March has marched on, and April is here! Spring is a lovely time to do some problem solving, and I have the Calendar of Problems from 30 years ago for your math enjoyment. I have a few more old Mathematics Teacher1 issues from my attic, so I’ll be sharing these monthly for the academic year.
Use these with your students, or solve them yourself; try them for problems of the week, fast finishers, extra credit, or just for fun! Tell us about your worked-out methods either here in the comments, or on whatever platform you use2.
Never miss a post! Subscribe to Reflections and Tangents by email so you get a message when I’ve posted a new calendar or other content. Click on the FOLLOW button above right, or the SUBSCRIBE button at the bottom of the post. Thanks!
I’ll post the solutions pages at the end of the month. Happy solving!
If the image isn’t readable, the pdf of the April 1996 calendar is HERE.
SOLUTIONS!! The Answers will be posted at the end of the month.
Notes & Resources
1The Mathematics Teacher journal is a legacy journal from NCTM — the National Council of Teachers of Mathematics — the professional organization supporting math educators in the US and Canada. There are bountiful resources available to members at https://www.nctm.org/, along with some free resources.
2The hashtag MTBoS is an acronym for “Math Teacher Blog-o-Sphere” and is an online community of math educators using a variety of platforms (BlueSky, Twitter, Facebook, Mastodon, etc.). If you are looking for helpful educators, shared resources, and thoughtful discussions, find us wherever you are online. Check out the energetic BlueSky group using the hashtag iTeachMath or the math(s) teacher folks on Mathstodon.xyz by searching for the hashtag ClassroomMath.
If you want to get an email notification when I post the next month’s problems, enter your email address here:
This website is NOT TO BE USED for generative AI training or machine learning. Any data mining, scraping, or extraction for the purpose of training artificial intelligence models is strictly forbidden.
It is March, and spring can’t come quickly enough for my friends in the northeast US. No matter what the weather, I have the March 2001 Calendar of Problems from 25 years ago for your problem solving enjoyment. I have a few more old Mathematics Teacher1 issues from my attic, so I’ll be sharing these monthly for the academic year.
Use these with your students, or solve them yourself; try them for problems of the week, fast finishers, extra credit, or just for fun! Maybe plan a “Pi Day” problem solving party on 3/14. Tell us about your worked-out methods either here in the comments, or on whatever platform you use2.
Never miss a post! Subscribe to Reflections and Tangents by email so you get a message when I’ve posted a new calendar or other content. Click on the FOLLOW button above right, or the SUBSCRIBE button at the bottom of the post. Thanks!
I’ll post the solutions pages at the end of the month. Happy solving!
If the image isn’t readable, the pdf of the March 2001 calendar is HERE.
SOLUTIONS!! The Answers to the March 2001 calendar are HERE.
Notes & Resources
1The Mathematics Teacher journal is a legacy journal from NCTM — the National Council of Teachers of Mathematics — the professional organization supporting math educators in the US and Canada. There are bountiful resources available to members at https://www.nctm.org/, along with some free resources.
2The hashtag MTBoS is an acronym for “Math Teacher Blog-o-Sphere” and is an online community of math educators using a variety of platforms (BlueSky, Twitter, Facebook, Mastodon, etc.). If you are looking for helpful educators, shared resources, and thoughtful discussions, find us wherever you are online. Check out the energetic BlueSky group using the hashtag iTeachMath or the math(s) teacher folks on Mathstodon.xyz by searching for the hashtag ClassroomMath.
If you want to get an email notification when I post the next month’s problems, enter your email address here:
This website is NOT TO BE USED for generative AI training or machine learning. Any data mining, scraping, or extraction for the purpose of training artificial intelligence models is strictly forbidden.
It’s been ten years since I started writing here on the “Reflections and Tangents” blog, so I think it’s a good time to reflect on how I got here and how it’s going.
I came late to blogging, compared to many others in math education. In February 2016, I attended a PD session at T3IC entitled “Blogging: Sharing Your Voice Beyond the Walls”. Jennifer Wilson and Jill Gough framed blogging as a way to connect with other teachers outside our buildings, sharing ideas, lessons, advice, and issues we are working on in our teaching practice.
Since I wasn’t in the classroom, I picked a “lesson” from Family Math Night at my children’s elementary school. For eight years I had helped Danielle Legnard, our outstanding math specialist, plan and run an evening of interactive math fun for kids and their families. My favorite station was Body Benchmarks, because it engaged everyone from toddlers to adults in measuring, graphing, calculating, and predicting. (That’s Danielle with my son Jason at one year’s FMN.)
My first post went live exactly ten years ago, and the “Reflections and Tangents” blog was born, with the tag line Thoughts on Math, Education, and Technology.
I’ve created over 100 posts since then and decided to share some highlights here. I have many more blog ideas rattling around in my head (so many thoughts, so little time!) so consider subscribing with your email so you never miss a post.
Technology
One of the blog’s main themes is how might I help teachers use technology to illuminate a math topic so their students learn it more successfully? My most popular post does exactly that; Rational Functions from 2017 shared three ideas for student explorations, using four different technology platforms (TI-84+ and TI-Nspire calculators, GeoGebra, and Desmos).
My ongoing series Go For Geometry! is also technology-focused, with eight episodes so far, working through geometry topics using four dynamic geometry platforms. Stay tuned for episode 9 coming soon!
For TI-84+CE users, the Back To School Tour of the TI-84 links to several posts covering features of the TI-84 family of calculators in all high school math classes.
Another theme here on the blog: can I explore an interesting math topic deeply and share some joyful ideas? My Pythagorean Party! post from 2024 fits that bill; I dived into some visuals, proofs, and applications of that great theorem. I ❤️ Candy Math and Exploring e both investigate exponential growth, decay, and how to simulate randomness, and Circles Are All Right covers a topic from geometry class that doesn’t always get a lot of attention.
For your problem-solving fun, I’ve been sharing the problem calendars from old NCTM Mathematics Teacher journals for the past four academic years. Check out one of the vintage Calendar of Problems, with solutions posted at the end of each month. My Puzzle Pastimes post has more puzzling fun about jigsaws and other puzzles, and twice I’ve guest hosted the Carnival of Mathematics blog (installments 219 and 239), recapping math-y and maths-y items and news from around the internet.
Another favorite post of mine in this theme is Shout Out For Squares, which celebrates the the geometric, numerical, and algebraic wonders of squares. That post ties in nicely with Area Arrangements, which applies an area model to multiplying and dividing with numbers, algebraic expressions, and radicals.
There are several blogs that haven’t seen many eyeballs but they are fun math explorations worth reading: Leap Years & License Plates on divisibility and counting; Problems with Parenthesescovering several common errors; Easy Angles created by folding paper; Quarantine Queries on math words beginning with Q; Super Sevens about my favorite number; Powerful Pairs of numbers encountered in math; Useful Units explaining unit conversions, unit fractions, and more; and finally Prime Percents solving percent increase and decrease problems.
Education
Several of my posts have the theme what pedagogical routines or structures can I share that I’ve found useful to teach a topic? I like to consolidate related math concepts into a “big idea” and wrote about eight of them in One “Big Rule” To Rule Them All. I highlighted how one of the Standards for Mathematical Practice can help my students in Searching For Structure, and shared an idea for fostering students’ ability to justify and prove in Beginning With Because.
One of my mantras with students is “show your mathematical thinking” which is a big improvement on “show your work” IMHO. Two older posts I recently revisited on this idea are That Voice In Your Head and Great Thinking; they include a set of prompts for students to engage with as they study and tackle problems.
There are many class “thinking routines” that you can use to help your students build understanding of math topics. One of my favorites is Same and Different which has students analyze how two or three math situations are related; that post and a follow-up on calculus include over 40 sets of images you can use with your students. In fact, I will be a guest facilitator for the Math Routine Collaborative discussing Same and Different in a few weeks on March 15 — sign up and join us. Math talks (for all ages and grade levels) are the subject of Mental Math Monday.
I’ve written some posts over the years about how I start my school year and other suggestions for teaching . Check out Setting the Stage (with messages for my students) from 2016; Moving the Needle (setting goals for developing student agency and confidence as learners) from 2018; Lessons Learned (things I learned from my students) from 2022; Birthdays & Being Seen (ideas for building relationships with students) from 2023; and Post-It Notes & Other Pedagogical Advice (ideas/ reminders/ suggestions for both new and experienced teachers) from 2024.
Math class almost always involves grades, tests, and assessments, and several posts tackle this subject: check out the Assessment & Testing category on the blog. And let’s not forget about the Resources page of the website, with my articles, webinars, and presentation materials.
Wrapping Up and a Big Thank You
The most important thing I’ve learned in these 10 years is how we get ideas and energy from each other when we connect with other math teachers. Writing this blog has kept me in touch with educators all over the US and the world, and I’ve become a better teacher because of this experience. I wrote in 2025 about how critically important it is to Find Your (Math) People, spotlighting several wonderful colleagues and friends who enabled me to grow and learn.
Earlier this month, I was honored and humbled to win the Teachers Teaching with Technology Leadership Award for my years helping educators implement calculator technology successfully in their classrooms. I have learned so much on this journey, especially about the power of sharing ideas with others in supportive collaboration. My last theme is SMALL BUT MIGHTY; even when I thought my ideas were small and insignificant, they became impactful and mighty lessons for others when I shared them here on “Reflections and Tangents”. I hope you’ve found something useful on my website for your teaching practice and that you will share them with your colleagues.
THANK YOU for reading and subscribing and allowing me to share with you.
2026 T3 Leadership Award winners Katie Allard Martinez & myself (left) My “small but mighty” crew of Sister Alice Hess, Jean McKenny, and Gail Burrill (right)
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Are you teaching probability in your high school Algebra 1 or Algebra 2 class? Want to streamline operations and do simulations with your students? Read on to hear about using the TI-84+CE and the Prob Sim App to help.1
Introductory Commands
The common probability operations of factorials, permutations, and combinations are built into the TI-84+CE handheld. The fastest way to access these are in the ALPHA-WINDOW shortcut menu, or press MATH and arrow over to PROB.
(Left) ALPHA-WINDOW menu items 7, 8, 9; (Right) MATH-PROB menu items
I like to have students work several counting problems by hand, so they have experience simplifying expressions with factorials. Then they can move on and let the calculator do the work.
29 Baby Girls! Modeling Real Data
In December of 2023 Noyes Health Center at the University of Rochester in Rochester, NY had quite the string of female births in their Maternity Center.
From Noyes Health: “We are on quite the girl streak lately,” said Brooke Sikes, Director of the Family Birthing Center at UR Medicine Noyes Health. “We have had 29 babies in a row that are girls! It is really exciting, it must be some kind of record.”
“Brooke emailed me this morning to let me know about all of the baby girls who have been born here and thought it would be a good post for social media,” said Lynn White, Director of Marketing, Public Relations and the Foundation for Noyes Health. “She was definitely right! It’s just a cool story – really, what are the odds of delivering 29 girls in a row? I told her to keep me updated on the streak as more moms deliver their babies. The community seems really invested to see how long this streak can continue. I am right there with them.”
I often used this example as an opener for a lesson in simple probability to introduce the idea of independence and dependence. It started with the question “What is the probability of having 29 female babies born in a row?” We would flip coins to simulate the event. As you can imagine, coins went flying everywhere and our results are often subject to human error. With an actual coin you are also limited to a 50-50 chance for each outcome. It is at this point that I look to technology to help us.
(Left) Prob Sim App is item 0 in APPS menu; (Right) Simulation choices in the App.
Within the Prob Sim App, there are lots of options available to simulate probabilities. A simulation of 29 births can be modeled using “Toss Coins“, deciding ahead of time which toss represents a female birth (T or H). Press the WINDOW button to toss the simulated coin 29 times (or press ZOOM or TRACE to get 10 or 50 tosses at a time). Using the arrow keys you can view the frequency of each type of toss as shown below right.
(Left) results of simulation; (Right) use arrow keys to show category frequency
I have my students run the simulation multiple times to see if they can recreate 29 of the same gender births in a row.
Within the app you have the option to change settings as needed and if you select ADV from the menu in the settings you can change the weight or the probabilities associated with the coin flips. Maybe it is not really a 50-50 chance of having a baby girl or baby boy in Rochester. What would the probabilities have to be in order to create this unique event of 29 baby girls born in a row? Were the events independent? You would think so, but we can test that hypothesis as well.
(Left) Settings screen in Prob Sim App; (Right) Press ADV to change weighting of coin probabilities
The individual tosses are recorded in a table and can be saved as named lists if you want to do further analysis in the STAT editor.
(Left) Data in the Table; (Middle) Save data to lists; (Right) Lists appear in LIST NAMES menu.
If your students are ready for more, see the Resources below for a possible extension of the 29 female births situation.2
Candy Math Probabilities
Another common introductory activity is to analyze a small bag of M&Ms looking for the percent distribution with a bag and comparing results from bag to bag then pooling the numbers of each color to obtain a larger sample size, highlighting the fact that larger sample sizes should be better approximations for the actual percentages set at the factory.
2007 was the last time I was able to obtain the percentages from the M&M Mars company. Here are the percentages:
Based on my trials in class, these percentages seem to still hold true.
The Prob Sim app can be used to help bring the idea of large sample sizes home to your students. For this simulation, we used the “Spinner“. In Settings you can partition the spinner to 6 sections each representing one of the M&M colors (I used pink to represent yellow). I also set the graph to record probabilities not frequency. In the ADV settings you can manually set the probabilities to match what is used at the factory. How many trials does it take to meet the set probabilities?
Screens from Prob Sim App showing a 6-partition spinner with unequal weights, & graph of results.
From here you can transfer your data to the lists and continue to analyze.3
Saving the spin data into TI-84+CE lists and a box-and-whisker plot of results
Other Prob Sim App Options
Here are the other simulations available to you via the Prob Sim App besides the Toss Coins and Spinner used above.
Other simulation options in the Prob Sim App
Using the Prob Sim App serves as a powerful, low-barrier entry point for students to develop the conceptual understanding of randomness and the Law of Large Numbers, providing the foundation necessary before transitioning into confidence intervals and hypothesis testing. I find that my students enjoy comparing their real data to the numbers generated by the calculator and can model many more outcomes in a short period of time.
Wrapping Up
The probability simulation app on the TI-84 brings statistical ideas to life in a way that allows for exploration. Students can experiment, question results, and compare simulated outcomes to theoretical expectations. Ultimately, these simulations transform probability from an abstract concept into a dynamic, visual, and engaging experience in statistics and probability.
I hope you are excited about how to use the counting commands and the Prob Sim app on your TI-84+CE calculators to build the foundation for an Algebra 2 unit of probability and statistics or as an introductory unit in Statistics. Check the Resources below for possible extensions.
Notes & Resources
Karen Latham is a mathematics teacher at The Pike School in Andover MA. She has over 30 years of teaching experience and enjoys using technology in her math classes to enhance learning and engage students at all levels.
1 The TI-84+CE model with color screen is the most up-to-date model, but the counting commands and the Prob Sim App are available on the entire TI-84+ family. The Texas Instruments website has OS updates and other resources.
If you don’t have a class set of TI-84+ calculators in your classroom but want to do these activities, consider using the TI-SmartView Emulator software to display the Prob Sim App to your class. Or use any random number generator and assign outcomes according to the desired probability weights.
2 A possible extension to the 29 female births situation is to test whether the female birthrate is more than 50% using a coin flip simulation. Specify the null and alternative hypotheses and record 50 trials of 29 births each. More detail here: Extension for 29 Female Births Scenario
3 For more information on using the Statistics Lists on the TI-84+ family of calculators, see this PDF: How To Scatterplots.
This post is one of a series from “A Back-to-School Tour of the TI-84” covering tips for using the TI-84 Plus family in all high school math subjects. Check them all out!
If you love using candy in math class, there’s more to explore in my post “I ❤️ Candy Math“.
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This website is NOT TO BE USED for generative AI training or machine learning. Any data mining, scraping, or extraction for the purpose of training artificial intelligence models is strictly forbidden.
February is here and if you need a distraction from winter ❄️ weather, I have the February 2016 Calendar of Problems from 10 years ago for your wintertime problem solving enjoyment. I have a few more old Mathematics Teacher1 issues from my attic, so I’ll be sharing these monthly for the academic year.
Use these with your students, or solve them yourself; try them for problems of the week, fast finishers, extra credit, or just for fun! Tell us about your worked-out methods either here in the comments, or on whatever platform you use2.
Never miss a post! Subscribe to Reflections and Tangents by email so you get a message when I’ve posted a new calendar or other content. Click on the FOLLOW button above right, or the SUBSCRIBE button at the bottom of the post. Thanks!
I’ll post the solutions pages at the end of the month. Happy solving!
If the image isn’t readable, the pdf of the February 2016 calendar is HERE.
SOLUTIONS!! The Answers to the February 2016 calendar are HERE.
Notes & Resources
1The Mathematics Teacher journal is a legacy journal from NCTM — the National Council of Teachers of Mathematics — the professional organization supporting math educators in the US and Canada. There are bountiful resources available to members at https://www.nctm.org/, along with some free resources.
2The hashtag MTBoS is an acronym for “Math Teacher Blog-o-Sphere” and is an online community of math educators using a variety of platforms (BlueSky, Twitter, Facebook, Mastodon, etc.). If you are looking for helpful educators, shared resources, and thoughtful discussions, find us wherever you are online. Check out the energetic BlueSky group using the hashtag iTeachMath or the math(s) teacher folks on Mathstodon.xyz by searching for the hashtag ClassroomMath.
If you want to get an email notification when I post the next month’s problems, enter your email address here:
This website is NOT TO BE USED for generative AI training or machine learning. Any data mining, scraping, or extraction for the purpose of training artificial intelligence models is strictly forbidden.
It’s time for congruent triangles in Geometry class! One of my favorite ways to get students prepared for the congruence theorems (SSS, SAS, ASA, SAA, Hypotenuse-Leg) is to analyze triangles using transformational geometry.
The three “rigid motion” transformations that preserve distances and create congruent image figures are Translation, Reflection, and Rotation. We’ve covered the Rotation tool in Episode 7, so let’s introduce the others.
Translations: Shifts and Slides
The Translate tool shifts the preimage object using a vector that determines the distance and direction of the shift. Begin with a shape that doesn’t have particular symmetry, such as a scalene triangle, L shape, flag shape, or general quadrilateral. Also construct a vector on the screen (or a segment for Cabri Jr.).
Then choose the Translate tool, the object to be translated, and the vector to complete the transformation.
You can click on the vector once or click on the two endpoints separately to perform the translation.
For Desmos, you must select the object to be translated before the Translate tool becomes available. Use Box Select to select the triangle and its 3 vertex points; if you only click on the triangle, the points themselves will not translate.
For Cabri Jr. on TI-84+CE, the direction in which the segment was created determines the direction of the translation. When selecting the preimage triangle, be sure the whole triangle is dashed & flashing, not just one side (these will alternate, so wait before pressing enter).
Have students examine the translation, and ask them to “Notice and Wonder” about the result. What changes, what stays the same? I use the vocabulary Preimage and Image to refer to the two figures. [You can label the points or not for this exercise; on GeoGebra and TI-Nspire, if labels are displayed on the preimage before translating, then the image will have labels using the “prime” symbol, such as A and A’.]
Then have students “Drag and Observe”, beginning by dragging one endpoint of the vector:
What happens to the location of the preimage?
What happens to the location of the image?
What do you observe about the size and shape of the preimage and image as the vector is dragged?
What happens if you turn the vector around to face the opposite way?
Now try to click and drag on one vertex of your preimage; how would you describe the result? Make some measurements if desired to confirm your thinking. Are you able to drag on a vertex of the image1?
Students should conclude that the translation results in a figure congruent to the preimage; all segment lengths and angle measures are the same.
Don’t Flip Out! Reflecting Over a Line
Now let’s take a look at the Reflect tool, which flips a figure over a line or linear object. Begin with an asymmetrical preimage object as before, and create a line on the screen that doesn’t intersect your preimage.
Then choose the Reflect tool, the preimage object, and the line of reflection.
Have students measure a side and an angle of both the preimage and image, and describe what they see happening in a reflection transformation. They can drag on a vertex of their preimage and observe the consequence. How is the reflection the same as a translation, and how is it different? What happens if the line of reflection moves?
Next, have students investigate how far a preimage point and its corresponding image point are from the line of reflection.
Connect the preimage point and its corresponding image point with a segment.
Find the point of intersection of this segment with the line of reflection.
Measure the distances from the intersection point to the other points.
What do you notice? Why is this segment well suited for this measurement? What is the relationship of the segment to the line of reflection2?
Extension: Composite Reflections
A wonderful extension is to perform a second reflection, which can be done two ways. Try reflecting the (first) image over another line parallel to the first line, or try reflecting it over a non-parallel line. What do you observe about the (second, final) image? Is there a single transformation that can accomplish the same result3?
Reflecting a preimage (far left) over parallel lines using DesmosReflecting a preimage (far left) over non-parallel lines using GeoGebra
I’ve done this extension successfully as a “Type II” technology exploration, where students explore freely without a set of specific directions4. Or you can provide a more structured worksheet to help focus the investigation.
Low-Tech Alternatives
Reflections can easily be accomplished by folding a piece of paper and using the fold as a reflection line. Create a figure on one side of the line, then reflect it by poking your pencil point (or a compass point) through the folded paper at each vertex. You can use a Sharpie to outline your original figure to see it more clearly through the paper, or use patty paper.
Low-tech translations can be done on graph paper. I will share more about transformations on the coordinate plane in an upcoming episode.
Wrapping Up
Once students have explored each of the rigid transformations with technology, bring them back to congruent triangles. Many typical triangle congruence proofs lend themselves to a transformational approach; I start by asking “what transformation shows that the triangles are congruent?” Since the transformations help identify how the triangles are congruent, students are better able to analyze the diagrams from textbook 2-column proofs and decide which congruence theorem they will use.
Notes & Resources
If you are brand new at Dynamic Geometry, here are introductory HOW TO Guides for all platforms.
Here is the lab activity to explore composite reflections as a PDF and an editable Word file: Go For Geometry Episode 8 Files, along with some other translation and reflection activities.
If you are giving directions to students, consider labeling points with letters for easier references to follow. On GeoGebra and TI-Nspire, if labels are displayed on the preimage before translating, then the image will have labels using the “prime” symbol, such as A and A’.
Translations create congruent figures. Reflections create congruent figures with opposite orientation of vertices (if preimage vertices are named in clockwise order, the image vertices will be named in counter-clockwise order). Corresponding points are equal distances from the line of reflection.
1 In Desmos, you can move and manipulate the image as well as the preimage. Similar to Geometer’s Sketchpad, the Desmos platform treats the line of reflection as a “mirror line” so either figure can move independently. In contrast, GeoGebra, Cabri Jr., and TI-Nspire use a dependency paradigm in which the image depends on the preimage; therefore only the preimage can move independently.
2 The segment connecting corresponding points of a reflection is perpendicular to the line of reflection, which is needed in order to measure the distance from a point to a line. In fact, the reflection line is the perpendicular bisector of the segment, which guarantees that the corresponding points are equidistant from the line of reflection.
3 Composite reflections over parallel lines result in a translated figure, moving twice the distance between the parallel lines from the preimage. Composite reflections over non-parallel lines result in a rotated figure, with point of intersection of the lines as center of rotation, and twice the angle between the lines as angle of rotation.
This website is NOT TO BE USED for generative AI training or machine learning. Any data mining, scraping, or extraction for the purpose of training artificial intelligence models is strictly forbidden.
Happy New Year and welcome to 2026! Here is the January 1998 Calendar of Problems from 28 years ago for some wintertime problem solving enjoyment. I have a few more old Mathematics Teacher1 issues from my attic, so I’ll be sharing these monthly for the academic year.
Use these with your students, or solve them yourself; try them for problems of the week, fast finishers, extra credit, or just for fun! Tell us about your worked-out methods either here in the comments, or on whatever platform you use2.
Never miss a post! Subscribe to Reflections and Tangents by email so you get a message when I’ve posted a new calendar or other content. Click on the FOLLOW button above right, or the SUBSCRIBE button at the bottom of the post. Thanks!
I’ll post the solutions pages at the end of the month. Happy solving!
If the image isn’t readable, the pdf of the January 1998 calendar is HERE.
SOLUTIONS!! The Answers to the January 1998 calendar are HERE.
Notes & Resources
1The Mathematics Teacher journal is a legacy journal from NCTM — the National Council of Teachers of Mathematics — the professional organization supporting math educators in the US and Canada. There are bountiful resources available to members at https://www.nctm.org/, along with some free resources.
2The hashtag MTBoS is an acronym for “Math Teacher Blog-o-Sphere” and is an online community of math educators using a variety of platforms (BlueSky, Twitter, Facebook, Mastodon, etc.). If you are looking for helpful educators, shared resources, and thoughtful discussions, find us wherever you are online. Check out the energetic BlueSky group using the hashtag iTeachMath or the math(s) teacher folks on Mathstodon.xyz by searching for the hashtag ClassroomMath.
If you want to get an email notification when I post the next month’s problems, enter your email address here:
This website is NOT TO BE USED for generative AI training or machine learning. Any data mining, scraping, or extraction for the purpose of training artificial intelligence models is strictly forbidden.
The year is flying by and December is upon us! I had planned to share a December calendar of problems from the early 2000s, but I was digging around and realized that 2025 is the 40th anniversary of the NCTM Calendar of Problems!
Apparently in 1983 and 1984, the Mathematics Teacher1 journal began printing a few “Problems of the Month” in each issue. At the 61st Annual Meeting in Detroit Michigan in April 1983, the editorial board sponsored a “Best Problems Contest” session to choose problems for publication through spring of 1985. And in September of 1985, the problems were presented in calendar format for the first time. There wasn’t a problem for every date, and some fun facts and math historical figures were included.
Here is the December 1985 Calendar of Problems from 40 years ago for you and your students to work on. Use these with your students, or solve them yourself; try them for problems of the week, fast finishers, extra credit, or just for fun! Tell us about your worked-out methods either here in the comments, or on whatever platform you use2.
Happy 40th birthday to the NCTM Calendar of Problems! And coincidentally, this month is the anniversary of me sharing these calendars with all of you; my friend Shelli Temple reminded me of the Mathematics Teacher calendars back in December 2022. ENJOY!
I’ll post the solutions pages at the end of the month. Happy solving!
If the image isn’t readable, the pdf of the December 1985 calendar is HERE.
SOLUTIONS!! The Answers to the December 1985 calendar are HERE.
Notes & Resources
1The Mathematics Teacher journal is a legacy journal from NCTM — the National Council of Teachers of Mathematics — the professional organization supporting math educators in the US and Canada. There are bountiful resources available to members at https://www.nctm.org/, along with some free resources.
2The hashtag MTBoS is an acronym for “Math Teacher Blog-o-Sphere” and is an online community of math educators using a variety of platforms (BlueSky, Twitter, Facebook, Mastodon, etc.). If you are looking for helpful educators, shared resources, and thoughtful discussions, find us wherever you are online. Check out the energetic BlueSky group using the hashtag iTeachMath or the math(s) teacher folks on Mathstodon.xyz by searching for the hashtag ClassroomMath.
If you want to get an email notification when I post the next month’s problems, enter your email address here:
This website is NOT TO BE USED for generative AI training or machine learning. Any data mining, scraping, or extraction for the purpose of training artificial intelligence models is strictly forbidden.
Wow, November has blown in with some wild weather, but at least we can get an extra hour of sleep tonight as we “fall back” to standard time. It’s a busy month at school, as the first marking period wraps up, so I am giving thanks for the monthly problem solving calendar!
Here is the 2015 Calendar of Problems from 10 years ago for you and your students to work on. I have a few more old Mathematics Teacher1 issues from my attic, so I’ll be sharing these monthly for the upcoming academic year.
Use these with your students, or solve them yourself; try them for problems of the week, fast finishers, extra credit, or just for fun! Tell us about your worked-out methods either here in the comments, or on whatever platform you use2.
I’ll post the solutions pages at the end of the month. Happy solving!
If the image isn’t readable, the pdf of the November 2015 calendar is HERE.
SOLUTIONS!! The Answers to the November 2015 calendar are HERE.
Notes & Resources
1The Mathematics Teacher journal is a legacy journal from NCTM — the National Council of Teachers of Mathematics — the professional organization supporting math educators in the US and Canada. There are bountiful resources available to members at https://www.nctm.org/, along with some free resources.
2The hashtag MTBoS is an acronym for “Math Teacher Blog-o-Sphere” and is an online community of math educators using a variety of platforms (BlueSky, Twitter, Facebook, Mastodon, etc.). If you are looking for helpful educators, shared resources, and thoughtful discussions, find us wherever you are online. Check out the energetic BlueSky group using the hashtag iTeachMath or the math(s) teacher folks on Mathstodon.xyz by searching for the hashtag ClassroomMath.
If you want to get an email notification when I post the next month’s problems, enter your email address here:
This website is NOT TO BE USED for generative AI training or machine learning. Any data mining, scraping, or extraction for the purpose of training artificial intelligence models is strictly forbidden.
October is here, and with it the crisp fall air here in the northeast US. No matter where you are, you can get a breath of fresh air with some problem solving in your math classes! Here is the 2015 Calendar of Problems from 10 years ago for you and your students to work on; there was a “Lots of Algebra” special theme that month. I have a few more old Mathematics Teacher1 issues from my attic, so I’ll be sharing these monthly for the upcoming academic year.
Use these with your students, or solve them yourself; try them for problems of the week, fast finishers, extra credit, or just for fun! Tell us about your worked-out methods either here in the comments, or on whatever platform you use2.
I’ll post the solutions pages at the end of the month. Happy solving!
If the image isn’t readable, the pdf of the October 2015 calendar is HERE.
SOLUTIONS!! The Answers to the October 2015 calendar are HERE.
Notes & Resources
1The Mathematics Teacher journal is a legacy journal from NCTM — the National Council of Teachers of Mathematics — the professional organization supporting math educators in the US and Canada. There are bountiful resources available to members at https://www.nctm.org/, along with some free resources.
2The hashtag MTBoS is an acronym for “Math Teacher Blog-o-Sphere” and is an online community of math educators using a variety of platforms (BlueSky, Twitter, Facebook, Mastodon, etc.). If you are looking for helpful educators, shared resources, and thoughtful discussions, find us wherever you are online. Check out the energetic new BlueSky group using the hashtag iTeachMath or the math(s) teacher folks on Mathstodon.xyz by searching for the hashtag ClassroomMath.
If you want to get an email notification when I post the next month’s problems, enter your email address here:
This website is NOT TO BE USED for generative AI training or machine learning. Any data mining, scraping, or extraction for the purpose of training artificial intelligence models is strictly forbidden.
Reflections and Tangents 