high school algebra courses (both Algebra 1, Algebra 2, and Pre-Calculus focus heavily on it) and is typically a trickier topic for students, so reviewing it at key points throughout the year has really helped improved my students’ long-term skills. We review with a fun Connect4 game, which is essentially like BINGO but 4×4 instead of 5×5. It’s incredibly low prep for us teachers, and the students can never get enough!

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Right before Winter break, I typically review solving one-variable inequalities because we move onto rearranging/graphing two-variable inequalities and systems of inequalities right after we return from break. Having a firm reference is a total plus and makes the future lessons go off much, much easier! To review, I normally use my BINGO game with some individual student whiteboards. Again, as a teacher, this activity is just about as close to no-prep as you can get (just print out a few BINGO cards and you’re set!), but students love it!

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In both cases, since these are topics students have seen before, they think it’s an “easy day,” and are SO into it. What they don’t realize is how important it is to interleave practice and spiral back to core concepts, so this ends up being a total win-win situation.

This is also a great opportunity to do some of the non-content related activities that you’ve been dying to use all year long. Team-building and perseverance-building activities are perfect for this time of year! Here are a few ideas:

  • Play 31-derful (a team-building, strategy/perseverance activity). Here’s a digital version.  (NOTE: this activity is pronounced “thirty-wonderful”). You could totally play this game with a regular deck of cards, too!
  • Spend a class period doing Number Challenges. Here’s a full blog post with free downloads! This activity is great because it reviews order of operation skills, group work norms, and focuses on building perseverance.
  • Play Petals Around the Rose. This is a free online activity where students must figure out the rule for getting the score of a roll of 5 dice. This game is AMAZING! It is a total testament to perseverance. Students will both love it and hate it all at the same time, but they’ll hate it in the best of possible ways–trust me, they will ask you to play it again. Don’t give them any spoilers! They may not figure it out in one class, so keep them waiting. If you have an extra 2 minutes at the end of a class period a week later, play Petals Around the Rose. Everyone finish their quiz early? Play Petals Around the Rose. The only thing you can tell them is that (1) the name of the game is Petals Around the Rose, and the name of the game is everything, and (2) the score is either zero or even.
  • Do a team-building activity like The Maze. This activity is super-low prep and gets your whole class to listen and work as one. Plus, it’s super fun!

 

Since this time of year is so hectic, I wanted to treat you a bit, so I’m participating in a giveaway! There are two ways you can win:

****Giveaway Open W 11/21 – Su 11/25****

  1. Leave a comment below telling me (a) what the hardest part of the holiday season is for you as a teacher, and (b) what product you’d most like to win from my store (<$10). I will randomly select a winner, and you will be emailed the product of your choosing.
  2. Enter the Rafflecopter Giveaway for a chance to win a $50 gift card to amazon.com! Again, a winner will be chosen randomly and contacted by email. Make sure to enter the gift card giveaway here!

For additional chances to win, check out these fabulous ladies’ blog posts! I’ve teamed up with each incredible woman, below, to write posts about keeping engagement high and students motivated at this difficult time of the year. Each blog post will have another opportunity to win, so make sure to check them out!

  • Jean from Flamingo Math is writing all about how to keep your students motivated mid-year! Read her tips here!
  • Kristin from Samson’s Shoppe is sharing her top three tips for how you can survive the holiday and testing season! Read her three tips here.
  • Carolyn from Engaging Science Labs shares a super hands-on activity for making a periodic table! As a math teacher, I got a bunch of ideas from per post about how I could apply it to my own classroom!

 

Number Challenges – A Team-Building Perseverance Challenge

If you’re looking for a great way to get your students working together, talking about math (particularly the order of operations), and working on perseverance, then search no further! This set of Number Challenges is perfect for any secondary math class.

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Originally, taken from Math Equals Love, I wanted to reformat her activity because I didn’t have as much wall-space as she did, and I also wanted to add an extra element of reflection to turn the lesson’s focus more to perseverance, than order of operations (the math is definitely a welcome addition, though!).

I used this activity on the first day of school with my Algebra 1 students, but I think it would be perfect for a “top-up” lesson right before a big break. What I mean by that is, throughout the year, some messages need to be revisited and “topped up.” Perseverance and working as a group are always great things to revisit and place an emphasis on so that skills don’t backslide. Sometimes we have to intentionally be explicit when we teach students how to do these skills, so activities like these are a great framework for a larger conversation about the many “soft skills” that come up in a math classroom (like perseverance and teamwork).

To find the original activity instructions, check out Math Equal’s Love’s original blog post! Here’s a link to the plastic pockets I used, which allowed students to write on the papers with a dry erase marker (this is not an affiliate link)!

Here’s the copy of the number challenges! Print them double sided and place them inside of the plastic pockets so students can work on them with dry erase markers! I make two for each level and had groups of 3 working on different number challenges. When they finished one challenge, there was always a different number challenge waiting to go.

Here’s the perseverance reflection form that I had students fill out as an exit slip. It made for fantastic conversations the next day!

If you give it a try, let me know how it goes!

The Maze – A Teambuilding Challenge for Middle & High Schoolers

Teambuilders are not normally “my thing.” Maybe I just don’t have the personality to sell them correctly, but I’ve found they normally are a bit of a letdown, especially with older high schoolers.

On top of that, many of them are designed for the most extroverted of students, which doesn’t sit well with me. Again, that could just be due to my naturally introverted nature.

With all of the above in mind, let me tell you, The Maze went off beautifully! From freshmen to senior, shy to outgoing, everyone loved it!

Here’s how it works:

Create a 4×4 grid. You can use painters/masking tape, chalk (if you’d like to go outside), softball/baseball bases, you name it!

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Next, you’ll need to design a secret path through the maze. Here’s the path that I made. IMG_4330

From here, have students make a line or a circle around the grid and have someone start. Students can only move in the four main directions–left, right, forward, and backward. If they are correct, say nothing and allow them to keep going. If they mess up, they go to the back of the line and the next student gets to try.

Students get SO into this and do an incredible job at watching and listening to their classmates. Natural leaders will surface and help coordinate the efforts. As more students try out the maze, the faster and faster they go–always learning from the students before them and being guided by their classmates. By the time someone finally makes it through the maze, the success is celebrated as a class!

After students have made it through the maze, here are some possible future variations:

  • let a student make their own maze and be in charge
  • make students do the maze in total silence, only with non-verbal communication
  • increase the size of the maze. 5×5, 6×6…10×10?!

What are your favorite team building activities for secondary students? Share in the comments below!

Question Stack Templates (10, 12, and 16 problems)

Question stacks have become quite popular on math teacher Twitter due to the blog posts from Math Equals Love.

Making them can sometimes be challenging, so here’s an editable question stack template you can use to save time (it’s a PowerPoint file).

As a pro tip: To make a really quick answer stack, I use Kuta worksheets and add screenshots (using the built-in snip program on my computer) in each box of the original problem and then the answer in the answer box. I’ve uploaded the file in PowerPoint format because it’s much easier to move around screenshot pictures in PowerPoint than it is in Word. If you’d rather hand type things, then please do! The file is 100% editable.

-Audrey