Category Archives: Algebra

Really Radical

April 22, 2026Algebra, Arithmetic, PreCalculuskdcampe

Algebra 2 students are studying radical expressions this week. Sometimes this unit has felt like a sea of disconnected rules and unfamiliar operations that bog students down and hampers their understanding: many situations are “do this” except if you’re supposed to do something else.

This time, we are working through some well-chosen problems in order to illuminate a few general rules that help students make sense of the material.

Name the Notation & Know the Numbers

We begin by identifying the radical sign, index, and radicand (“stuff under the root”) and making clear the various ways we could say the notation in words.

Radical symbol showing cube root of 2.
3 is the index
2 is the radicand

$\text{ }$ $\sqrt{2}$ $\text{ }$ can be read out loud as “root 2”, “radical 2”, or “square root of 2”.

$\text{ }$ $\sqrt[3]{2}$ $\text{ }$ is “cube root of 2” not “3 root 2”.

We review the perfect square numbers up to 15², the perfect cubes and fourth powers up to base 5, and remind ourselves how easy it is to compute powers of 10.¹⤵️

Roots of Products & Quotients

Questions 1 to 5:
1. sqrt(120)
2. cube root of 120
3. fraction of sqrt(40) over sqrt(5)
4. sqrt(x^2 times y^3)
5. fraction of sqrt(x^3) over sqrt(5x)

This first set is based on the biconditional

\sqrt{pq} \iff \sqrt{p} \text{} \cdot \text{} \sqrt{q}

and its cousin

\sqrt{\frac{p}{q}} \iff \frac{\sqrt{p}}{\sqrt{q}}

In some of the examples, students must find a perfect square factor (or perfect cube factor), then separate the radicals to simplify. In others, we first combine the radicals to divide away a common factor beforehand.

Also notice in #2, that we don’t have to find the perfect cube factor right away (my students sometimes put on their “concentrating face” until they find the needed factor) but instead, build on knowing 120 = 4•30, then factor 30 into 2•15 to get the 8 we want. And I say about #5 that “the kids inside the house can’t play with the kids outside the house” in order to remember that we cannot further simplify $\text{ }$ $\sqrt{5}$ $\text{ }$ over 5.

Like Terms & Other Operations

Once students grasp simplifying a radical, they turn to operations. Adding and subtracting require like terms, meaning the same index and radicand. Multiplying situations involve the distributive property and noticing when conjugates are helpful.²⤵️

Questions 6 to 9
6. sqrt(28) + 4•sqrt(63) –7•sqrt(2)
7. cube root of 81 + cube root of 24
8. sqrt(2) times the quantity 2 – sqrt(2)
9. (3 + sqrt 7) times (3 – sqrt 7)

Remind students that conjugates save you time since you don’t need to perform all four partial products of the “double distribution” (also known as FOIL). Beware of situations when you cannot skip steps such as (x + 1)² which means (x + 1)(x + 1).

I highlight the reminder to write the index in the “hook” of the radical symbol so it isn’t misinterpreted as an exponent. And there’s two ways to think about $\text{ }$ $\sqrt{2}$ $\text{ }$ • $\text{ }$ $\sqrt{2}$ $\text{ }$ ; either multiply the radicands to get $\text{ }$ $\sqrt{4}$ $\text{ }$ or use inverse operations — since squaring undoes the square root.

Devious Denominators

Historically, rationalizing the denominator was used because it made computations (by hand) easier. It also makes adding and subtracting like terms possible, and standardizes what an expression should look like in “simplest form”.³⤵️ Even though calculators are readily available, it nevertheless persists as a topic in many high school math classes.

This set teases out what to do with various denominators, whether single terms of square or higher roots, or binomial denominators requiring the conjugate.

Questions 10 to 14
10. fraction of 1 over sqrt 2
11. fraction of 1 over cube root 2
12. fraction of 1 over cube root 4
13. fraction of 6 + sqrt 15 over 4 – sqrt 15
14. fraction of 2 over the quantity 2 sqrt 3 – 4

I note to students that the reason why this works is that multiplying top and bottom of a fraction by the same thing is multiplying by a value of 1, which changes the form of the fraction, not the value of the fraction.

In the final step of #14, either factor the common factor in the numerator, then divide away; or “distribute the denominator” into separate fractions. This second method avoids mistakes when there isn’t a common factor of all terms.

Variables in the Radicand

When variables appear in the radicand, students are often told to assume that “all variables are positive” so we don’t need to use absolute value when simplifying.⁴⤵️

Usually it’s no problem for students to simplify the first two of these, but often they say the third one equals x³, because 9 is a perfect square.

Questions 15 to 18
15. sqrt of x^2
16. sqrt of x^4
17. sqrt of x^9
18. sqrt of x^16

We work through the following sequence of calculations⁵⤵️ to illuminate the issue (and review the exponent law for multiplying same base). What do you notice about “perfect square” variables?

Table of perfect square variables,
sqrt of x^2 = x because x•x = x^2
sqrt of x^4 = x^2 because x^2•x^2 = x^4
Continues through
sqrt of x^12 = x^6 because x^6•x^6 = x^12

It turns out that a variable is a perfect square when its exponent is EVEN, not when its exponent is a perfect square. Students also might notice that the square root results in an exponent that is half of the original exponent (more on this below).

I confirm this understanding by asking for the square root of x¹⁶ , which is x⁸, before turning back to the square root of x⁹. We go through all the steps explicitly for this, but I name the middle two steps as “thinking steps” that students might not need to write out once they learn this process.

sqrt of x^9 = sqrt of x^8 • sqrt of x = x^4 • sqrt of x

Then we turn our attention to perfect cube variables. Students notice that exponents that are multiples of 3 will be perfect cubes, and the cube root divides the exponent by 3.

Continuing on, we examine perfect fourth powers, which will be multiples of 4. Taking the fourth root divides the exponent by 4.

Questions 19 and 20
19. cube root of x^48
20. fourth root of x^24

When variables appear in the denominators, figure out how many more factors are needed to make the required power, as we did with numerical denominators for higher index roots.

Tap into the “Power” of Fractional Exponents

Understanding how to simplify a radical expression with variables in the radicand paves the way for the powerful idea of fractional exponents to represent roots.

A fractional exponent represents both the power and the index of the root in one place.

X with the fractional exponent P/R
P represents the power, R represents the root

Therefore, any root can be represented as a unit fraction:

Radicals represented as unit fraction exponents.
sqrt x = x ^ 1/2
cube root x = x ^ 1/3
nth root x = x^ 1/n

This supports our observation about how square roots divide the exponent by 2 and cube roots divide the exponent by 3.

Back to square root of of x⁹, we can think about it this way (and notice how a mixed number comes in to help out!):

And we want students to be flexible about whether to do the power or root first. There are 2 ways to interpret the fractional exponent.

x with fractional exponent 2/3
= cube root of x^2
= (cube root of x)^2

If you don’t have a calculator, what would you do if asked for 64 to the 3/2 power? Do you want to figure out 64³ first or the square root of 64?

Speaking of calculators, the fractional powers are often easier to enter than the roots themselves. Use the ^ exponentiation carat and the stacked fraction symbol. On the TI-84 family, square roots have their own button, and any-index roots are found in the Math Menu or the Alpha-Window shortcut menu.⁶⤵️

Questions 21 to 25
21. the fraction 81/16 raised to the 1/4 power
22. y to the 2/3 power raised to -9
23. 3x^(1/4) • 4x^(2/3)
24. Fraction with numerator sqrt of x^4y and denominator 4th root of x^2y^8
25. 64 to the 2/3 power times 64 to the 2/3 power

Question 21 uses a fractional exponent instead of a radical symbol. #22 utilizes the exponent law of multiplying exponents when raising a power to another power. In #23, we add exponents when multiplying like bases, and eventually rewrite the answer in radical form.

Many of my students feel that the fractional exponents are easier to handle than roots, because they use those common exponent laws. The remaining two problems are much more detailed. Notice that there are a few different ways to think about the steps, and both ways lead to correct results.

Wrapping Up

The Radical Expressions unit isn’t so scary when we focus on a few important rules and tap into the power of fractional exponents. Taking the time to annotate our work can help students see the thinking behind the steps of the procedure.

Notes & Resources:

All of the examples in this post are available here: Radical Expressions Practice Sheet.

Note that in British English and maths curriculum, radicals are known as “surds”. More on this from the amazing Ben Orlin in US vs. UK: Mathematical Terminology.

¹ Divisibility rules for 2, 3, 4, 5, and 9 are worth reviewing. Check out my post Leap Years & License Plates from 2016. ⤴️.

^{1 continued}Also, Steve Walker (@stevemaths.bksy.social) suggests the excellent method of teaching simplifying radicals by prime factorization. I use this when first teaching radicals in 7th/8th grade or Algebra 1, especially if prime factorization is in the curriculum. Jonathan Hall (@studymaths.bsky.social) shows the prime factorization method in this video using the online Prime Factor Tiles manipulative. My Algebra 2 students are already challenged to figure out any factors of the radicand, so I focus on divisibility rules to help get square factors efficiently.

² More about conjugates and why they are so amazing in my post Powerful Pairs. ⤴️

³ See Why Do We Rationalize the Denominator by Brett Berry. And John Chase (@mrchasemath) also has thoughts in his Rationalization Rant from 2012. And of course “simplest form” is mathematically ambiguous, so I try give my students directions that are as clear as possible; for example, I say “results should have no radicals in the denominator” instead of “write in simplest form”.⤴️

⁴ Technically, sqrt(x²) = |x| because the principle square root is asked for. This can be a point of confusion; when students are solving an equation such as x² = 9, the solution is ±3, because the inverse operation of square rooting must consider both positive and negative values of the variable. ⤴️

⁵ If needed, we remind ourselves that x is actually x¹, which is one of several “invisible 1’s” that happen in math notation. Can you think of some others? ⤴️

⁶ See more about the TI-84 family important keystrokes and menu items in the post Keys For Success. ⤴️

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April Calendar Problems

April 1, 2026Algebra, Arithmetic, Calendar Problems, Geometry, PreCalculus, Problem Solvingmathematicskdcampe

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:

March Calendar Problems

March 1, 2026Algebra, Arithmetic, Calendar Problems, Geometry, PreCalculus, Problem Solvingmathematicskdcampe

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.

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

If you want to get an email notification when I post the next month’s problems, enter your email address here:

Making the Most of Probability!

February 9, 2026Algebra, Class Activity, Data & Statistics, TI-84+Familykdcampe

Guest Blog by Karen Latham

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 image shows listing of ALPHA-WINDOW menu items on TI-84+CE. Permutation, Combination, and Factorial are items 7, 8, and 9.

Right image shows the MATH-PROB menu. Permutation, Combination, Factorial are items 2, 3, and 4. — (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 image shows the APPS menu; Prob Sim App is item 0.
Right image shows 6 simulation choices in the Prob Sim App, described in the main text. — (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 image shows bar graph of 29 coin tosses, more heads than tails.
Right image shows the frequency of each category by highlighting with arrow keys (18 heads, 11 tails) — (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 image shows Prob Sim App settings.
Right image shows ADV advance menu where you can change the weighting of the coin probabilities. — (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 image shows coin toss data in a table.
Middle image shows option to save data to lists on TI-84+CE
Right image shows those lists at the bottom of the List Names menu. — (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.

Color percentages for regular M&Ms.
Blue 24%
Brown 13%
Green 16%
Orange 20%
Red 13%
Yellow 14%

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?

4 Screens from Prob Sim App showing setting up a 6-partition spinner with unequal weights, & bar graph of results. — 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

Screens showing saving data into the TI-84+CE lists, along with a box-and-whisker plot of the results. — 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.

Prob Sim App screens showing 4 other simulation options: Toss Dice, Pick Marbles, Draw Cards, Random Numbers — 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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February Calendar Problems

February 1, 2026Algebra, Arithmetic, Calendar Problems, Geometry, PreCalculus, Problem Solvingmathematicskdcampe

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.

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

If you want to get an email notification when I post the next month’s problems, enter your email address here:

January Calendar Problems

January 1, 2026Algebra, Arithmetic, Calendar Problems, Geometry, PreCalculus, Problem Solvingmathematicskdcampe

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.

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

If you want to get an email notification when I post the next month’s problems, enter your email address here:

December Calendar Problems

December 1, 2025Algebra, Arithmetic, Calendar Problems, Geometry, PreCalculus, Problem Solvingmathematicskdcampe

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

If you want to get an email notification when I post the next month’s problems, enter your email address here:

November Calendar Problems

November 1, 2025Algebra, Arithmetic, Calendar Problems, Geometry, PreCalculus, Problem Solvingmathematicskdcampe

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.

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

If you want to get an email notification when I post the next month’s problems, enter your email address here:

October Calendar Problems

October 1, 2025Algebra, Arithmetic, Calendar Problems, Geometry, PreCalculus, Problem Solvingmathematicskdcampe

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.

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

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:

September Calendar Problems

September 1, 2025Algebra, Arithmetic, Calendar Problems, Geometry, PreCalculus, Problem Solvingkdcampe

September is here, and so is the school year for my US friends. Start a habit of doing some problem solving in your math classes this year! Here is the 1990 Calendar of Problems from 35 years ago for you and your students. I have a few more old Mathematics Teacher¹ issues from my attic, so I’ll be sharing these monthly for the upcoming academic year.

I’ll post the solutions pages at the end of the month. Happy solving!

If the image isn’t readable, the pdf of the September 1990 calendar is HERE.

SOLUTIONS!! The Answers to the September 1990 calendare are HERE.

Notes & 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:

	kdcampe on Really Radical
	quantummechanic1964 on Really Radical
	Really Radical \| Ref… on Keys For Success
	Really Radical \| Ref… on Powerful Pairs
	Really Radical \| Ref… on Leap Years & License …

Name the Notation & Know the Numbers

Roots of Products & Quotients

Like Terms & Other Operations

Devious Denominators

Variables in the Radicand

Tap into the “Power” of Fractional Exponents

Wrapping Up

Notes & Resources:

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Guest Blog by Karen Latham

Introductory Commands

29 Baby Girls! Modeling Real Data

Candy Math Probabilities

Other Prob Sim App Options

Wrapping Up

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