Education math TPT

Irrational Numbers – More than Infinite

Irrational numbers are numerous and yet, you can’t think of any of them. “But I can think of pi!” you might say to yourself. Well, ok. How does it go, then? Is it a fraction of some number we are already familiar with? No it isn’t.

Today, we have many things that are absolutely too complicated to understand completely, such as quantum physics. Unless you spend your whole life researching it, of course. But there is something much more familiar yet still surprisingly complicated: the irrational numbers.

Let’s think of it this way: You start in the morning with a notebook and start writing random decimals to a number. For example, you start with 0.628465963 and add random digits until you have five pages full at lunchtime. What you now have in your hands, it’s a rational number, not irrational. That’s because you can write it as a fraction. The numerator will be all the digits after the decimal point and the denominator is a power of ten; it has one and as many zeros as your number has decimals.

So, any number you can create decimal by decimal will be a rational number. Irrational numbers will look like special cases, square roots etc. And you would probably think: “Well, there must be only a limited amount of irrational numbers, then.” 

But that is not the case. There are a lot more irrational numbers than rational numbers. That’s where the infinity really comes into play. If you think of a decimal number as an endless journey to infinity, digit by digit, you realize that every time we take the next step, there will be ten directions we can go. And at the next step, again ten different directions. So numbers we get this way is countless. And only rare cases are rationals, like those that happen to have repeating decimals. If you want a rounded estimate, 0% of all real numbers are rational, the rest about 100% are irrational. 

Whoa! That was something. If you want to familiarize with the subject more, I made a free pdf material that you can download from my tpt shop. It has a concept understanding crossword and a story about how we even know that irrationals really exist.

If you need to teach this subject to let’s say, eight graders, there is presentation & worksheet bundles in my shop: 

Version for Google Slides™

Version for PowerPoint

These are essentially the same, but one has presentations for PowerPoint and the other for Google Slides™.

Hopefully you enjoyed this article! Irrationals are so intriguing, because they are easy and very complicated at the same time. If you want to challenge something, please leave a comment. 

The writer used to be a math teacher in Finland and has a master’s degree in math.

Education TPT

Free Valentine’s Day Products in TPT

February and St. Valentine’s day is coming, and especially with younger students it’s time to use themed materials! I found also some fresh materials for older students. I divided these into three groups: Primary school, Middle school (and up) and for your own creations. Some of them are even for commercial use. Enjoy!

Primary school

Valentine’s Day Flashcards in Spanish (grades K-5)
Cards with Spanish words, related pictures and English translation.

Heart Tiles – Memory Game (Not grade specific)
As a memory game, this suits better for kindergarten or primary school. Nevertheless, I wanted to include this because I really like the grapchis. Creating 15 different shapes from heart is not that simple.

16 Free printable Valentine’s Day Bookmarks (Not grade specific)
Valentine & love themed printable bookmarks

Heart Mandalas for Valentine’s Day: Art Lesson for Grades K-7
Detailed instructions for art lesson about hearts and mandalas.

Middle school and up

Romeo and Juliet Persuasive Letter (grades 9-12)
Contains one page introduction to Shakespeare and Romeo & Juliet and task to write a persuasive letter to relatives of one of them. Certainly creative way to approach this love story!

Science Valentines for Middle School (grades 5-9)
16 mini Valentine cards with science puns that are suitable for middle school students. Includes colored and black and white options.

For your own creations

Valentine’s Day Game Board (with editable game cards) (grades 2-6)
Valentine’s day themed game board with cards. The aim of the game is to ask questions and to answer them. Cards are in PowerPoint format and you’ll have to type the questions before playing.

Valentine Borders and Frames Collection (Not grade specific)
Huge pack of borders even for commercial use, if you just mention Willow Designs. Definitely worth downloading!

Valentine’s Day Clip Art Set (K-6)
17 png images in a zip package for decoration purposes.

Valentine’s Day Task Card Template for Commercial Use (Not grade specific)
Four identical task card templates for letter size products. Free for commercial use as long as the shop is mentioned.

Lower part of the image by stux from Pixabay (Cubid by me)


10 free posters in Teachers Pay Teachers

Today, I’ll be listing posters that you can print out and hang to your classroom wall. I can tell you there are many of them even if you take only the new ones into account, so I’ve done some picking and chosen those that look beautiful to my own eye. Subjects vary from mathematics to English language art and from sexual health education to physics. Resources are ordered by grade. Most of the posters are not that grade specific, but I’ve omitted kindergarten and preschool materials. Sometimes I’ve narrowed down very wide age ranges, that is represented by /.

Habits of discussion (Not grade specific)
Short guide for students to communicate respectfully.

Order of operations (grades 1-8 / 4-8)
Great when studying order of operations including powers and parenthesis. Description says for grades 1-8, but I’d say this could be confusing before powers have been introduced at all.

Ground rules for sexual health education (grades 4-12)
Encourages students to be respectful and speak about themselves or in general level, not about others.

Branches of Mathematics (grades 5-10)
Simplified interpretation about different fields of mathematics. Helps bit older studets to form a picture what mathematics can be.

Author’s purpose posters (Not grade specific / middle school and up)
Five posters each presenting one author purpose. It says on the description that this is not grade specific, but I think it fits best when you start reading longer and more diverse texts, so not in the very first grades.

Just Right Books Posters (Not grade specific / middle school and up)
Guides students to choose the right level book (I can imagine that is not always easy). Again, middle school and up is my opinion, not grade specific is author’s view.

Law of reflection (7-12)
For physics, law of reflection. Clear poster and worksheet is also included.

Shakespeare’s poets (grades 9-12)

Six Shakespeare’s poets with beautiful backgrounds. Also available in black and white.

Organic compound concept map (grades 11 – higher education)
Colorful and clear concept map. Note that this is in jpg form.

A Christmas Carol Character Profile Posters (grades 8-12)
Seven posters each presenting one character: Ebenezer Scrooge, Bob Cratchit, The Ghost of Christmas Past, The Ghost of Christmas Present, The Ghost of Christmas Yet to Come, Jacob Marley and Tiny Tim.

Hopefully you will enjoy these and other beautiful resources!